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nara\_wpe.benchmark\_online\_wpe module
=======================================
.. automodule:: benchmark_online_wpe
:members:
:undoc-members:
:show-inheritance:
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{
"redpajama_set_name": "RedPajamaGithub"
}
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Q: Set parameter within a step of a Pipeline (XGB : eval_set) I am trying to fit an XGBoost model to my data with an early stopping round and therefore an eval_set parameter. However, I am using a pipeline that does preprocessing before the model fitting step. I would want to set the parameter "eval_set" to that particular step and have used the syntax "stepname__eval_set=.." which doesn't seem to work.
Here is my code :
XGB=XGBRegressor(n_estimators=10000,learning_rate=0.05,verbose=False)
myPip=Pipeline(steps=[("preprocessing",preprocessor),
("model",XGB)])
myPip.fit(X_train2,y_train,model__eval_set=[(X_val2,y_val)],model__early_stopping_rounds=5)
It returns the following error
ValueError Traceback (most recent call last)
C:\Users\PCGZ~1\AppData\Local\Temp/ipykernel_17976/459508294.py in <module>
2 myPip=Pipeline(steps=[("preprocessing",preprocessor),
3 ("model",XGB)])
----> 4 myPip.fit(X_train2,y_train,model__eval_set=[(X_val2,y_val)],model__early_stopping_rounds=5)
5 y_pred_val=myPip.predict(X_val2)
6 y_pred_train=myPip.predict(X_train2)
~\anaconda3\lib\site-packages\sklearn\pipeline.py in fit(self, X, y, **fit_params)
344 if self._final_estimator != 'passthrough':
345 fit_params_last_step = fit_params_steps[self.steps[-1][0]]
--> 346 self._final_estimator.fit(Xt, y, **fit_params_last_step)
347
348 return self
~\anaconda3\lib\site-packages\xgboost\core.py in inner_f(*args, **kwargs)
618 for k, arg in zip(sig.parameters, args):
619 kwargs[k] = arg
--> 620 return func(**kwargs)
621
622 return inner_f
~\anaconda3\lib\site-packages\xgboost\sklearn.py in fit(self, X, y, sample_weight, base_margin, eval_set, eval_metric, early_stopping_rounds, verbose, xgb_model, sample_weight_eval_set, base_margin_eval_set, feature_weights, callbacks)
1012 with config_context(verbosity=self.verbosity):
1013 evals_result: TrainingCallback.EvalsLog = {}
-> 1014 train_dmatrix, evals = _wrap_evaluation_matrices(
1015 missing=self.missing,
1016 X=X,
~\anaconda3\lib\site-packages\xgboost\sklearn.py in _wrap_evaluation_matrices(missing, X, y, group, qid, sample_weight, base_margin, feature_weights, eval_set, sample_weight_eval_set, base_margin_eval_set, eval_group, eval_qid, create_dmatrix, enable_categorical, feature_types)
497 evals.append(train_dmatrix)
498 else:
--> 499 m = create_dmatrix(
500 data=valid_X,
501 label=valid_y,
~\anaconda3\lib\site-packages\xgboost\sklearn.py in _create_dmatrix(self, ref, **kwargs)
932 except TypeError: # `QuantileDMatrix` supports lesser types than DMatrix
933 pass
--> 934 return DMatrix(**kwargs, nthread=self.n_jobs)
935
936 def _set_evaluation_result(self, evals_result: TrainingCallback.EvalsLog) -> None:
~\anaconda3\lib\site-packages\xgboost\core.py in inner_f(*args, **kwargs)
618 for k, arg in zip(sig.parameters, args):
619 kwargs[k] = arg
--> 620 return func(**kwargs)
621
622 return inner_f
~\anaconda3\lib\site-packages\xgboost\core.py in __init__(self, data, label, weight, base_margin, missing, silent, feature_names, feature_types, nthread, group, qid, label_lower_bound, label_upper_bound, feature_weights, enable_categorical)
741 return
742
--> 743 handle, feature_names, feature_types = dispatch_data_backend(
744 data,
745 missing=self.missing,
~\anaconda3\lib\site-packages\xgboost\data.py in dispatch_data_backend(data, missing, threads, feature_names, feature_types, enable_categorical)
955 return _from_tuple(data, missing, threads, feature_names, feature_types)
956 if _is_pandas_df(data):
--> 957 return _from_pandas_df(data, enable_categorical, missing, threads,
958 feature_names, feature_types)
959 if _is_pandas_series(data):
~\anaconda3\lib\site-packages\xgboost\data.py in _from_pandas_df(data, enable_categorical, missing, nthread, feature_names, feature_types)
402 feature_types: Optional[FeatureTypes],
403 ) -> DispatchedDataBackendReturnType:
--> 404 data, feature_names, feature_types = _transform_pandas_df(
405 data, enable_categorical, feature_names, feature_types
406 )
~\anaconda3\lib\site-packages\xgboost\data.py in _transform_pandas_df(data, enable_categorical, feature_names, feature_types, meta, meta_type)
376 for dtype in data.dtypes
377 ):
--> 378 _invalid_dataframe_dtype(data)
379
380 feature_names, feature_types = _pandas_feature_info(
~\anaconda3\lib\site-packages\xgboost\data.py in _invalid_dataframe_dtype(data)
268 type_err = "DataFrame.dtypes for data must be int, float, bool or category."
269 msg = f"""{type_err} {_ENABLE_CAT_ERR} {err}"""
--> 270 raise ValueError(msg)
271
272
ValueError: DataFrame.dtypes for data must be int, float, bool or category. When categorical type is supplied, The experimental DMatrix parameter`enable_categorical` must be set to `True`. Invalid columns:MSZoning: object, Street: object, LotShape: object, LandContour: object, Utilities: object, LotConfig: object, LandSlope: object, Neighborhood: object, Condition1: object, Condition2: object, BldgType: object, HouseStyle: object, RoofStyle: object, RoofMatl: object, Exterior1st: object, Exterior2nd: object, MasVnrType: object, ExterQual: object, ExterCond: object, Foundation: object, BsmtQual: object, BsmtCond: object, BsmtExposure: object, BsmtFinType1: object, BsmtFinType2: object, Heating: object, HeatingQC: object, CentralAir: object, Electrical: object, KitchenQual: object, Functional: object, GarageType: object, GarageFinish: object, GarageQual: object, GarageCond: object, PavedDrive: object, SaleType: object, SaleCondition: object
PS : The prepocessing pipeline isn't the issue, since the pipeline worked fine with other models that do not take the eval_set parameter.
Thank you in advance for your kindly help.
A: I have found "a" solution for this particular problem : which was passing the eval_set parameter (which was unprocessed data) to the model that was fitted using preprocessed data. Trying to evaluate it with unprocessed data that ultimately had a different column structure gave the error shown above.
The idea is to perform the pipeline step by step, just like so :
XGB=XGBRegressor(n_estimators=10000,learning_rate=0.05,verbose=False)
#This is our original Pipeline
myPip=Pipeline(steps=[("preprocessing",preprocessor),
("model",XGB)])
#We fit the preprocessing step on the unprocessed training data
myPip[0].fit(X_train2,y_train)
#And transform both the training and validation data
X_trainXGB=myPip[0].transform(X_train2)
X_valXGB=myPip[0].transform(X_val2)
#We fit the model on the clean data
myPip[1].fit(X_trainXGB,y_train,eval_set=[(X_valXGB,y_val)],early_stopping_rounds=5)
#And predict the result using the preprocessed (transformed) validation data
y_preds=myPip[1].predict(X_valXGB)
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
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\section{Conclusion}
Multi-Label Continual Learning (MLCL) focuses on solving multi-label classification in continual learning.
It is challenging to construct convincing label relationships and reduce forgetting in MLCL because of the partial label problem.
This paper proposed a novel AGCN++ based on an auto-updated expert mechanism to solve the problem of MLCL.
The key of our AGCN++ is to construct label relationships in a partial label data stream and reduce catastrophic forgetting to improve overall performance.
We studied MLCL in both IL-MLCL and CL-MLCL scenarios.
In relationship construction, we showed the effectiveness of leveraging soft or hard label statistics to update the correlation matrix, even in the partial label data stream.
We also showed the effectiveness of {PLE in reducing the accumulation of errors in the construction of label relationships and suppressing forgetting.}
In terms of forgetting, we proposed an effective distillation loss and a novel relationship-preserving loss to mitigate class- and relationship-level forgetting.
Extensive experiments demonstrate that the proposed AGCN++ can capture well the label dependencies, thus achieving better MLCL performance in the IL-MLCL and CL-MLCL.
Future work will study how to improve the construction of the old-old block using the correlation of only soft labels instead of inheriting the previously constructed ACM. It is believed that the performance will be further enhanced.
\section*{Acknowledgments}
This work was supported by the Natural Science Foundation of China (No. 61876121), the Postgraduate Research \& Practice Innovation Program of Jiangsu Province (No. SJCX21-1414), Suzhou Science and Technology Development Plan (Science and Technology Innovation for Social Development) Project (No. ss202133).
\ifCLASSOPTIONcaptionsoff
\newpage
\fi
\bibliographystyle{IEEEtran}
\section{Experiments}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{train_data}
\caption{Dataset construction of Split-COCO and Split-WIDE.}
\label{fig:dataset}
\end{figure}
\begin{table*}[t]
\centering
\caption{We report 7 metrics (\%) for multi-label classification after the whole data stream is seen once on \textbf{Split-WIDE} in both IL-MLCL and CL-MLCL scenarios. The Multi-Task is offline trained as the \textbf{upper bound}, and Fine-Tuning is the \textbf{lower bound}.}
\resizebox{.99\linewidth}{!}{
\begin{tabular}{c|rrrrrrr|rrrrrrr}
\hline
\toprule
\multirow{2}{*}{{Method}}
& \multicolumn{7}{c|}{\textbf{Split-WIDE IL-MLCL}}& \multicolumn{7}{c}{\textbf{Split-WIDE CL-MLCL}} \\
\cline{2-15}
&{mAP} $\uparrow$&{CP} $\uparrow$&{CR} $\uparrow$&{CF1} $\uparrow$&{OP} $\uparrow$&{OR} $\uparrow$&{OF1} $\uparrow$&{mAP} $\uparrow$&{CP} $\uparrow$&{CR} $\uparrow$&{CF1} $\uparrow$&{OP} $\uparrow$&{OR} $\uparrow$&{OF1} $\uparrow$ \\
\hline
\hline
{Multi-Task}&66.17&69.15&55.30&61.45&77.74&66.30&71.57
&69.19&60.60&43.96&50.33&78.45&59.39&66.67 \\
\hline\hline
{Fine-Tuning}&20.33&15.21&37.85&19.10&25.15&61.62&35.72
&41.82&44.48&34.73&39.00&52.94&42.97&47.43 \\
\rowcolor{mygray}
Forgetting $\downarrow$&40.85&36.95&27.20&31.20&27.22&12.14&15.10
&18.20&20.23&41.83&28.07&3.29&16.63&11.56 \\
\hline
{EWC}~\cite{kirkpatrick2017overcoming}&22.03&15.99&39.53&22.78&24.92&62.97&35.70
&45.04&45.33&{37.13}&40.82&54.36&{53.81}&54.08 \\
\rowcolor{mygray}
Forgetting $\downarrow$&34.86&35.51&24.23&28.18&28.41&9.55&15.17
&14.73&18.31&38.72&25.17&2.20&7.09&4.06 \\
\hline
{LwF}~\cite{li2017learning}&29.46&21.65&46.96&29.64&30.77&69.70&42.69
&46.44&51.05&33.01&40.09&54.24&46.40&50.01 \\
\rowcolor{mygray}
Forgetting $\downarrow$&20.26&29.21&17.02&18.99&20.94&3.84&5.73
&12.68&9.08&42.93&26.05&2.23&14.33&9.31 \\
\hline
{AGEM}~\cite{chaudhry2018efficient}&32.47&23.26&58.44&33.28&26.36&74.40&38.93
&46.83&50.48&27.67&35.75&47.93&35.18&40.58 \\
\rowcolor{mygray}
Forgetting $\downarrow$&16.42&28.09&8.67&15.71&26.55&6.95&9.73
&11.91&10.05&48.36&33.55&11.21&21.56&17.22\\
\hline
{ER}~\cite{rolnick2019experience}&34.03&24.64&60.02&34.94&26.62&75.57&39.37
&48.08&54.33&31.16&39.61&53.40&38.84&44.98 \\
\rowcolor{mygray}
Forgetting $\downarrow$&15.15&26.18&7.14&11.80&26.45&6.25&8.61
&9.24&7.13&45.32&27.58&2.96&19.28&14.53\\
\hline
{PRS}~\cite{kim2020imbalanced}&{39.70}&\textbf{52.77}&18.24&26.48&\textbf{60.81}&14.05&22.19
&51.42&\textbf{58.26}&37.64&45.73&\textbf{55.66}&48.90&52.06 \\
\rowcolor{mygray}
Forgetting $\downarrow$&11.24&4.08&43.22&34.48&2.34&55.73&43.76
&7.86&2.21&37.12&16.68&1.90&11.36&7.13 \\
\hline
{SCR}~\cite{mai2021supervised}&35.34&28.33&54.34&35.47&32.21&70.28&41.92
&49.23&53.87&36.86&43.77&50.16&47.58&48.84 \\
\rowcolor{mygray}
Forgetting $\downarrow$&14.26&21.29&9.56&10.17&23.09&7.26&8.04
&8.34&7.89&39.22&20.56&6.62&13.56&10.78 \\
\hline
{AGCN}&{42.15}&26.04&\textbf{70.21}&{37.99}&29.53&\textbf{84.02}&{43.70}
&{54.20}&56.24&{39.10}&{46.13}&53.94&{56.84}&{55.35} \\
\rowcolor{mygray}
Forgetting $\downarrow$&10.34&25.44&1.35&5.82&25.23&1.12&4.12
&5.27&4.56&34.54&14.34&2.49&5.40&3.26 \\
\hline
\textbf{AGCN++}&\textbf{45.73}&33.08&{61.57}&\textbf{43.04}&32.29&{75.62}&\textbf{45.26}
&\textbf{57.07}&55.07&\textbf{54.26}&\textbf{54.66}&49.03&\textbf{74.96}&\textbf{59.29} \\
\rowcolor{mygray}
Forgetting $\downarrow$&8.32&17.28&7.44&2.13&22.11&5.52&3.98
&4.45&3.56&19.48&10.64&6.13&0.18&1.02 \\
\bottomrule
\end{tabular}}
\label{tab:results_WIDE}
\end{table*}
\begin{table*}[t]
\centering
\caption{We report seven metrics (\%) for multi-label classification after the whole data stream is seen once on \textbf{Split-COCO} in both IL-MLCL and CL-MLCL scenarios. The Multi-Task is offline trained as the \textbf{upper bound}, and Fine-Tuning is the \textbf{lower bound}.}
\resizebox{.99\linewidth}{!}{
\begin{tabular}{c|rrrrrrr|rrrrrrr}
\hline
\toprule
\multirow{2}{*}{{Method}}
& \multicolumn{7}{c|}{\textbf{Split-COCO IL-MLCL}}& \multicolumn{7}{c}{\textbf{Split-COCO CL-MLCL}} \\
\cline{2-15}
&{mAP} $\uparrow$&{CP} $\uparrow$&{CR} $\uparrow$&{CF1} $\uparrow$&{OP} $\uparrow$&{OR} $\uparrow$&{OF1} $\uparrow$&{mAP} $\uparrow$&{CP} $\uparrow$&{CR} $\uparrow$&{CF1} $\uparrow$&{OP} $\uparrow$&{OR} $\uparrow$&{OF1} $\uparrow$ \\
\hline
\hline
{Multi-Task}&65.85&71.64&54.31&61.79&77.24&58.03&66.27
&68.33&73.06&49.82&61.49&89.31&64.99&74.98\\
\hline\hline
{Fine-Tuning}&9.83&6.90&18.52&10.54&21.63&41.25&28.83
&32.35& 33.34&29.10&31.01&57.03&45.56&50.56
\\
\rowcolor{mygray}
Forgetting $\downarrow$&58.04&48.96&64.30&63.54&18.24&38.76&20.60
&31.78&33.32&32.14&33.90&16.61&9.22&12.24 \\
\hline
{EWC}~\cite{kirkpatrick2017overcoming}&12.20&9.70&17.54&12.50&23.63&39.84&29.67
&35.83& 31.88&33.05&32.18&57.62&46.98&51.60 \\
\rowcolor{mygray}
Forgetting $\downarrow$&45.61&42.68&60.50&55.44&15.34&40.59&19.85
&27.66&37.82&26.29&30.29&16.24&7.18&10.16 \\
\hline
{LwF}~\cite{li2017learning}&19.95&18.02&28.44&21.69&33.14&57.83&40.68
&40.87& 44.36&{35.07}&39.07&61.72&48.10&53.95 \\
\rowcolor{mygray}
Forgetting $\downarrow$&41.16&29.73&44.01&39.85&8.70&19.38&11.43
&21.15&22.70&25.90&23.64&12.29&4.99&7.67 \\
\hline
{AGEM}~\cite{chaudhry2018efficient}&23.31&22.34&42.10&27.25&29.95&62.32&37.94
&42.25& 64.40&19.28&29.08&57.64&12.62&18.59 \\
\rowcolor{mygray}
Forgetting $\downarrow$&34.52&17.12&20.36&18.92&13.02&11.35&12.94
&19.75&9.11&45.66&35.37&15.94&34.80&39.92 \\
\hline
{ER}~\cite{rolnick2019experience}&25.03&26.45&41.14&30.54&30.32&61.84&38.38
&43.54&\textbf{71.15}&16.65&26.60&62.89&17.72&26.44 \\
\rowcolor{mygray}
Forgetting $\downarrow$&33.46&14.96&22.28&17.28&11.80&12.49&12.34
&17.13&1.14&47.73&38.34&11.79&30.32&32.66 \\
\hline
{PRS}~\cite{kim2020imbalanced}&{31.08}&\textbf{56.07}&22.74&32.27&\textbf{57.87}&14.24&22.25
&46.39&58.56&29.41&38.20&58.84&{50.54}&54.25 \\
\rowcolor{mygray}
Forgetting $\downarrow$&28.82&1.32&50.59&16.21&0.34&58.37&30.43
&13.07&13.52&31.23&24.56&14.21&6.09&6.36 \\
\hline
{SCR}~\cite{mai2021supervised}&25.75&25.22&{49.35}&30.63&29.40&{69.91}&39.10
&44.96&54.00&29.25&37.82&41.47&40.40&40.46 \\
\rowcolor{mygray}
Forgetting $\downarrow$&32.02&15.27&16.02&15.98&13.58&6.52&11.96
&15.33&19.88&31.89&25.12&30.04&13.24&19.26 \\
\hline
{AGCN}&{34.11}&31.80&{47.73}&{35.49}&34.38&{67.72}&{42.37}
&{48.82}&55.73&30.83&{39.18}&\textbf{74.27}&47.06&{56.76} \\
\rowcolor{mygray}
Forgetting $\downarrow$&23.71&12.21&17.81&14.79&8.03&9.86&8.16
&10.40&18.72&30.39&22.38&1.63&6.71&3.97 \\
\hline
\textbf{AGCN++}&\textbf{38.23}&32.51&\textbf{60.47}&\textbf{41.38}&34.32&\textbf{75.34}&\textbf{45.26}
&\textbf{53.49}&46.66&\textbf{52.96}&\textbf{49.55}&55.14&\textbf{64.74}&\textbf{59.32} \\
\rowcolor{mygray}
Forgetting $\downarrow$&20.12&11.13&9.08&11.34&8.82&3.68&6.78
&7.24&24.88&6.34&14.52&23.67&1.34&1.24 \\
\bottomrule
\end{tabular}}
\label{tab:results_COCO}
\end{table*}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{different_class}
\caption{mAP (\%) of different classes setting in both IL- and CL-MLCL.}
\label{fig:different_class}
\end{figure}
\begin{figure*}
\centering
\includegraphics[width=\linewidth]{learning_curves}
\caption{{mAP (\%) on two benchmarks in both IL- and CL-MLCL.}}
\label{fig:learning_curves}
\end{figure*}
\subsection{Datasets}
\subsubsection{Dataset description}
We use two datasets, Split-COCO and Split-WIDE, to evaluate the effectiveness of the proposed method.
\textbf{Split-COCO}.
We choose the 40 most frequent concepts from 80 classes of MS-COCO~\cite{lin2014microsoft} to construct Split-COCO, which has 65082 examples for training and 27,173 examples for validation.
The 40 classes are split into ten different and non-overlapping tasks, each containing four classes.
\textbf{Split-WIDE}.
NUS-WIDE~\cite{chua2009nus} is a raw web-crawled multi-label image dataset. We further curate a sequential class-incremental dataset from NUS-WIDE. Following~\cite{jiang2017deep}, we choose the 21 most frequent concepts from 81 classes of NUS-WIDE to construct the Split-WIDE, which has 144,858 examples for training and 41,146 examples for validation. Split-WIDE has a larger scale than Split-COCO.
We split the Split-WIDE into 7 tasks, where each task contains 3 classes.
\subsubsection{Dataset collection}
{We enlist the curation details of Split-COCO and Split-WIDE.
In the previous continual learning methods, Shmelkov {\em et al.\/}\, \cite{shmelkov2017incremental} selects 20 out of 80 classes to create 2 tasks for SLCL, each with 10 classes.
Nguyen {\em et al.\/}\, \cite{nguyen2019contcap} tailor MSCOCO for continual learning of captioning. They select 24 out of 80 classes to create two tasks.
PRS~\cite{kim2020imbalanced} needs more low-frequency classes to study the imbalanced problem. They curate four tasks with 70 classes using MSCOCO.
Compared to these previous splitting, on the one hand, we set more tasks to test the robustness of the algorithm over more tasks to create a continual setting.
On the other hand, we selected more frequent concepts from the original dataset to reduce the long-tail effect of the original data.
Multi-label datasets inherently have intersecting concepts among the data points. Hence, a naive splitting strategy may lead to a dangerous amount of data loss. This motivates us to minimize data loss during the split.
Moreover, to test diverse research environments, the second objective is to keep the size of the splits balanced optionally.
To split the well-known MS-COCO and NUS-WIDE into several different tasks fairly and uniformly, we introduce two kinds of labelling in the datasets.
\textit{1) Specific-labelling}: If an image only has the labels that belong to the task-special class set $\mathcal{C}^t$ of task $t$, we regard it as a specific-labelling image for task $t$;
\textit{2) Mixed-labelling}: If an image not only has the task-specific labels but also has the old labels belonging to the class set $\mathcal{C}^{t-1}_{\text{seen}}$, we regard it as a mixed-labelling image.}
In IL-MLCL, because the model learns from the task-specific labels $\mathcal{C}^t$, the training data is labelled without old labels, so IL-MLCL will suffer from the partial label problem, which mainly appears in the mixed-labelling image. The IL-MLCL and CL-MLCL share the same training images.
A randomly data-splitting approach may lead to the imbalance of specific-labelling and mixed-labelling images for each task.
We split two datasets into sequential tasks with the following strategies to ensure a proper proportion.
We first count the number of labels for each image.
Then, we give priority to leaving specific-label images for each task. The mixed-labelling images are then allocated to other tasks. The dataset construction is presented in Fig~\ref{fig:dataset}.
\subsection{Evaluation metrics}
\noindent
\textbf{Multi-label evaluation}. Following these multi-label learning methods~\cite{chen2019multi,chen2020knowledge,chen2021learning}, 7 metrics are leveraged in MLCL.
(1) the average precision (AP) on each label and the mean average precision (\textbf{mAP}) over all labels;
(2) the per-class F1-measure (\textbf{CF1});
(3) the overall F1-measure (\textbf{OF1}). The mAP, CF1 and OF1 are relatively more important for multi-label performance evaluation.
Moreover, we adopt 4 other metrics: per-class precision (CP), per-class recall (CR), overall precision (OP) and overall recall (CR).
\begin{equation*}
\label{eq:metrics}
\begin{aligned}
& \text{OP}=\frac{\sum_iN_i^c}{\sum_iN_i^p},~~~~~~~
~~~~~~~~\text{CP}=\frac{1}{C}\sum_i\frac{N_i^c}{N_i^p},\\
& \text{OR}=\frac{\sum_iN_i^c}{\sum_iN_i^g},~~~~~~~
~~~~~~~~\text{CR}=\frac{1}{C}\sum_i\frac{N_i^c}{N_i^g},\\
& \text{OF1}=\frac{2 \times \text{OP} \times \text{OR}}{\text{OP}+\text{OR}},~
\text{CF1}=\frac{2 \times \text{CP} \times \text{CR}}{\text{CP}+\text{CR}},
\end{aligned}
\end{equation*}
where $i$ is the class label and $C$ is the number of labels. $N_i^c$ is the number of correctly predicted images for class $i$, $N^p_i$ is the number of predicted images for class $i$ and $N_i^g$ is the number of ground-truth for class $i$.
\noindent
\textbf{Forgetting measure}~\cite{chaudhry2018riemannian}.
This metric denotes the above multi-label metric value difference for each task between testing when it was first trained, and the last task was trained.
For example, the forgetting measure of mAP for a task $t$ can be computed by its performance difference between task $T$ and $t$ was trained. $F_{t}$, average forgetting after the model has been trained continually up till task $t\in\{1,\cdots,T\}$ is defined as:
\begin{equation} \label{eq:forget}
F_{t}=\frac{1}{t-1} \sum_{j=1}^{t-1} f_{j}^{t},
\end{equation}
where $f_{j}^{t}$ is the forgetting on task $j$ after the model is trained up till task $t$ and computed as
\begin{equation}
f_{j}^{t}=\max _{l \in\{1, \cdots, k-1\}} a_{l, j}-a_{t, j},
\end{equation}
where $a$ denotes every metric in MLCL like mAP, CF1 and OF1. We evaluate the final forgetting ($F_{T}$) after training the final task.
\begin{table*}[t]
\centering
\caption{We report 3 more important metrics (\%) for multi-label classification after the whole data stream is seen once on 8-way Split-COCO and 7-way Split-WIDE in both IL-MLCL and CL-MLCL scenarios. }
\resizebox{.85\linewidth}{!}{
\begin{tabular}{c|rrr|rrr|rrr|rrr}
\toprule
\multirow{2}{*}{{Method}}
& \multicolumn{3}{c|}{{Split-COCO (IL 8-way)}} & \multicolumn{3}{c|}{{Split-COCO (CL 8-way)}} & \multicolumn{3}{c|}{{Split-WIDE (IL 7-way)}} & \multicolumn{3}{c}{{Split-WIDE (CL 7-way)}} \\ \cline{2-13}
&{mAP}&{CF1}&{OF1}&{mAP}&{CF1}&{OF1}&{mAP}&{CF1}&{OF1}&{mAP}&{CF1}&{OF1} \\
\hline\hline
{Multi-Task}&72.24&64.34&72.35
&74.63&68.87&79.74&64.71&58.86&53.82
&68.84&58.64&60.23 \\
\hline\hline
{Fine-Tuning}&16.89&8.82&46.63
&62.69&56.87&68.45&39.26&34.51&50.10
&55.46&41.76&57.01 \\
\hline
{EWC}~\cite{kirkpatrick2017overcoming}&23.47&11.03&47.82
&63.10&56.91&68.60&39.56&33.20&47.69
&56.73&{51.46}&66.07 \\
\hline
{LwF}~\cite{li2017learning}&{36.67}&{37.38}&{46.98}
&63.66&58.39&69.74&{40.14}&{43.64}&{56.22}
&57.48&{54.90}&68.24 \\
\hline
{AGEM}~\cite{chaudhry2018efficient}&40.43&33.50&45.75
&63.92&55.30&69.34&42.33&40.66&52.94
&57.52&45.36&58.25 \\
\hline
{ER}~\cite{rolnick2019experience}&42.23&39.89&46.24
&{64.22}&{58.80}&{70.29} &46.39&47.63&58.71
&58.12&47.11&55.30\\
\hline
{PRS}~\cite{kim2020imbalanced}&{61.56}&47.81&33.09
&{66.61}&{60.13}&{70.89}
&{47.45}&44.71&60.55
&{58.15}&54.39&{68.92}\\
\hline
{AGCN}&{{62.60}}&{{57.85}}&{{59.29}}
&{{70.24}}&{{63.12}}&{{74.21}} &{{54.11}}&{{53.71}}&{{67.04}}
&{{58.98}}&{{55.32}}&{{69.28}}\\
\hline
\textbf{AGCN++}&\textbf{{65.92}}&\textbf{{60.02}}&\textbf{{68.82}}
&\textbf{{73.41}}&\textbf{{68.55}}&\textbf{{74.54}} &\textbf{{56.63}}&\textbf{{57.51}}&\textbf{{73.58}}
&\textbf{{61.04}}&\textbf{{60.22}}&\textbf{{72.40}}\\
\bottomrule
\end{tabular}}
\label{tab:more_class}
\end{table*}
\begin{table*}
\centering
\caption{Ablation studies (\%) for ACM $\mathbf{A}^t$ and $\textbf{PLE}$ on Split-WIDE and Split-COCO.
}
\resizebox{\linewidth}{!}{
\begin{tabular}{c|cc|cccccc|cccccc}
\toprule
\multicolumn{3}{c}{}&\multicolumn{6}{c}{Split-WIDE}&\multicolumn{6}{c}{Split-COCO}\\
\multicolumn{3}{c}{}&\multicolumn{3}{c}{AGCN++ (w/ PLE)}&\multicolumn{3}{c}{AGCN (w/o PLE)}&\multicolumn{3}{c}{AGCN++ (w/ PLE)}&\multicolumn{3}{c}{AGCN (w/o PLE)}\\
&$\mathbf{A}^{t-1}$ \& $\mathbf{B}^t$ & $\mathbf{R}^t$ \& $\mathbf{Q}^t$
&{mAP} $\uparrow$&{CF1} $\uparrow$&{OF1} $\uparrow$
&{mAP} $\uparrow$&{CF1} $\uparrow$&{OF1} $\uparrow$
&{mAP} $\uparrow$&{CF1} $\uparrow$&{OF1} $\uparrow$
&{mAP} $\uparrow$&{CF1} $\uparrow$&\textbf{OF1} $\uparrow$\\
\hline
\multirow{2}{*}{IL-MLCL}
& $\surd$ & $\times$
& 42.25 & 40.47 & 42.98
& 38.05 & 34.03 & 42.71
& 35.19 & 39.98 & 37.62
& 31.52 & 30.37 & 34.87 \\
& $\surd$ & $\surd$
& \textbf{45.73} & \textbf{43.04} & \textbf{45.26}
& \textbf{42.15} & \textbf{37.99} & \textbf{43.70}
& \textbf{38.23} & \textbf{41.38} & \textbf{45.26}
& \textbf{34.11} & \textbf{35.49} & \textbf{42.37}\\
\hline
\multirow{2}{*}{CL-MLCL}
& $\surd$ & $\times$
& 54.72 & 50.41 & 48.84
& 49.47 & 44.73 & 52.13
& 51.51 & 47.13 & 56.97
& 44.53 & 35.55 & 53.57\\
& $\surd$ & $\surd$
& \textbf{57.07} & \textbf{54.66} & \textbf{59.29}
& \textbf{54.20} & \textbf{46.13} & \textbf{55.35}
& \textbf{53.49} & \textbf{49.55} & \textbf{59.32}
& \textbf{48.82} & \textbf{39.18} & \textbf{56.76}\\
\bottomrule
\end{tabular}}
\label{tab:ACM_ab}
\end{table*}
\subsection{Implementation details}
Following existing multi-label image classification methods ~\cite{chen2019multi,chen2020knowledge,chen2021learning}, we employ ResNet101~\cite{he2016deep} as the image feature extractor pre-trained on ImageNet~\cite{deng2009imagenet}. We adopt Adam~\cite{kingma2014adam} as the optimizer of network with $\beta_1=0.9$, $\beta_2=0.999$, and $\epsilon=10^{-4}$. Following~\cite{chen2019multi,chen2020knowledge}, our AGCN++ consists of two GCN layers with output dimensionality of 1024 and 2048, respectively. The input images are randomly cropped and resized to $448\times448$ with random horizontal flips for data augmentation. The network is trained for a single epoch like most continual learning methods done~\cite{de2021continual,bang2021rainbow,lyu2020multi,rebuffi2017icarl}.
\subsection{Baseline methods}
MLCL is a new paradigm of continual learning. We compare our method with several essential and state-of-art continual learning methods, including
(1) \textit{EWC}~\cite{kirkpatrick2017overcoming}, which regularizes the training loss to avoid catastrophic forgetting;
(2) \textit{LwF}~\cite{li2017learning}, which uses the distillation loss by saving task-specific parameters;
(3) \textit{ER}~\cite{rolnick2019experience}, which saves a few training data from the old tasks and retrains them in the current training;
(4) \textit{AGEM}~\cite{chaudhry2018efficient} resets the training gradient by combining the gradient on the memory and training data;
(5) \textit{PRS}~\cite{kim2020imbalanced}, which uses an improved reservoir sampling strategy to study the imbalanced problem.
PRS studies similar problems with us. Still, they focus more on the imbalanced problem but ignore the label relationships and the problem of partial labels for MLCL image recognition.
(6) \textit{SCR}~\cite{mai2021supervised}, which proposes the NCM classifier to improve SLCL performance. SCR is an algorithm designed to improve the top-1 accuracy of single-label recognition.
Similar to~\cite{kim2020imbalanced,mai2021supervised,zhou2022few}, we use a \textit{Multi-Task} baseline, which is trained on a single pass over shuffled data from all tasks. It can be seen as the performance upper bound. We also compare with the \textit{Fine-Tuning}, which performs training without any continual learning technique. Thus, it can be regarded as the performance lower bound.
Note that, to extend some SLCL methods to MLCL, we turn the final Softmax layer in each of these methods into a Sigmoid. Other details follow their original settings.
\subsection{Main results}
\subsubsection{Split-WIDE results}
In Table~\ref{tab:results_WIDE}, with the establishment of relationships and inhibition of class-level and relationship-level forgetting using distillation and relationship-preserving loss, our method shows better performance than the other state-of-art performances in both IL-MLCL and CL-MLCL scenarios.
In particular, AGCN and AGCN++ perform better than other comparison methods on three more essential evaluation metrics, including mAP, CF1 and OF1, which means the effectiveness in multi-label classification.
Also, in the forgetting value evaluated after task $T$, we achieve a better forgetting measure, which means the stability of the proposed method in MLCL.
In the IL-MLCL scenario, because we use soft labels to replace hard labels in the old task label space and establish and remember the label relationships, the AGCN++ outperforms the most state-of-art performances by a large margin: 45.73\% vs. 42.15\% (+ 3.58\%) on mAP, 43.04\% vs. 37.99\% (+ 5.05\%) on CF1 and 45.26\% vs. 43.70\% (+ 1.56\%) on OF1, as shown in Table~\ref{tab:results_WIDE}.
Like IL-MLCL, CL-MLCL still needs to model complete label dependencies between label relationships and reduce forgetting.
The AGCN++ shows better performance than the others in CL-MLCL: 57.07\% vs. 54.20\% (+ 2.87\%) on mAP, 54.66\% vs. 46.13\% (+ 8.53\%) on CF1 and 59.29\% vs. 55.35\% (+ 3.94\%) on OF1, as demonstrated in Table~\ref{tab:results_WIDE}, which suggests that AGCN++ is effective in a large-scale multi-label dataset.
\subsubsection{Split-COCO results}
Split-COCO is split into ten tasks, as mentioned in~\cite{delange2021continual}, compared with methods PRS~\cite{kim2020imbalanced} and ER~\cite{rolnick2019experience}, our approach can protect privacy better because AGCN++ does not collect data from the original dataset. As shown in Table~\ref{tab:results_COCO}, in IL-MLCL and CL-MLCL, AGCN++ achieves better performance than the others in most metrics.
AGCN++ also has a low rate of forgetting old knowledge.
With the AGCN++ combining intra- and inter-task label relationships, the proposed AGCN++ outperforms the most state-of-art performances in IL-MLCL: 38.23\% vs. 34.11\% (+ 4.12\%) on mAP, 41.38\% vs. 35.49\% (+ 5.89\%) on CF1 and 45.26\% vs. 42.37\ (+ 2.89\%) on OF1. This means soft labels can effectively replace hard labels in the old task label space to alleviate the partial label problem.
AGCN++ is also better in CL-MLCL: 53.49\% vs. 48.82\% (+ 4.67\%) on mAP, 49.55\% vs. 39.18\% (+ 10.37\%) on CF1 and 59.32\% vs. 56.76\% (+ 2.56\%) on OF1.
This means ACM is effective for both IL-MLCL and CL-MLCL scenarios in Split-COCO. As illustrated above, AGCN++ can be a uniform MLCL method for IL-MLCL and CL-MLCL.
\subsection{More MLCL settings}
In order to prove the robustness of the method, we verify the effectiveness of AGCN and AGCN++ under other MLCL settings.
{First, as shown in Table~\ref{tab:more_class}, we increase the number of classes of each task to verify that the proposed PLE and ACM can effectively handle more label relationships in a task. Specifically, 8-way for Split-COCO and 7-way for Split-WIDE. As shown in Table~\ref{tab:more_class}, our AGCN and AGCN++ can still achieve better results in three more important metrics, mAP, CF1 and OF1. Take the mAP, for example. For Split-COCO, 65.92\% vs. 62.60\% (+ 3.32\%) in IL 8-way and 73.41\% vs. 70.24\% (+ 3.17\%) in CL 8-way. For Split-WIDE, 56.63\% vs. 54.11\% (+ 2.52\%) in IL 7-way and 61.04\% vs. 58.98\% (+ 2.06\%) in CL 7-way.}
Second, considering in the real world, different tasks often have different numbers of classes. So we provide a different number of classes for each task in a random manner. Specifically, the task setting is "7 : 4 : 1 : 6: 2 : 2 : 5 : 7 : 3 : 3". As shown in Fig~\ref{fig:different_class}, our method performs better than other comparison methods in every task.
These experiments can prove the effectiveness of AGCN++ from more angles.
\subsection{mAP curves}
Similar to~\cite{mai2021supervised,bang2021rainbow,zhou2022few}, we show the mAP trends of different methods in Fig.~\ref{fig:learning_curves} for sequential learning.
These curves indicate the performance along the MLCL progress.
In two MLCL scenarios, Fig.~\ref{fig:learning_curves} illustrates the mAP changes as tasks are being learned on two benchmarks.
The mAP curves show that AGCN and AGCN++ can perform better through the MLCL process.
In addition, their algorithm is applied after the first task for most continual learning methods. Our AGCN and AGCN++ has modelled the label dependencies from the first task. As distillation loss and relationship-preserving loss are applied to subsequent tasks, the algorithm's performance exceeds other methods in each task.
\begin{table*}[t]
\centering
\caption{Ablation studies (\%) for loss weights and relationship-preserving loss on Split-WIDE and Split-COCO for IL- and CL-MLCL.}
\resizebox{0.86\linewidth}{!}{
\begin{tabular}{c|ccc|ccc|ccc|ccc}
\toprule
&\multicolumn{6}{c}{Split-WIDE}&\multicolumn{6}{c}{Split-COCO}\\
& $\lambda_1$ & $\lambda_2$ &$\lambda_3$ &{mAP} $\uparrow$&{CF1} $\uparrow$&{OF1} $\uparrow$
& $\lambda_1$ & $\lambda_2$ &$\lambda_3$ &{mAP} $\uparrow$&{CF1} $\uparrow$&{OF1} $\uparrow$\\
\hline
\multirow{4}{*}{IL-MLCL}
&$0.10$ & $0.90$ & $0$ & 42.04 & 38.76 & 42.12
&$0.15$ & $0.85$ & $0$ & 36.77 & 39.95 & 39.10
\\
& \multicolumn{3}{c|}{\cellcolor{mygray}Forgetting $\downarrow$} & \cellcolor{mygray}10.48 & \cellcolor{mygray}5.24 & \cellcolor{mygray}6.42
& \multicolumn{3}{c|}{\cellcolor{mygray}Forgetting $\downarrow$} & \cellcolor{mygray}22.34 & \cellcolor{mygray}12.73 & \cellcolor{mygray}13.32
\\
\cline{2-13}
&$0.10$ & $0.90$ & $ 10^4 $ & \textbf{45.73} & \textbf{43.04} & \textbf{45.26}
&$0.15$ & $0.85$ & $ 10^4 $ & \textbf{38.23} & \textbf{41.38} & \textbf{45.26}
\\
&\multicolumn{3}{c|}{\cellcolor{mygray}Forgetting $\downarrow$} & \cellcolor{mygray}8.32 & \cellcolor{mygray}2.13 & \cellcolor{mygray}3.98
&\multicolumn{3}{c|}{\cellcolor{mygray}Forgetting $\downarrow$} & \cellcolor{mygray}20.12 & \cellcolor{mygray}11.34 & \cellcolor{mygray}6.78
\\
\bottomrule
\multirow{4}{*}{CL-MLCL}
&$0.70$ & $0.30$ & $0$ & 55.68 & 51.58 & 49.24
&$0.40$ & $0.60$ & $0$ & {50.98} & 46.82 & 54.70
\\
& \multicolumn{3}{c|}{\cellcolor{mygray}Forgetting $\downarrow$} &\cellcolor{mygray}5.04 &\cellcolor{mygray}12.56 &\cellcolor{mygray}10.24
& \multicolumn{3}{c|}{\cellcolor{mygray}Forgetting $\downarrow$} & \cellcolor{mygray}12.87 & \cellcolor{mygray}22.80 & \cellcolor{mygray}6.62
\\
\cline{2-13}
&$0.70$ & $0.30$ & $ 10^3 $ & \textbf{57.07} & \textbf{54.66} & \textbf{59.29}
&$0.40$ & $0.60$ & $ 10^4 $ & \textbf{53.49} & \textbf{49.55} & \textbf{59.32}
\\
&\multicolumn{3}{c|}{\cellcolor{mygray}Forgetting $\downarrow$} & \cellcolor{mygray}4.45 &\cellcolor{mygray} 10.64 & \cellcolor{mygray}1.02
&\multicolumn{3}{c|}{\cellcolor{mygray}Forgetting $\downarrow$} & \cellcolor{mygray}7.24 & \cellcolor{mygray}14.52 & \cellcolor{mygray}1.24
\\
\bottomrule
\end{tabular}}
\label{tab:weight}
\end{table*}
\begin{figure*}[t]
\centering
\includegraphics[width=0.9\linewidth]{visual_ACM}
\caption{ACM visualization. It shows the intra- and inter-task label relationships are constructed well.}
\label{fig:ACM_visual}
\end{figure*}
\subsection{Ablation studies}
\subsubsection{ACM and PLE effectiveness}
We perform ablation experiments on ACM to test the effectiveness of the intra- and inter-task relationships for both AGCN and AGCN++.
As shown in Sec.~\ref{sec:acm}, $\mathbf{R}^t$ (Old-New) and $\mathbf{Q}^t$ (New-Old) are used to model inter-task label dependencies cross old and new tasks, $\mathbf{B}^t$ (New-New) is used to model intra-task label dependencies, and while $\mathbf{R}^t$ and $\mathbf{Q}^t$ are unavailable, neither are $\mathbf{R}^{t-1}$ and $\mathbf{Q}^{t-1}$ in block $\mathbf{A}^{t-1}$, the $\mathbf{A}^{t-1}$ that inherit from the old task only build intra-task relationships.
As shown in Table~\ref{tab:ACM_ab}, if we do not build the label relationships across old and new tasks (w/o $\mathbf{R}^t$ \& $\mathbf{Q}^t$), the performance of AGCN (Line 1 and 3) is already better than most non-AGCN methods.
For example, the comparison between AGCN (w/o $\mathbf{R}^t$ \& $\mathbf{Q}^t$) and LwF (w/o $\mathbf{A}^{t-1}$ \& $\mathbf{B}^t$ and $\mathbf{R}^t$ \& $\mathbf{Q}^t$) on mAP is: 38.05\% vs. 29.46\% (Split-WIDE, IL-MLCL), 49.47\% vs. 46.44\% (Split-WIDE, CL-MLCL), 31.52\% vs. 19.95\% (Split-COCO, IL-MLCL) and 44.53\% vs. 40.87\% (Split-COCO, CL-MLCL), as shown in Table~\ref{tab:ACM_ab}, Table~\ref{tab:results_WIDE} and Table~\ref{tab:results_COCO}. AGCN is also better than most non-AGCN methods on CF1 and OF1.
This means only intra-task label relationships are effective for MLCL image recognition.
When the inter-task block matrices $\mathbf{R}^t$ and $\mathbf{Q}^t$ are available, AGCN with both intra- and inter-task relationships (Line 2 and 4) can perform even better in all three metrics.
For example, mAP comparisons of AGCN (w/ $\mathbf{A}^{t-1}$ \& $\mathbf{B}^t$, $\mathbf{R}^t$ \& $\mathbf{Q}^t$) and PRS on two datasets in two scenarios: 42.15\% vs. 39.70\% (Split-WIDE, IL-MLCL), 54.20\% vs. 51.42\% (Split-WIDE, CL-MLCL), 34.11\% vs. 31.08\% (Split-COCO, IL-MLCL) and 48.82\% vs. 46.39\% (Split-WIDE, CL-MLCL), as shown in Table~\ref{tab:ACM_ab}, Table~\ref{tab:results_WIDE} and Table~\ref{tab:results_COCO}, which means the inter-task relationships can enhance the multi-label recognition.
{And AGCN++ (w/ PLE) outperforms AGCN (w/o PLE) either (w/o $\mathbf{R}^t$ \& $\mathbf{Q}^t$) or (w/ $\mathbf{A}^{t-1}$ \& $\mathbf{B}^t$, $\mathbf{R}^t$ \& $\mathbf{Q}^t$) in all three metrics, which can prove the effectiveness of PLE. When w/o $\mathbf{R}^t$ \& $\mathbf{Q}^t$, for mAP, 42.25\% vs. 38.05\% (Split-WIDE, IL-MLCL), 54.72\% vs. 49.47\% (Split-WIDE, CL-MLCL), 35.19\% vs. 31.52\% (Split-COCO, IL-MLCL), 51.51\% vs. 44.53\% (Split-COCO, CL-MLCL).
When w/ $\mathbf{A}^{t-1}$ \& $\mathbf{B}^t$, $\mathbf{R}^t$ \& $\mathbf{Q}^t$, for mAP, 45.73\% vs. 42.15\% (Split-WIDE, IL-MLCL), 57.07\% vs. 54.20\% (Split-WIDE, CL-MLCL), 38.23\% vs. 34.11\% (Split-COCO, IL-MLCL), 53.49\% vs. 48.82\% (Split-COCO, CL-MLCL).}
\subsubsection{Hyperparameter selection}
Then, we analyze the influences of loss weights and relationship-preserving loss on two benchmarks, as shown in Table~\ref{tab:weight}.
When the relationship-preserving loss is unavailable, loss weight $\lambda_3$ is set to 0. The loss weights of others: $\lambda_1=0.10$, $\lambda_2=0.90$ for Split-WIDE in IL-MLCL, $\lambda_1=0.70$, $\lambda_2=0.30$ for Split-WIDE in CL-MLCL, $\lambda_1=0.15$, $\lambda_2=0.85$ for Split-COCO in IL-MLCL and $\lambda_1=0.40$, $\lambda_2=0.60$ for Split-COCO in CL-MLCL,
By adding the relationship-preserving loss $\ell_\text{gph}$, the performance gets more gains, and the values of forgetting are also lower, which means the mitigation of relationship-level catastrophic forgetting is quite essential for MLCL image recognition, and the relationship-preserving loss is effective.
We select the best $\lambda_3$ as the hyper-parameters, \textit{i.e.}, $\lambda_3=10^4$ for Split-WIDE in IL-MLCL, $\lambda_3=10^3$ for Split-WIDE in CL-MLCL, $\lambda_3=10^4$ for Split-COCO in IL-MLCL and $\lambda_3=10^4$ for Split-COCO in CL-MLCL.
\subsection{Visualization of ACM}
As shown in Fig.~\ref{fig:ACM_visual}, to verify the effectiveness of the constructed ACM, we offer the ACM visualizations on Split-WIDE and Split-COCO for IL-MLCL and CL-MLCL.
We introduce the oracle augmented correlation matrix (oracle ACM) as the upper bound, which is constructed offline using hard label statistics of all tasks from corresponding datasets. \textbf{d} represents the Euclidean distance between the matrix and Oracle ACM. A smaller value of d means that the matrix is closer to oracle ACM, which proves that this ACM is better constructed.
As shown in Fig.~\ref{fig:ACM_visual}, the proposed ACM in both scenarios is close to the oracle ACM. This indicates constructing ACM with soft or hard label statistics is effective. {Note that in CL-MLCL, the ACM is constructed using only hard labels from the dataset, the ACMs of AGCN++ and AGCN are the same in the CL-MLCL scenario under the same dataset. And in IL-MLCL, the ACM is constructed with the soft labels produced by the model, so the ACM of AGCN++ is better constructed.} {In IL-MLCL, we can also observe that the ACM built in AGCN++ is closer to the Oracle ACM than in AGCN, 4.01\% vs. 4.18\% (Split-COCO) and 4.28\% vs. 4.54\% (Split-WIDE), which can prove that the PLE has reduced the accumulation of errors in the construction of label relationships.}
\section{Introduction}
\IEEEPARstart{M}ACHINE learning approaches have been reported to exhibit human-level performance on some tasks, such as Atari games~\cite{silver2018general} or object recognition~\cite{russakovsky2015imagenet}.
However, they always assume that no novel knowledge will be input into models, which is impractical in the real world.
To meet the scenario, continual learning develops intelligent systems that can continuously learn new tasks from sequential datasets while preserving learned knowledge of old tasks~\cite{chen2018lifelong}.
Recently, class-incremental continual learning~\cite{rebuffi2017icarl} builds an adaptively evolvable classifier for the seen classes at any time, where the learner has no access to the task-ID at inference time~\cite{van2019three} just like the real-life applications.
{Compared to traditional continual learning, a class-incremental model has to distinguish between all seen classes from all tasks. Therefore is more challenging. }
For privacy and storage reasons, the training data for old tasks is unavailable when new tasks arrive.
As the model incrementally learns new knowledge, old knowledge is overwritten and gets a drop in performance, known as catastrophic forgetting~\cite{kirkpatrick2017overcoming}.
Thus, the major challenge of MLCL is to learn new tasks without catastrophically forgetting previous tasks over time.
\begin{figure}[t]
\centering
\includegraphics[width=\linewidth]{figs/lml}
\caption{
The inference process of MLCL.
An MLCL model can recognize more labels by learning incremental classes given multi-label images. With learning three classes at each task, the MLCL model can recognize these labels continuously.
}
\label{fig:lml}
\end{figure}
Due to many researchers' efforts, many methods for class-incremental continual learning have been proposed.
The rehearsal-based methods~\cite{mai2021supervised,bang2021rainbow,lyu2020multi,kim2020imbalanced,sun2022exploring} stores samples from raw datasets or generates pseudo-samples with a generative model~\cite{9161395,ye2021lifelong}, these samples are replayed while learning a new task to prevent forgetting.
The regularization-based methods~\cite{9552512,9757872,kirkpatrick2017overcoming,li2017learning,zhou2022few} have an additional regularization term introduced in the loss function, consolidating previous knowledge when learning on new tasks.
And the parameter isolation methods~\cite{mallya2018packnet,mallya2018piggyback,aljundi2017expert} dedicates different model parameters to each task to alleviate any possible forgetting. Moreover, some recent transformer-based methods~\cite{zhou2022learning,douillard2022dytox,wang2022dualprompt,wang2022sprompt} have also achieved good performance.
However, most existing methods for class-incremental continual learning only consider the input images are {single-labelled}, and we call them Single-Label Continual Learning (SLCL).
SLCL is limited in practical applications such as movie categorization and scene classification, where \emph{multi-label} data is widely used.
As shown in Fig.~\ref{fig:lml}, an image contains multiple labels, including ``sky'', ``grass'', ``person'' and ``dog'', etc., which shows the multi-label space is much larger than the single-label space via label combination.
Because of the co-occurrence of multiple labels, the label space of the multi-label dataset is much larger than that of the single-label one.
In the recent, using a neural network to tackle Multi-Label (ML) image classification problems has achieved impressive results~\cite{zhu2017learning,li2017improving}, which consider constructing label relationships to improve the classification by using recurrent neural network~\cite{wang2016cnn,lyu2019attend} and graph convolutional network~\cite{chen2019multi,chen2020knowledge,chen2021learning}.
This paper puts the multi-task classification into an incremental scenario, \textit{i.e.}, class-incremental classification, and studies how to sequentially learn new classes for Multi-label Continual Learning (MLCL).
The inference process of MLCL is in Fig.~\ref{fig:lml}.
Given testing images, the model can incrementally recognize multiple labels as new classes are learned continuously.
Because of the unavailability of data with future and past classes in continual learning, the \emph{partial label problem} poses a significant challenge in building multi-label relationships and reducing catastrophic forgetting in MLCL than SLCL.
The partial label problem means that each task in MLCL cannot be trained independently since the label spaces for different tasks are overlapped.
For example, as shown in Fig.~\ref{fig:lml}, the label ``sky'' is present in all three tasks. It is one of the overlapped labels for three tasks.
For task $1$, ``sky'' is the future latent label, and for task $3$, "sky" is the past latent label. If the past latent label is not annotated in the current training, the past-missing partial label problem will occur, and similarly, the future-missing partial label problem will occur.
An MLCL model should incrementally recognize multiple labels as new classes are learned continuously.
Practically, we solve the MLCL problems in two real-world labelling scenarios, \textit{i.e.}, the current training dataset has past and current labels (Continuous Labelling MLCL, \textit{CL-MLCL}) or only current labels (Independent Labelling MLCL, \textit{IL-MLCL}).
The IL-MLCL has past-missing and future-missing partial label problems, while CL-MLCL has only the future-missing partial label problem.
As for both scenarios, the partial label problem poses a significant challenge in building multi-label relationships and keeping them from catastrophic forgetting.
It is crucial to study a feasible solution to solve the partial label problem in MLCL.
\textit{This motivates us to design a unified MLCL solution to the sequential multi-label classification problem by considering the label relationships across tasks in both IL-MLCL and CL-MLCL scenarios.}
This paper is an extension of our previous work, Augmented Graph Convolutional Network (AGCN)~\cite{9859622}, and we complete the real-world scenario of MLCL (IL-MLCL and CL-MLCL) and propose an improved version, AGCN++.
Our AGCN++ has three major parts.
First, to relate partial labels across tasks, we propose to construct an Augmented Correlation Matrix (ACM) sequentially in MLCL. We design a unified ACM constructor.
For CL-MLCL, ACM is updated by the hard label statistics from new training data at each task.
For IL-MLCL, an auto-updated expert network is designed to generate predictions of the old tasks. These predictions are used as soft labels to represent the old classes in constructing ACM.
{Second, due to partial label problems, effective class representation is difficult to build. In our early conference work, the AGCN model utilized pre-given semantic information (\textit{i.e.}~word embedding) as class representation.
The fixed class representation will lead to the accumulation of errors in constructing label relationships due to partial label problems. Then, this will skew predictions and lead to more serious forgetting.
So in this work, AGCN++ utilizes a partial label encoder (PLE) to decompose each partial image's feature into dynamic class representations. These class-specific representations will vary from image to image and are input as graph nodes into AGCN++. Moreover, unlike AGCN, which directly adds graph nodes manually, PLE can automatically generate graph nodes for each partial label image. Utilizing PLE to get the graph nodes can also reduce the impact of the low quality of word embeddings. So AGCN++ can generate a more convincing ACM and suppress forgetting.}
Third, we propose to encode the dynamically constructed ACM and graph nodes. The AGCN++ model correlates the label spaces of both the old and new tasks in a convolutional architecture and mines the latent correlation for every two classes. This information will be combined with the visual features for prediction.
Moreover, to further mitigate the forgetting, a distillation loss function and a relationship-preserving graph loss function are designed for class-level forgetting and relationship-level forgetting, respectively.
In this paper, we construct two multi-label image classification datasets, Split-COCO and Split-WIDE, based on widely-used multi-label datasets MS-COCO and NUS-WIDE.
The results on Split-COCO and Split-WIDE show that the proposed AGCN++ effectively reduces catastrophic forgetting for MLCL image recognition and can build convincing correlation across tasks whenever the labels of previous tasks are missing (IL-MLCL) or not (CL-MLCL).
Moreover, our methods can effectively reduce catastrophic forgetting in two scenarios.
This paper extends our AGCN~\cite{9859622} with the following new contents:
\begin{enumerate}
\item We complete the real-world scenario of MLCL from IL-MLCL to CL-MLCL scenarios, and a unified AGCN++ model is redesigned to capture label dependencies to improve multi-label recognition in the data stream;
\item We propose a novel partial label encoder (PLE) to decompose the global image features into dynamic graph nodes for each partial label image, which reduces the accumulation of errors in the construction of label relationships and suppresses forgetting; %
\item We propose a unified ACM constructor. The ACM is dynamically constructed using soft or hard labels to build label relationships across sequential tasks of MLCL to solve the partial label problem for IL-MLCL and CL-MLCL. The distillation loss and relationship-preserving loss readjust to IL-MLCL and CL-MLCL to mitigate the class- and relationship-level catastrophic forgetting;
\item More experimental results are provided, including {extensive comparisons on two different scenarios settings and more ablation studies, etc.} More ablation studies and new SOTA MLCL results are provided.
\end{enumerate}
\section{Multi-Label Continual Learning}
\begin{figure*}[t]
\centering
\includegraphics[width=\linewidth]{framework}
\caption{
The overall framework of AGCN++ and AGCN.
(a) AGCN++ model. The model is mainly composed of three points: PLE, ACM, and stacked GCN encoder. PLE decomposes the image feature extracted by the CNN into a group of class-specific representations. The stacked GCN encodes these representations and ACM into graph features. $\hat{y}$ denotes the class-incremental prediction scores.
(b) Compared with AGCN++, AGCN directly uses word embedding as graph nodes. Graph nodes and ACM are input into GCN. The graph feature and image feature do the matrix multiplication to get the prediction.
}
\label{fig:framework}
\end{figure*}
\begin{figure}[t]
\centering
\includegraphics[width=0.78\linewidth]{PLE}
\caption{Partial label encoder (PLE) in task $t$.}
\label{fig:PLE}
\end{figure}
\subsection{Definition of MLCL}
Given $T$ tasks with respect to training datasets $\{\mathcal{D}^{1}_\text{trn},\cdots,\mathcal{D}^{T}_\text{trn}\}$ and test datasets $\{\mathcal{D}^{1}_\text{tst},\cdots,\mathcal{D}^{T}_\text{tst}\}$, the total class numbers increase gradually with the sequential tasks in MLCL and the model is constantly learning new knowledge.
A continual learning system trains on the training sets from $\mathcal{D}^{1}_\text{trn}$ to $\mathcal{D}^{T}_\text{trn}$ sequentially and evaluate on all seen test sets at any time.
For the $t$-th new task, the new and task-specific classes are to be trained, namely $\mathcal{C}^t$.
\textit{MLCL aims at learning a multi-label classifier to discriminate the increasing number of classes in the continual learning process.}
We denote $\mathcal{C}_\text{seen}^t=\bigcup_{n=1}^{t}\mathcal{C}^n$ as seen classes at task $t$, which contains old class set $\mathcal{C}_\text{seen}^{t-1}$ and new class set $\mathcal{C}^t$, that is, $\mathcal{C}_\text{seen}^t=\mathcal{C}_\text{seen}^{t-1}\cup\mathcal{C}^t$, and $\mathcal{C}_\text{seen}^{t-1}\cap\mathcal{C}^t=\varnothing$.
\subsection{MLCL scenarios}
In this section, considering academic and practical requirements, we introduce the two scenarios in MLCL.
In one scenario, we adopt strict continual learning and cannot obtain the old class like most single-Label continual learning methods~\cite{lyu2020multi,kim2020imbalanced,9161395,ye2021lifelong}. In the other scenario, we consider the real-world setting.
IL-MLCL setting has hard task boundaries, so the old classes are unavailable. Conversely, similar to the settings in~\cite{bang2021rainbow} and~\cite{aljundi2019gradient}, CL-MLCL setup makes the task boundaries faint. It is closer to the real world, where new classes do not show up exclusively. The difference between the two scenarios is the training label space for old classes.
\subsubsection{Continuous labelling (CL-MLCL)}
CL-MLCL is a more realistic scenario where the data distribution shifts gradually without hard task boundaries. The annotator of CL-MLCL needs to label all seen classes.
The class numbers of training data increase gradually with the sequential tasks, \textit{i.e.}, $\mathcal{C}_\text{seen}^t$ for training data of task $t$. As shown in Table~\ref{tab:scenarios}, the label space $\mathcal{Y}\subseteq\mathcal{C}_\text{seen}^t$.
The past latent label is annotated, so the old and new labels coexist for a current sample in CL-MLCL.
This scenario is labor-costly, especially when the class number is large. {Because the past latent label is annotated, only the \emph{future-missing partial label} problem will occur in CL-MLCL, and no past-missing partial label problem will occur.}
\subsubsection{Independent labelling (IL-MLCL)}
In this scenario, the annotator only labels the new classes in $\mathcal{C}^t$ for training data in task $t$, as shown in Table~\ref{tab:scenarios}.
This means the training label space is independently labelled with sequential class-incremental tasks.
The old and new labels do not overlap in new task samples in IL-MLCL.
The training label space $\mathcal{Y}$ of IL-MLCL at task $t$ is right the task-specific label (new labels) set $\mathcal{C}^t$.
IL-MLCL can reduce the labelling cost, but due to the lack of old labels in the IL-MLCL label space, the past latent label is not annotated, so a \emph{past-missing partial label} problem will be caused together with \emph{future-missing partial label}.
\subsubsection{Test phase and the goal}
During the test phase, the ground truth for each data point contains all the old classes $\mathcal{C}_\text{seen}^{t-1}$ and task-specific classes $\mathcal{C}^t$ for both CL-MLCL and IL-MLCL.
That is, as shown in Table~\ref{tab:scenarios}, the label space in the test phase is the all seen classes $\mathcal{C}_\text{seen}^t$.
This paper aims to propose a unified approach to solve the MLCL problem in both IL-MLCL and CL-MLCL scenarios.
\begin{table}[t]
\centering
\caption{
Training and testing label sets of task $t$ in two scenarios, CL-MLCL and IL-MLCL.
}
\resizebox{.8\linewidth}{!}{
\begin{tabular}{c|c|c}
\toprule
& \textbf{CL-MLCL} & \textbf{IL-MLCL} \\
\midrule
Trian & $\mathcal{C}_\text{seen}^t=\mathcal{C}_\text{seen}^{t-1}\cup\mathcal{C}^t$ & $\mathcal{C}^t$ \\
Test & $\mathcal{C}_\text{seen}^t=\mathcal{C}_\text{seen}^{t-1}\cup\mathcal{C}^t$ & $\mathcal{C}_\text{seen}^t=\mathcal{C}_\text{seen}^{t-1}\cup\mathcal{C}^t$ \\
\bottomrule
\end{tabular}}
\label{tab:scenarios}
\end{table}
\section{Methodology}
\subsection{Overview of the proposed method}
In multi-label learning, label relationships are verified effective to improve the recognition~\cite{chen2019multi,chen2020knowledge,chen2021learning}.
However, it is challenging to construct convincing label relationships in MLCL image recognition because of the \textit{partial label} problem.
The partial label problem results in difficulty in constructing the inter-task label relationships.
Moreover, forgetting happens not only at the class level but also at the relationship level, which may damage performance.
For effective multi-label recognition, we propose an AGCN++ to construct and update the intra- and inter-task label relationships during the training process.
As shown in Fig.~\ref{fig:framework} (a), AGCN++ model is mainly composed of three parts:
1) {\textbf{Partial label encoder (PLE)} decomposes the image feature extracted by the CNN into a group of class-specific representations, these representations are used as graph nodes to feed the GCN model.}
2) \textbf{Augmented Correlation Matrix (ACM)} provides the label relationships among all seen classes $\mathcal{C}^t_{\text{seen}}$ and is augmented to capture the intra- and inter-task label dependencies.
3) Graph Convolutional Network encodes \textbf{ACM} and graph nodes \textbf{$\mathbf{H}^t$} into label representations $\mathbf{\hat{y}}_\text{gph}$ for label relationships.
{We construct auto-updated expert networks consisting of $\text{CNN}_\text{xpt}$ and $\text{GCN}_\text{xpt}$. After each task has been trained, the model is saved as the expert model to provide soft labels $\mathbf{\hat{z}}$}.
As shown in Fig.~\ref{fig:framework} (a) and (b), the most significant difference between AGCN and AGCN++ is that AGCN++ can extract graph nodes from the original image through PLE. GCN encodes ACM and graph nodes to get $\mathbf{\hat{y}}_\text{gph}$. By adding $\mathbf{\hat{y}}_\text{cal}$ and $\mathbf{\hat{y}}_\text{gph}$, the soft label generated by the model can better replace the past-missing partial label, more convincing ACM (see Fig.~\ref{fig:ACM_visual}) can be developed for IL-MLCL, and the forgetting of CL-MLCL and IL-MLCL can be reduced through knowledge distillation. These can improve the performance of the model.
\subsection{Partial label encoder}
\label{sec:ple}
Due to the partial label problems in MLCL, effective class representation is difficult to build. In AGCN, the model utilized pre-given word embedding as fixed class representation, which will lead to the accumulation of errors in the construction of label relationships. Then, this will skew predictions and lead to more serious forgetting.
{Inspired by~\cite{zhou2016learning}, we propose the partial label encoder (PLE), which decomposes the global image features for each partial label into dynamic representations continuously as classes increment. These class-specific representations will vary from image and are used as augmented graph nodes. PLE will reduce the accumulation of errors in the construction of label relationships and suppress forgetting. And the resulting graph nodes are automatically augmented as the number of classes increases in MLCL.
PLE initializes with image features and model parameters and continuously updates graph nodes.
As shown in Fig~\ref{fig:PLE}, $\text{CNN}(x)\in\mathbb{R}^{D}$, $\text{CNN}_\text{xpt}(x)\in\mathbb{R}^{D}$, $D$ represents the image feature dimensionality.
We use a fully connected layer fc$(\cdot)$ to achieve two goals.
One is to get the prediction without adding label dependencies $\mathbf{\hat{y}}_\text{cal}$
\begin{equation}\label{eq:cal}
\mathbf{\hat{y}}_\text{cal} = \text{fc}(\text{CNN}(x)) \in\mathbb{R}^{|\mathcal{C}_\text{seen}^t|}.
\end{equation}
The other is to make the image feature aware of class information by doing Hadamard Product with its parameters.
\begin{equation}\label{eq:h}
\mathbf{H}^{t} = \Theta \odot \text{cat}(p,q) \in\mathbb{R}^{|\mathcal{C}_\text{seen}^t| \times D},
\end{equation}
where $\odot$ is the Hadamard Product.
$p$ and $q$ are multiple copies of respective image features.
$p = \text{Duplicate}(\text{CNN}_\text{xpt}(x))\in\mathbb{R}^{|\mathcal{C}_\text{seen}^{t-1}|\times D}$, $q = \text{Duplicate}(\text{CNN}(x))\in\mathbb{R}^{|\mathcal{C}^{t}|\times D}$. {For example, $\text{CNN}(x)\in\mathbb{R}^{1\times D}$ is copied $D$ times to get $q\in\mathbb{R}^{|\mathcal{C}^{t}|\times D}$.} $\Theta\in\mathbb{R}^{|\mathcal{C}_\text{seen}^{t}|\times D}$ represents the {class-specific} fc layer parameters. The dimension of $\Theta$ is continuously expanded to accommodate the class-incremental characteristic in continual learning.
In Eq.~\eqref{eq:h}, $\mathbf{H}^{t}$ represents the class-aware graph node and automatically augments as the new task progresses.
We then encode $\mathbf{H}^{t}$ by Graph Convolutional Network (GCN) to get graph representation $\mathbf{\hat{y}}_\text{gph}$.
\begin{equation}\label{eq:gph}
\mathbf{\hat{y}}_\text{gph} = \text{GCN}(\mathbf{A}^t, \mathbf{H}^{t})\in\mathbb{R}^{|\mathcal{C}_\text{seen}^t|},
\end{equation}
where $\mathbf{A}^t$ denotes the Augmented Correlation Matrix (ACM, see the next section for details).
GCN is a two-layer stacked graph model similar to ML-GCN~\cite{chen2019multi,chen2021learning}.
ACM $\mathbf{A}^t$ and graph node $\mathbf{H}^{t}$ can be augmented as the class number increments.
With the established ACM, GCN provides dynamic label relationships to CNN for prediction.
Moreover, we introduce the prediction $\mathbf{\hat{y}}_\text{cal}$ without adding label dependencies, which is combined with $\mathbf{\hat{y}}_\text{gph}$ as the final multi-label prediction $\mathbf{\hat{y}}\in\mathbb{R}^{|\mathcal{C}_\text{seen}^{t}|}$ of our model:
\begin{equation}\label{eq:predict}
\mathbf{\hat{y}} = \sigma\left( \mathbf{\hat{y}}_\text{cal} + \mathbf{\hat{y}}_\text{gph}\right),
\end{equation}
where $\sigma(\cdot)$ represents the Sigmoid function.
ACM represents the auto-updated dependency among all seen classes in the MLCL image recognition system.
The next section will introduce how to establish and augment ACM in AGCN++.
\subsection{Augmented Correlation Matrix}
\label{sec:acm}
Most existing multi-label learning algorithms~\cite{chen2019multi,chen2020knowledge,chen2021learning} rely on constructing the inferring label correlation matrix $\mathbf{A}$ by the hard label statistics among the class set $\mathcal{C}$: $\mathbf{A}_{ij}=P(\mathcal{C}_i|\mathcal{C}_j)|_{i \neq j}$.
The correlation matrix represents a fully-connected graph.
When a new task comes, the graph should be augmented automatically.
\emph{However, in MLCL, the label correlation matrix is hard to infer directly by statistics because of the partial label problem.}
To tackle the problem, as shown in Fig.~\ref{fig:ACM_unified} (b), we introduce an auto-updated expert network inspired by ~\cite{li2017learning} and~\cite{zhou2022few}, which is used to provide missing past labels.
The \textit{soft labels} ${\mathbf{\hat{z}}}$ is obtained by feeding data of the current task into the expert model, \textit{i.e.}~$\mathbf{\hat{z}}=\text{expert}(x)$.
Based on the soft labels, as shown in Fig.~\ref{fig:ACM_unified} (a), we construct an Augmented Correlation Matrix (ACM) $\mathbf{A}^t$ in IL-MLCL and CL-MLCL:
\begin{equation}\label{eq:acm}
{\mathbf{A}}^{t}=\begin{bmatrix} {\mathbf{A}}^{t-1} & \mathbf{R}^t \\ \mathbf{Q}^t & \mathbf{B}^t \end{bmatrix}\iff\begin{bmatrix} \text{Old-Old} & \text{Old-New} \\ \text{New-Old} & \text{New-New} \end{bmatrix},
\end{equation}
in which we take four block matrices including $\mathbf{A}^{t-1}$ and $\mathbf{B}^t$, $\mathbf{R}^t$ and $\mathbf{Q}^t$ to represent intra- and inter-task label relationships between old and old classes, new and new classes, old and new classes as well as new and old classes respectively.
For the first task, $\mathbf{A}^1=\mathbf{B}^1$.
For $t>1$, $\mathbf{A}^t\in\mathbb{R}^{|\mathcal{C}_\text{seen}^t|\times|\mathcal{C}_\text{seen}^t|}$.
It is worth noting that the block $\mathbf{A}^{t-1}$ (Old-Old) can be derived from the old task, so we focus on how to compute the other three blocks in the ACM.
\begin{figure*}[t]
\centering
\includegraphics[width=0.88\linewidth]{ACM_unified}
\caption{
(a) The unified construction of ACM $\mathbf{A}^t$ using Eq.~\eqref{eq:acm}. $\mathbf{A}^{t-1}$ is the completely-built ACM of task $t-1$ in two scenarios. (b) The ACM constructor for IL-MLCL and CL-MLCL. For IL-MLCL, $\mathbf{B}^t$ is constructed using hard labels from a dataset of task $t$ using Eq.~\eqref{eq:hard-hard}; the $\mathbf{R}^t$ is constructed by hard labels from a dataset of task $t$ and soft labels from the expert using Eq.~\eqref{eq:soft-hard}, the expert is the saved model of task $t-1$; the $\mathbf{Q}^t$ is constructed by $\mathbf{R}^t$ based on Bayes' rule using Eq.~\eqref{eq:hard-soft}. For CL-MLCL, the ACM is constructed using hard label statistics in four blocks, including Old-Old, New-New, Old-New and New-Old blocks by Eq.~\eqref{eq:hard-hard}, Eq.~\eqref{eq:soft-hard} and Eq.~\eqref{eq:hard-soft}.}
\label{fig:ACM_unified}
\end{figure*
\noindent
\textbf{New-New block} ($\mathbf{B}^t\in\mathbb{R}^{|\mathcal{C}^t|\times|\mathcal{C}^t|}$).
As shown in Fig.~\ref{fig:ACM_unified} (a), this block computes the intra-task label relationships among the new classes, and the conditional probability in $\mathbf{B}^t$ can be calculated using the hard label statistics from the training dataset similar to the common multi-label learning:
\begin{equation}\label{eq:hard-hard}
\mathbf{B}^t_{ij} = P(\mathcal{C}^t_{i}\in\mathcal{C}^t|\mathcal{C}^t_{j}\in\mathcal{C}^t) = \frac{N_{ij}}{N_{j}},
\end{equation}
where $N_{ij}$ is the number of examples with both class $\mathcal{C}^t_{i}$ and $\mathcal{C}^t_{j}$, $N_{j}$ is the number of examples with class $\mathcal{C}^t_{j}$.
Due to the data stream, $N_{ij}$ and $N_{j}$ are accumulated and updated at each step of the training process.
This block is shared by both IL- and CL-MLCL because the new class data is always available.
\noindent
\textbf{Old-New block} ($\mathbf{R}^t\in\mathbb{R}^{|\mathcal{C}_\text{seen}^{t-1}|\times|\mathcal{C}^t|}$).
As shown in Fig.~\ref{fig:ACM_unified} (b), for CL-MLCL, this block can be directly obtained by the hard label statistics.
For IL-MLCL, given an image $\mathbf{x}$, for old classes, ${\hat{z}}_{i}$ (predicted probability) generated by the expert can be considered as the soft label for the $i$-th class.
Thus, the product ${\hat{z}}_{i}{{{y}}_{j}}$ can be regarded as an alternative of the cooccurrences of ${\mathcal{C}_\text{seen}^{t-1}}_i$ and $\mathcal{C}^t_{j}$.
Thus, $\sum_{\mathbf{x}}{\hat{z}}_{i}{{{y}}_{j}}$ means the online mini-batch accumulation
\begin{equation}\label{eq:soft-hard}
\begin{aligned}
\mathbf{R}^t_{ij} &= P({\mathcal{C}_\text{seen}^{t-1}}_i\in{\mathcal{C}_\text{seen}^{t-1}}|\mathcal{C}^t_{j}\in\mathcal{C}^t) \\
&=
\left\{
\begin{aligned}
&\frac{N_{ij}}{N_{j}},&\quad &\text{if CL-MLCL},\\
&\frac{\sum_{\mathbf{x}}{\hat{z}}_{i}{{{y}}_{j}}}{N_j},&\quad &\text{if IL-MLCL},
\end{aligned}
\right.
\end{aligned}
\end{equation}
where $N_{ij}$ is the accumulated number of examples with both class ${\mathcal{C}_\text{seen}^{t-1}}_i$ and $\mathcal{C}^t_{j}$, $N_{j}$ is the accumulated number of examples with class $\mathcal{C}^t_{j}$.
\noindent
\textbf{New-Old block} ($\mathbf{Q}^t\in\mathbb{R}^{|\mathcal{C}^t|\times|\mathcal{C}_\text{seen}^{t-1}|}$).
As shown in Fig.~\ref{fig:ACM_unified} (b), for CL-MLCL, the inter-task relationship between new and old classes can be computed using hard label statistics.
For IL-MLCL, based on the Bayes' rule, we can obtain this block by
\begin{equation}\label{eq:hard-soft}
\begin{aligned}
\mathbf{Q}^t_{ji} &= P(\mathcal{C}^t_{j}\in\mathcal{C}^t|{\mathcal{C}_\text{seen}^{t-1}}_i\in{\mathcal{C}_\text{seen}^{t-1}})
\\&=
\left\{\begin{aligned}
&\frac{N_{ij}}{N_{i}},&\quad &\text{if CL-MLCL},\\
&\frac{P({\mathcal{C}_\text{seen}^{t-1}}_i|\mathcal{C}^t_j)P(\mathcal{C}^t_j)}{P({\mathcal{C}_\text{seen}^{t-1}}_i)}=\frac{\mathbf{R}^t_{ij}N_j}{\sum_{\mathbf{x}}{\hat{z}}_{i}},&\quad &\text{if IL-MLCL},
\end{aligned}
\right.
\end{aligned}
\end{equation}
where $N_{ij}$ is the accumulated number of examples with both class ${\mathcal{C}_\text{seen}^{t-1}}_i$ and $\mathcal{C}^t_{j}$, $N_{i}$ is the accumulated number of examples with class ${\mathcal{C}_\text{seen}^{t-1}}_i$.
{Finally, we construct an ACM using the soft and hard label statistics (IL-MLCL) or only the hard label statistics (CL-MLCL). Based on the established ACM, the GCN can capture the label dependencies across different tasks, improving the performance of continual multi-label recognition tasks.}
\begin{algorithm}[t]
\caption{Training procedure of AGCN++.}
\label{alg:main}
\LinesNumbered
\small\KwIn{$\mathcal{D}^t_\text{trn}$}
\small
\For{$t=1:T$}{
\For{$(\mathbf{x},\mathbf{y}) \sim$ $\mathcal{D}^t_\text{trn}$}{
\eIf{$t=1$}{
Compute $\mathbf{A}^1$ with $\mathbf{y}$ using Eq.~\eqref{eq:hard-hard}\;
$\mathbf{H}^1,~\mathbf{\hat{y}}_\text{cal} = \text{PLE}(\text{CNN}(x))$\;
$\mathbf{\hat{y}}_\text{gph} = \text{GCN}(\mathbf{A}^1, \mathbf{H}^{1})$\;
$\mathbf{\hat{y}} = \sigma\left( \mathbf{\hat{y}}_\text{cal} \oplus \mathbf{\hat{y}}_\text{gph}\right)$\;
$\ell=\ell_\text{cls}(\mathbf{y},\mathbf{\hat{y}})$
}{
$\mathbf{\hat{z}}=\text{expert}(x)$\; \tcp{\small get soft labels.
Compute $\mathbf{B}^t$ with $\mathbf{y}$ using Eq.~\eqref{eq:hard-hard};\\
Compute $\mathbf{R}^t$ and $\mathbf{Q}^t$ using Eq.~\eqref{eq:soft-hard} and \eqref{eq:hard-soft}\;
${\mathbf{A}}^{t}=\begin{bmatrix} {\mathbf{A}}^{t-1} & \mathbf{R}^t \\ \mathbf{Q}^t & \mathbf{B}^t \end{bmatrix}$\;
\tcp{\small compute ACM of task $t$.}
$\mathbf{H}^t,~\mathbf{\hat{y}}_\text{cal} = \text{PLE}(\text{CNN}(x))$\;
$\mathbf{\hat{y}}_\text{gph} = \text{GCN}(\mathbf{A}^t, \mathbf{H}^{t})$\;
\tcp{\small get new graph represnetation.
$\mathbf{y}^{\prime}_\text{gph}=\text{GCN}_\text{xpt}(\mathbf{A}^{t-1}, \mathbf{H}^{t-1})$\;
\tcp{\small get target represnetation.}
$\mathbf{\hat{y}} = \sigma\left( \mathbf{\hat{y}}_\text{cal} \oplus \mathbf{\hat{y}}_\text{gph}\right)$\;
\tcp{\small get class prediction.}
$\ell=\lambda_1\ell_\text{cls}(\mathbf{y},\mathbf{\hat{y}})+\lambda_2\ell_\text{dst}(\mathbf{\hat{z}},\mathbf{\hat{y}}_\text{old})$\\$~~~~~+\lambda_3\ell_\text{gph}(\mathbf{y}^{\prime}_\text{gph},\mathbf{\hat{y}}_\text{gph})$\;
\tcp{\small compute the final loss.}
}
Update $\text{AGCN++}$ model by minimizing $\ell$ \\
}
Update expert model \\
\tcp{\small save parameters to the expert model.}
}
\end{algorithm}
\subsection{Objective function}
\label{sec:loss}
As mentioned above, The class-incremental prediction scores $\mathbf{\hat{y}}$ for an image $\mathbf{x}$ can be calculated by Eq.~\eqref{eq:predict}.
The prediction $\mathbf{\hat{y}} = [\mathbf{\hat{y}}_\text{old}~\mathbf{\hat{y}}_\text{new}]\in\mathbb{R}^{|\mathcal{C}_\text{seen}^{t}|}$, where $\mathbf{\hat{y}}_\text{old}\in\mathbb{R}^{|\mathcal{C}_\text{seen}^{t-1}|}$ for old classes and $\mathbf{\hat{y}}_\text{new}\in\mathbb{R}^{|\mathcal{C}^t|}$ for new classes when $t>1$, $\mathcal{C}_\text{seen}^t=\mathcal{C}_\text{seen}^{t-1}\cup\mathcal{C}^t$. By binarizing the ground truth to hard labels $\mathbf{y} = [y_1, \cdots, y_{|\mathcal{C}|}], y_i\in\{0,1\}$, we train the current task using the Cross Entropy loss:
\begin{equation}\label{eq:current_loss}
\ell_\text{cls}(\mathbf{y},\mathbf{\hat{y}})=
-\sum_{i=1}^{|\mathcal{C}|}\Big[y_i\log\left({{\hat{y}}}_{i}\right)+\left(1-{{y}}_{i}\right)\log\left(1-{{\hat{y}}}_{i}\right)\Big],
\end{equation}
where
$\mathcal{C}=\mathcal{C}_\text{seen}^t$ in CL-MLCL and $\mathcal{C}=\mathcal{C}^t$ in IL-MLCL.
However, like traditional SLCL, sequentially fine-tuning the model on the current task will lead to class-level forgetting of the old classes.
To mitigate the class-level catastrophic forgetting, based on the expert network, we construct the distillation loss as
\begin{equation}\label{eq:distillation} \ell_\text{dst}({\mathbf{\hat{z}}},\mathbf{\hat{y}}_\text{old})=-\sum_{i=1}^{|\mathcal{C}_\text{seen}^{t-1}|}\left[{{\hat{z}_i}}\log\left({\hat{y}}_{i}\right)+\left(1-{{\hat{z}}}_{i}\right)\log\left(1-{\hat{y}}_{i}\right)\right],
\end{equation}
where ${\mathbf{\hat{z}}}$ is the soft labels used to represent the prediction on old classes.
The soft labels ${\mathbf{\hat{z}}}$ are used to be the target feature for the old class prediction $\mathbf{\hat{y}}_\text{old}$.
Soft labels play two main roles in our paper: 1) ${\mathbf{\hat{z}}}$ are used to be the target feature of old classes to mitigate the class-level forgetting in IL-MLCL and CL-MLCL scenarios; 2) IL-MLCL has the past-missing partial label problem, soft labels are used as substitutes for old class labels to build label relationships across new and old classes.
To mitigate relationship-level forgetting across tasks, we constantly preserve the established relationships in the sequential tasks.
We compute the old graph representation to serve as a teacher to guide the training of the new GCN model.
The old graph representation in task $t$ is computed by $\mathbf{y}^{\prime}_\text{gph}=\text{GCN}_\text{xpt}(\mathbf{A}^{t-1}, \mathbf{H}^{t-1})$, $t>1$.
Then, we propose a relationship-preserving loss as a relationship constraint:
\begin{equation}\label{eq:graph_distillation}
\ell_\text{gph}(\mathbf{y}^{\prime}_\text{gph},\mathbf{\hat{y}}_\text{gph})=\sum^{|\mathcal{C}_\text{seen}^{t-1}|}_{i=1} \left\Vert{\mathbf{y}^{\prime}_{\text{gph},i}-\mathbf{\hat{y}}_{\text{gph},i}}\right\Vert^2.
\end{equation}
By minimizing $\ell_\text{gph}$ with the partial constraint of old node embedding, the changes of $\text{GCN}$ parameters are limited.
Thus, the forgetting of the established label relationships is alleviated with the progress of MLCL image recognition.
The final loss for the IL- and CL-MLCL model training is defined as
\begin{equation}\label{eq:final_loss}
\ell=\lambda_1\ell_\text{cls}(\mathbf{y},\mathbf{\hat{y}})+\lambda_2\ell_\text{dst}(\mathbf{\hat{z}},\mathbf{\hat{y}}_\text{old})+ \lambda_3\ell_\text{gph}(\mathbf{y}^{\prime}_\text{gph},\mathbf{\hat{y}}_\text{gph}),
\end{equation}
where $\ell_\text{cls}$ is the classification loss, $\ell_\text{dst}$ is used to mitigate the class-level forgetting and $\ell_\text{gph}$ is used to reduce the relationship-level forgetting. $\lambda_1$, $\lambda_2$ and $\lambda_3$ are the loss weights for $\ell_\text{cls}$, $\ell_\text{dst}$ and $\ell_\text{gph}$, respectively.
{The AGCN++ algorithm for both IL-MLCL and CL-MLCL scenarios is presented in Algorithm~\ref{alg:main} to show the detailed training procedure.
Given the training dataset $\mathcal{D}_\text{trn}^t$:
(1) For the first task, the intra-task correlation matrix $\mathbf{A}^1$ is constructed by the statistics of hard labels $\mathbf{y}$, After the input $\mathbf{x}$ is fed to the CNN, the class-specific feature $\mathbf{\hat{y}}_\text{cal}$ and the graph nodes $\mathbf{H}^{1}$ is obtained by PLE. Then the GCN encodes $\mathbf{A}^1$ and $\mathbf{H}^{1}$ to get graph representation $\mathbf{\hat{y}}_\text{gph}$. The prediction score $\mathbf{\hat{y}}$ is generated by $\mathbf{\hat{y}}_\text{cal}$ and $\mathbf{\hat{y}}_\text{gph}$ (Line 4-8).
(2) When $t>1$, the ACM $\mathbf{A}^t$ is augmented via soft labels $\mathbf{\hat{z}}$ and the Bayes' rule. Based on the $\mathbf{A}^t$, $\text{GCN}$ model can capture both intra- and inter-task label dependencies. Then, $\mathbf{\hat{z}}$ and $\mathbf{y}^{\prime}_\text{gph}$ as target features to build $\ell_\text{dst}$ and $\ell_\text{gph}$ respectively (Line 9-20).
(3) The AGCN++ and expert models are updated respectively (Line 21-23).}
\section{Related Work}
\subsection{Class-incremental continual learning}
Class-incremental continual learning~\cite{rebuffi2017icarl} builds a classifier that learns a sequence of new tasks corresponding to different classes.
The state-of-art methods for class-incremental continual learning can be categorized into three main branches to solve the catastrophic forgetting problem.
First, the regularization-based methods~\cite{li2017learning,kirkpatrick2017overcoming,zhou2022few,9552512,9757872}, this line of work introduces additional regularization terms in the loss function to consolidate previous knowledge when learning new tasks.
These methods are based on regularizing the parameters corresponding to the old tasks, penalizing the feature drift on the old tasks and avoiding storing raw inputs.
Kirkpatrick {\em et al.\/}\, \cite{kirkpatrick2017overcoming} limits changes to parameters based on their significance to the previous tasks using Fisher information;
LwF~\cite{li2017learning} is a data-focused method, and it leverages the knowledge distillation combined with a standard cross-entropy loss to mitigate forgetting and transfer knowledge by storing the previous parameters.
Thuseethan {\em et al.\/}\, \cite{9552512} propose an indicator loss, which is associated with the distillation mechanism that preserves the existing upcoming emotion knowledge.
Yang {\em et al.\/}\, \cite{9757872} introduce an attentive feature distillation approach to mitigate catastrophic forgetting while accounting for semantic spatial- and channel-level dependencies. The regularization-based procedures can protect privacy better because they do not collect samples from the original dataset.
Second, the rehearsal-based methods~\cite{ye2021lifelong,de2021continual,bang2021rainbow,lyu2020multi,rolnick2019experience,rebuffi2017icarl,chaudhry2018efficient,silver2020generating,shin2017continual}, which sample a limited subset of data from the previous tasks or a generative model as the memory.
The stored memory is replayed while learning new tasks to mitigate forgetting.
In ER~\cite{rolnick2019experience}, this memory is retrained as the extended training dataset during the current training;
RM~\cite{bang2021rainbow} is a replay method for the blurry setting;
iCaRL~\cite{rebuffi2017icarl} selects and stores samples closest to the feature mean of each class for replaying;
AGEM~\cite{chaudhry2018efficient} resets the training gradient by combining the gradient on the memory and training data;
Ye {\em et al.\/}\, \cite{ye2021lifelong} propose a Teacher-Student network framework. The Teacher module would remind the Student about the information learnt in the past.
Third, the parameter isolation based methods~\cite{aljundi2017expert,mallya2018packnet,mallya2018piggyback,serra2018overcoming}, which generate task-specific parameter expansion or sub-branch. When no limits apply to the size of networks, Expert Gate~\cite{aljundi2017expert} grows new branches for new tasks by dedicating a model copy to each task. PackNet~\cite{mallya2018packnet} iteratively assigns parameter subsets to consecutive tasks by constituting binary masks.
Though the existing methods have achieved successes in SLCL, they are hardly used in MLCL directly.
The overlook of the partial label problem means the inevitability of more serious forgetting in MLCL, let alone the construction of multi-label relationships and reducing the forgetting of the relationships.
\subsection{Multi-label image classification}
Compared with the traditional single-label classification problem, multi-label classification is more practical in the real world.
Earlier multi-label learning methods~\cite{yang2016exploit} prefer to build the model with the help of extra-label localisation information, which is assumed to include all possible foreground objects. And they aggregate the features from proposals to incorporate local information for multi-label prediction.
However, extra localisation information is costly, preventing the models from applying to end-to-end training approaches.
More recent advances are mainly by constructing the label relationships.
Some works~\cite{wang2016cnn,lyu2019attend} use the recurrent neural network (RNN) for multi-label recognition under a restrictive assumption that the label relationships are in order, which limits the complex relationships in label space.
Furthermore, some works \cite{chen2019multi,chen2020knowledge,chen2021learning} build label relationships using graph structure and use graph convolutional network (GCN) to enhance the representation.
The standard limit of these methods is that they can only construct the intra-task correlation matrix using the training data from the current task and fail to capture the inter-task label dependencies in a continual data stream.
They rely on prior knowledge to construct the correlation matrix, which is the key of GCN that aims to gain the label dependencies. These methods utilize the information of the whole training dataset to capture the co-occurrence patterns of objects in an offline way.
Some recent methods focus on the partial label problem~\cite{gong2021top,9343691,9529072} for offline multi-label learning. Compared with this offline way, we construct the correlations and use soft label statistics to solve the partial label problem for MLCL.
Kim {\em et al.\/}\, \cite{kim2020imbalanced} propose to extend the ER~\cite{rolnick2019experience} algorithm using an improved reservoir sampling strategy to study the imbalanced problem on multi-label datasets.
However, the label dependencies are ignored in this work \cite{kim2020imbalanced}.
In contrast, we propose to model label relationships sequentially in MLCL and consider mitigating the relationship-level forgetting in MLCL.
|
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{"url":"http:\/\/cafe.elharo.com\/ui\/the-90-second-rule\/","text":"# The 90 Second Rule\n\nWhile reading Paco Underhill\u2019s Why We Buy, I was struck by his discovery of the 90 second rule:\n\nWe\u2019ve interviewed lots of shoppers on the subject and have found this interesting result: When people wait up to about a minute and a half, their sense of how much time has elapsed is fairly accurate. Anything over ninety or so seconds, however, and their sense of time distorts\u2014if you ask how long they\u2019ve been waiting, their honest answer can often be a very exaggerated one. If they\u2019ve waited two minutes, they\u2019ll say it\u2019s been three or four. In the shopper\u2019s mind, the waiting period goes from being a transitional phase in a larger enterprise (purchasing goods) to being a full-fledged activity of its own. That\u2019s when time becomes very bad. Taking care of a customer in two minutes is a success; doing it in three minutes is a failure.\n\nI suspect the rule applies to a lot more than merely shopping. For example, outside my apartment on Eastern Parkway there is a stop light. Like many stop lights in New York City, there are buttons you can press to request a walk sign. Unlike many of the stoplights in NYC, these buttons actually work. That is, after pressing the button, the light changes; and if nobody presses the button, the light will never change. I\u2019ve timed this light repeatedly with my wristwatch, and it takes just barely under two minutes to change. That measurement is repeatable. Assuming nobody else has recently pressed the button, the elapsed time between pressing the button and getting a walk signal is always between one minute, 50 seconds, and one minute, 59 seconds. I suspect the signal is actually set to change after two minutes, and there\u2019s a systematic error that makes me undercount it a little.\n\nHowever if you ask locals how long the light takes, the estimates invariably run high. The lowest I\u2019ve ever heard anyone claim is three minutes. The highest is around six minutes. The average estimate for the light is probably about four minutes. No one ever guesses that it takes two minutes to change (even though it does) and most people swear up and down that it takes longer than that, and will not believe it\u2019s on a two minute timer unless you pull out a watch and time it with them.\n\nIn this case, I suspect the violation of the ninety second rule is actively dangerous since it encourages people to cross against heavy traffic rather than waiting for the light. Reducing the wait time to 90 seconds might make the intersection safer for pedestrians, who\u2019d be much more likely to wait for the light before crossing.\n\nI suspect the ninety second rule has been undernoticed and undervalued in the world of computer human interfaces because we mostly focus on the half-second rule instead. That is, anything that takes less than half a second is seen as instantaneous, and anything that takes more is not.\n\nRecently there\u2019s been some discussion of the four second rule; i.e. the amount of time that user will wait for a page to load before leaving and going to another site. I think that\u2019s probably a debased form of the half-second rule. That is, it\u2019s half a second the user doesn\u2019t notice plus 3.5 seconds of time they do notice before they take action. However, I suspect there are cases where the user expects to wait and therefore doesn\u2019t mind waiting, and it\u2019s in these cases where the ninety second rule applies instead.\n\nFor example, when doing test driven development, you want to be able to run all the tests after every change. This requires them to be reasonably fast, but how fast? 5 seconds is clearly fast enough. 30 minutes is way too long. Where\u2019s the happy medium? I hypothesize that it\u2019s right around 90 seconds. Anything less than that is fine. Anything more than that, and you should start looking at optimizing your tests, or subsetting the test suite so you run only the fastest and most critical tests. (Other tests can be migrated into the functional test suite. They\u2019re still run, just not as often.)\n\nHere\u2019s another example, in the World of Warcraft, monsters respawn a certain amount of time after they\u2019ve been killed. If you arrive at a site just after another party has killed the monster, your quest requires you have to wait for it to respawn. Probably 90 seconds is the maximum amount of time you want to make someone wait here. Beyond that, you risk the player losing interest and quitting. (Non-quest related monsters don\u2019t need to respawn so quickly.)\n\nGenerally speaking, you can get away with modal operations for 90 seconds or less, as long as you provide some feedback so the program doesn\u2019t look like it\u2019s hung. For example, if you\u2019re transferring files over the network, a progress bar is enough feedback if the files finish in under ninety seconds. However, if the transfer is going to take more than 90 seconds, start considering parallelizing the operation so the user can work with some of the files before the last one has finished transferring. If you\u2019re transferring a single large file like a movie, then consider playing it in streaming mode rather than downloading and then starting the movie. Furthermore, don\u2019t pre-buffer for more than 90 seconds.\n\nWhere else might the ninety second rule apply?\n\nIf you need an outside eye to measure how much your product is making users wait, and how it might be improved. I\u2019m available for consulting and expert design reviews. I specialize in end-user facing software and programmer-facing APIs, but I\u2019ve been known to help out with devices like cameras, refrigerators, microwaves, and watches from time to time too.\n\n### 12 Responses to \u201cThe 90 Second Rule\u201d\n\n1. James Abley Says:\n\nGreat post, Elliotte. I\u2019ve not been reading the junit list for a while, but I think there have been plenty of active discussions about exactly the sweet spot for time taken to run tests, with good contributions from C\u00c3\u00a9dric and JB.\n\nAs an aside, what time of year was that photo taken? The light \/ sky looks fantastic.\n\n2. Matt Says:\n\nLooks like a fine article, but I didn\u2019t finish it, I stopped after 90 seconds or so\n\n3. Labnotes \u00bb Rounded Corners - 74 Says:\n\n[...] Start your timer. Elliotte Rusty Harold about the 90 second rule: \u201cI suspect the ninety second rule has been undernoticed and undervalued in the world of computer human interfaces because we mostly focus on the half-second rule instead.\u201d [...]\n\n4. In 90 Seconds on iface thoughts Says:\n\n[...] Elliotte Rusty Harold muses whether the 90 second rule applies to cases beyond shopping. Taking care of a customer in two minutes is a success; doing it in three minutes is a failure. [...]\n\n5. mehere Says:\n\nNote that in Ireland and Britain, pedestrian crossings at junctions also \u201creally work\u201d, but in a way that sometimes confuses tourists: The lights have a preset cycle, but skip the break for pedestrian crossing if the button is not active. The occurence of the pedestrian crossing break deactivates the button after one run. Thus, if you don\u2019t press the button and it isn\u2019t lit up (active already), the break doesn\u2019t happen, and the lights just cycle through traffic control again. But if you do press the button, the break always occurs at the same point in the traffic light cycle, and thus takes a variable time to happen from button press time. I\u2019ve lost count of the times I\u2019ve seen american tourists waiting aimlessly at traffic lights, not realising they have to press the button, because the first few crossings, some local has pressed it and the americans have noticed the sequence seems to be preset like the \u201cfake\u201d buttons in the USA\u2026\n\n6. The 20-minute rule maker Says:\n\nI think there\u2019s also a 20-minute rule for something like this\u2026 I\u2019d like to make one up. For example, it states that any big event that lasts longer than 20 minutes will seem shorter than it actually is if you participate in it, and much longer if you\u2019re waiting for them.\n\nI\u2019m thinking of the possibilities for these rules; for example, a 2-hour rule for movies; if a movie lasts for less than 2 hours, then it will seem to last only 30 minutes.\n\n7. Aaron Says:\n\nAnother example is with $. I\u2019ve had many an argument with coworkers about the taxes we pay when we work overtime. Many, if not the the majority, of my coworkers believe that if we earn more than one day of overtime pay in a given week, the pay bumps us into the next tax bracket and thus, the government takes a higher percentage out of that particular paycheck. It\u2019s complete fiction; I\u2019ve done the math. I can pull out a calculator and show them and they refuse to believe me. I\u2019ve said to one coworker, \u201cI\u2019ve done the math, the numbers don\u2019t lie.\u201d And his response was, no joke, \u201cBut I\u2019ve been doing this for 20 years!\u201d If they take$250 out of $850, which is roughly 30%, the paycheck ends up$600. Without a calculator or a decent sense of proportion, when they take 30% out of 2000, and the paycheck ends up \\$1400, they might think, \u201cI got raped; they took out almost half!\u201d\n\nI think this boils down not merely to people being unable to gauge time or percentages, but being conditioned to look for things to complain about.\n\nI used to work in a restaurant and if a table had to wait 15 minutes, they would complain that they were waiting over 30.\n\n8. Dan Says:\n\nI\u2019m not sure you\u2019re correct about WoW. As I understand it, the dungeons are stateful \u2013 that is, each separate party that enters a dungeon explores their own instance of the entire dungeon, including monsters. After all, there are 40 million players and nowhere near 40 million different dungeons \u2013 you\u2019d have dozens of hundreds of parties all trying to cram in to kill one single quest-related monster.\n\n9. Jerome Says:\n\nProviding feedback about the wait time helps. I hypothesise that predicting the wait duration isn\u2019t always helpful, though, because \u2014 based on my anecdotal evidence \u2014 it\u2019s annoying because it\u2019s often wrong.\n\nA few decades ago, when phoning directory assistance, the phone company in Holland used a recording to announce the number of people in the queue. \u201cThere are 12 people waiting ahead of you.\u201d [\"Er zijn nog 12 wachtenden voor U.\"] And it would count down: 11, 8, 2, 2 (again), my turn!\n\nIn my experience, this was better than trying to predict the time to completion. We all know from experience that \u201cserving people\u201d in a queue takes a variable and unpredictable amount of time, whereas \u201cabout 2 minutes\u201d is a much more specific commitment.\n\n[On a different note: does it bug you, in the movies, that during the last 30 seconds before a time bomb blows up, the timer practically stops dead when the camera looks away at the sweaty face of the hero trying to cut the blue NO THE RED wire? Every ten seconds of action fits in a mere 3 seconds on the bomb's timer.]","date":"2013-06-19 16:11:55","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.29588690400123596, \"perplexity\": 1451.9851776752053}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-20\/segments\/1368708882773\/warc\/CC-MAIN-20130516125442-00008-ip-10-60-113-184.ec2.internal.warc.gz\"}"}
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{"url":"https:\/\/zbmath.org\/authors\/?q=ai%3Aahmad.ibrahim-a","text":"# zbMATH \u2014 the first resource for mathematics\n\nCompute Distance To:\n Documents Indexed: 136 Publications since 1975\nall top 5\n\n#### Co-Authors\n\n 55 single-authored 9 Lin, Pi-Erh 8 Kayid, Mohamed 7 Mugdadi, Abdel-Razzaq 4 Alwasel, Ibrahim A. 3 Amezziane, Mohamed 3 Cerrito, Patricia B. 3 Li, Qi 2 Al-Nachawati, H. M. 2 Kochar, Subhash C. 2 Mostafa, Sayed A. 2 Ran, Iris S. 1 Ahmed, Abdusalam R. 1 Al-Nahawati, H. 1 Basu, Amiya K. 1 Dorea, Chang Chung Yu 1 El-Bassiouny, Ahmed H. 1 Elbatal, Ibrahim 1 Fan, Yanqin 1 Gupta, Sudhir C. 1 Gupta, Suresh C. 1 Hendi, M. I. 1 King, M. I. Hendi 1 Leelahanon, Sittisak 1 Liang, Ye 1 Liu, Wei 1 Pellerey, Franco 1 Sepehrifar, Mohammad B. 1 Wang, Ningning 1 Wu, Ke-Tsai 1 Ye, Shangyuan 1 Zhang, Ying\nall top 5\n\n#### Serials\n\n 15 Journal of Nonparametric Statistics 11 Annals of the Institute of Statistical Mathematics 11 Journal of Statistical Planning and Inference 10 Statistics & Probability Letters 4 Metrika 3 The Annals of Statistics 3 Biometrika 3 Sankhy\u0101. Series A. Methods and Techniques 3 Communications in Statistics. Theory and Methods 3 Probability in the Engineering and Informational Sciences 2 Bulletin of Mathematical Statistics 2 Journal of the London Mathematical Society. Second Series 2 Journal of Multivariate Analysis 2 Metron 2 Scandinavian Actuarial Journal 2 Journal of Statistical Computation and Simulation 2 Computational Statistics and Data Analysis 2 Statistical Papers 2 Communications in Statistics 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Advances in Applied Probability 1 IEEE Transactions on Information Theory 1 Scandinavian Journal of Statistics 1 Arkiv f\u00f6r Matematik 1 Applied Mathematics and Computation 1 Biometrical Journal 1 Utilitas Mathematica 1 Zeitschrift f\u00fcr Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 Journal of Theoretical Probability 1 Applied Mathematical Modelling 1 SIAM Journal on Applied Mathematics 1 Stochastic Processes and their Applications 1 Arab Journal of Mathematical Sciences 1 Australian & New Zealand Journal of Statistics 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology 1 Calcutta Statistical Association Bulletin 1 Journal of Applied Probability and Statistics 1 Journal of Statistical Theory and Practice 1 Sankhy\u0101 1 Sankhy\u0101. Series A\nall top 5\n\n#### Fields\n\n 87 Statistics\u00a0(62-XX) 43 Probability theory and stochastic processes\u00a0(60-XX) 6 Numerical analysis\u00a0(65-XX) 3 Operations research, mathematical programming\u00a0(90-XX) 2 General and overarching topics; collections\u00a0(00-XX) 1 Game theory, economics, finance, and other social and behavioral sciences\u00a0(91-XX) 1 Information and communication theory, circuits\u00a0(94-XX)\n\n#### Citations contained in zbMATH Open\n\n94 Publications have been cited 741 times in 588 Documents Cited by Year\nEfficient estimation of a semiparametric partially linear varying coefficient model.\u00a0Zbl\u00a01064.62043\nAhmad, Ibrahim; Leelahanon, Sittisak; Li, Qi\n2005\nTesting symmetry of an unknown density function by kernel method.\u00a0Zbl\u00a00926.62032\n1996\nA nonparametric estimation of the entropy for absolutely continuous distributions.\u00a0Zbl\u00a00336.62001\n1976\nOn the mean inactivity time ordering with reliability applications.\u00a0Zbl\u00a01059.62105\n2004\nMoments inequalities of aging families of distributions with hypotheses testing applications.\u00a0Zbl\u00a00971.60014\n2001\nOn multivariate kernel estimation for samples from weighted distributions.\u00a0Zbl\u00a00810.62050\n1995\nA nonparametric test for the monotonicity of a failure rate function.\u00a0Zbl\u00a00349.62065\n1975\nAhmad, I.; Sajid, M.; Hayat, T.; Ayub, M.\n2008\nA class of statistics useful in testing increasing failure rate average and new better than used life distributions.\u00a0Zbl\u00a00804.62086\n1994\nUnsteady flow and heat transfer of a second grade fluid over a stretching sheet.\u00a0Zbl\u00a01221.76022\nSajid, M.; Ahmad, I.; Hayat, T.; Ayub, M.\n2009\nFurther results involving the MIT order and the IMIT class.\u00a0Zbl\u00a01075.60010\nAhmad, I. A.; Kayid, M.; Pellerey, F.\n2005\nCharacterizations of the RHR and MIT orderings and the DRHR and IMIT classes of life distributions.\u00a0Zbl\u00a01336.60027\n2005\nA goodness-of-fit test for exponentiality based on the memoryless property.\u00a0Zbl\u00a00924.62039\nAhmad, Ibrahim A.; Alwasel, Ibrahim A.\n1999\nMultiobjective mixed symmetric duality involving cones.\u00a0Zbl\u00a01189.90135\n2010\nNonparametric sequential estimation of a multiple regression function.\u00a0Zbl\u00a00372.62026\n1976\nFurther moments inequalities of life distributions with hypothesis testing applications: The IFRA, NBUC and DMRL classes.\u00a0Zbl\u00a01034.60014\n2004\nTesting for dispersive ordering.\u00a0Zbl\u00a00662.62044\nAhmad, Ibrahim A.; Kochar, Subhash C.\n1988\nUniform strong convergence of a generalized failure rate estimate.\u00a0Zbl\u00a00367.62045\n1976\nOn asymptotic properties of an estimate of a functional of a probability density.\u00a0Zbl\u00a00354.62036\n1976\nNondifferentiable second order symmetric duality in multiobjective programming.\u00a0Zbl\u00a01075.90067\n2005\nNonparametric estimation of joint discrete-continuous probability densities with applications.\u00a0Zbl\u00a00803.62033\nAhmad, Ibrahim A.; Cerrito, Patricia B.\n1994\nFitting a multiple regression function.\u00a0Zbl\u00a00537.62046\n1984\nMoment inequalities derived from comparing life with its equilibrium form.\u00a0Zbl\u00a01071.62093\n2005\nA new test for mean residual life times.\u00a0Zbl\u00a00751.62045\n1992\nOn nondifferentiable second order symmetric duality in mathematical programming.\u00a0Zbl\u00a01070.90105\n2004\nTesting independence by nonparametric kernel method.\u00a0Zbl\u00a00899.62049\n1997\nResiduals density estimation in nonparametric regression.\u00a0Zbl\u00a00785.62035\n1992\nJackknife estimation for a family of life distributions.\u00a0Zbl\u00a00731.62149\n1988\nSecond order nondifferentiable minimax fractional programming with square root terms.\u00a0Zbl\u00a01324.26013\n2013\nTesting new better than used classes of life distributions derived from a convex ordering using kernel methods.\u00a0Zbl\u00a00955.62099\nAhmad, I. A.; Hendi, M. I.; Al-Nachawati, H.\n1999\nModification of some goodness-of-fit statistics to yield asymptotically normal null distributions.\u00a0Zbl\u00a00817.62033\n1993\nOn the Berry-Esseen theorem for random U-statistics.\u00a0Zbl\u00a00463.60028\n1980\nNonparametric estimation of an affinity measure between two absolutely continuous distributions with hypotheses testing applications.\u00a0Zbl\u00a00453.62033\n1980\nStrong consistency of density estimation by orthogonal series methods for dependent variables with applications.\u00a0Zbl\u00a00445.62053\n1979\nA bandwidth selection for kernel density estimation of functions of random variables.\u00a0Zbl\u00a01429.62132\n2004\nMOL solvers for hyperbolic PDEs with source terms.\u00a0Zbl\u00a00986.65084\n2001\nOptimal bandwidths for kernel density estimators of functions of observations.\u00a0Zbl\u00a00965.62030\n2001\nTesting whether a survival distribution is new better than used of an unknown specified age.\u00a0Zbl\u00a00938.62111\n1998\nGoodness of fit tests based on the $$L_2$$-norm of multivariate probability density functions.\u00a0Zbl\u00a01360.62206\nAhmad, Ibrahim A.; Cerrito, Patricia B.\n1993\nNonparametric estimation of a vector-valued bivariate failure rate.\u00a0Zbl\u00a00369.62041\n1977\nSecond-order duality in nondifferentiable fractional programming.\u00a0Zbl\u00a01231.90355\nAhmad, I.; Husain, Z.; Al-Homidan, S.\n2011\nMinimax mixed integer symmetric duality for multiobjective variational problems.\u00a0Zbl\u00a01111.90050\n2007\nAn aging notion derived from the increasing convex ordering: the NBUCA class.\u00a0Zbl\u00a01077.62004\nAhmad, I. A.; Ahmed, A.; Elbatal, I.; Kayid, M.\n2006\nNondifferentiable second-order symmetric duality.\u00a0Zbl\u00a01141.90571\n2005\nA note on goodness-of-fit statistics with asymptotically normal distributions.\u00a0Zbl\u00a00982.62041\nAhmad, Ibrahim A.; Dorea, Chang C. Y.\n2001\nA note on nonparametric density estimation for dependent variables using a delta sequence.\u00a0Zbl\u00a00477.62022\n1981\nOn the Chernoff-Savage theorem for dependent sequences.\u00a0Zbl\u00a00457.62021\n1980\nHigher-order duality in nondifferentiable minimax fractional programming involving generalized convexity.\u00a0Zbl\u00a01279.26025\n2012\nAhmad, I.; Sajid, M.; Hayat, T.\n2009\nTesting normality using kernel methods.\u00a0Zbl\u00a01024.62018\n2003\nAn algorithm for ODEs from atmospheric dispersion problems.\u00a0Zbl\u00a00889.65085\n1997\nNonparametric estimation of the location and scale parameters based on density estimation.\u00a0Zbl\u00a00486.62038\n1982\nWeighted Hellinger distance as an error criterion for bandwidth selection in kernel estimation.\u00a0Zbl\u00a01099.62034\n2006\nData based bandwidth selection in kernel density estimation with parametric start via kernel contrasts.\u00a0Zbl\u00a01062.62056\nAhmad, Ibrahim A.; Ran, Iris S.\n2004\nAnalysis of kernel density estimation of functions of random variables.\u00a0Zbl\u00a01054.62030\n2003\nBivariate symmetry: definitions and basic properties.\u00a0Zbl\u00a01263.62013\nAhmad, Ibrahim A.; Cerrito, Patricia B.\n1991\nTesting whether F is more IFR than G.\u00a0Zbl\u00a00691.62046\nAhmad, I. A.; Kochar, S. C.\n1990\nIntegrated mean square properties of density estimation by orthogonal series methods for dependent variables.\u00a0Zbl\u00a00493.62039\n1982\nOn some asymptotic properties of U-statistics.\u00a0Zbl\u00a00468.62017\n1981\nA class of asymptotically distribution-free statistics similar to Student\u2019s t.\u00a0Zbl\u00a00319.62032\n1975\nA Berry-Ess\u00e9en inequality without higher order moments.\u00a0Zbl\u00a01356.60040\n2016\nProbability inequalities for bounded random vectors.\u00a0Zbl\u00a01266.60027\n2013\nOn testing alternative classes of life distribution with guaranteed survival times.\u00a0Zbl\u00a01452.62720\n2009\nOn comparison of the solutions for an axisymmetric flow.\u00a0Zbl\u00a01173.76039\nHayat, T.; Ahmad, I.; Javed, T.\n2009\nA general and fast convergent bandwidth selection method of kernel estimator.\u00a0Zbl\u00a01146.62025\n2007\nReversed preservation of stochastic orders for random minima and maxima with applications.\u00a0Zbl\u00a01114.60017\n2007\nBounds of moment generating functions of some life distributions.\u00a0Zbl\u00a01107.62013\n2005\nA simple and more efficient new approach to life testing.\u00a0Zbl\u00a01215.62105\n2004\nKernel contrasts: A data-based method of choosing smoothing parameters in nonparametric density estimation.\u00a0Zbl\u00a01049.62033\nAhmad, Ibrahim A.; Ran, Iris S.\n2004\nOn moment inequalities of the supremum of empirical processes with applications to kernel estimation.\u00a0Zbl\u00a00996.62028\n2002\nGoodness-of-fit statistics based on weighted $$L_ p$$-functionals.\u00a0Zbl\u00a00889.62036\n1997\nModification of some goodness of fit statistics. II: Two-sample and symmetry testing.\u00a0Zbl\u00a00893.62033\n1996\n$$L_p$$-consistency of multivariate density estimates.\u00a0Zbl\u00a00514.62061\n1982\nThe exact order of normal approximation in bivariate renewal theory.\u00a0Zbl\u00a00463.60030\n1981\nNonparametric estimation of Matusita\u2019s measure of affinity between absolutely continuous distributions.\u00a0Zbl\u00a00458.62033\n1980\nAsymptotic joint distribution of sample quantiles and sample mean with applications.\u00a0Zbl\u00a00432.62012\nLin, Pi-Erh; Wu, Ke-Tsai; Ahmad, Ibrahim A.\n1980\nA note on rates of convergence in the multidimensional CLT for maximum partial sums.\u00a0Zbl\u00a00406.60021\n1979\nA Berry-Esseen type theorem.\u00a0Zbl\u00a00355.60025\n1977\nSecond order fractional symmetric duality.\u00a0Zbl\u00a01313.90244\n2014\nMixed type symmetric duality for multiobjective variational problems with cone constraints.\u00a0Zbl\u00a01287.49036\nAhmad, I.; Husain, Z.; Al-Homidan, S.\n2014\nOn quasi-cancellativity of AG-groupoids.\u00a0Zbl\u00a01256.20061\nShah, M.; Ahmad, I.; Ali, A.\n2012\nEstimation of location and scale parameters based on kernel functional estimators.\u00a0Zbl\u00a01414.62067\n2011\nTesting behavior of the reversed hazard rate.\u00a0Zbl\u00a01217.62148\nKayid, M.; Al-Nahawati, H.; Ahmad, I. A.\n2011\nSome properties of classes of life distributions with unknown age.\u00a0Zbl\u00a01062.62020\n2004\nTesting exponentiality against positive ageing using kernel methods.\u00a0Zbl\u00a00972.62095\n2000\nNonparametric estimation of the expected duration of old age.\u00a0Zbl\u00a00939.62028\n1999\nOn the Poisson approximation of multinomial probabilities.\u00a0Zbl\u00a00562.62013\n1985\nOn $$L_ p$$-convergence rates for statistical functions with application to L-estimates.\u00a0Zbl\u00a00563.62013\n1983\nConsistency of a nonparametric estimation of a density functional.\u00a0Zbl\u00a00517.62043\n1983\nOn the normal approximation of an estimate of the mean residual life of a multicomponent system.\u00a0Zbl\u00a00509.62090\n1983\nA note on weak convergence of mean residual life of stationary mixing random variables.\u00a0Zbl\u00a00495.62045\n1983\nConditioned rates of convergence in the CLT for sums and maximum sums.\u00a0Zbl\u00a00449.60017\n1981\nOn concentration functions of random sums of independent random variables.\u00a0Zbl\u00a00428.60063\n1980\nA remark on the SLLN for random partial sums.\u00a0Zbl\u00a00424.60031\n1980\nA Berry-Ess\u00e9en inequality without higher order moments.\u00a0Zbl\u00a01356.60040\n2016\nSecond order fractional symmetric duality.\u00a0Zbl\u00a01313.90244\n2014\nMixed type symmetric duality for multiobjective variational problems with cone constraints.\u00a0Zbl\u00a01287.49036\nAhmad, I.; Husain, Z.; Al-Homidan, S.\n2014\nSecond order nondifferentiable minimax fractional programming with square root terms.\u00a0Zbl\u00a01324.26013\n2013\nProbability inequalities for bounded random vectors.\u00a0Zbl\u00a01266.60027\n2013\nHigher-order duality in nondifferentiable minimax fractional programming involving generalized convexity.\u00a0Zbl\u00a01279.26025\n2012\nOn quasi-cancellativity of AG-groupoids.\u00a0Zbl\u00a01256.20061\nShah, M.; Ahmad, I.; Ali, A.\n2012\nSecond-order duality in nondifferentiable fractional programming.\u00a0Zbl\u00a01231.90355\nAhmad, I.; Husain, Z.; Al-Homidan, S.\n2011\nEstimation of location and scale parameters based on kernel functional estimators.\u00a0Zbl\u00a01414.62067\n2011\nTesting behavior of the reversed hazard rate.\u00a0Zbl\u00a01217.62148\nKayid, M.; Al-Nahawati, H.; Ahmad, I. A.\n2011\nMultiobjective mixed symmetric duality involving cones.\u00a0Zbl\u00a01189.90135\n2010\nUnsteady flow and heat transfer of a second grade fluid over a stretching sheet.\u00a0Zbl\u00a01221.76022\nSajid, M.; Ahmad, I.; Hayat, T.; Ayub, M.\n2009\nAhmad, I.; Sajid, M.; Hayat, T.\n2009\nOn testing alternative classes of life distribution with guaranteed survival times.\u00a0Zbl\u00a01452.62720\n2009\nOn comparison of the solutions for an axisymmetric flow.\u00a0Zbl\u00a01173.76039\nHayat, T.; Ahmad, I.; Javed, T.\n2009\nAhmad, I.; Sajid, M.; Hayat, T.; Ayub, M.\n2008\nMinimax mixed integer symmetric duality for multiobjective variational problems.\u00a0Zbl\u00a01111.90050\n2007\nA general and fast convergent bandwidth selection method of kernel estimator.\u00a0Zbl\u00a01146.62025\n2007\nReversed preservation of stochastic orders for random minima and maxima with applications.\u00a0Zbl\u00a01114.60017\n2007\nAn aging notion derived from the increasing convex ordering: the NBUCA class.\u00a0Zbl\u00a01077.62004\nAhmad, I. A.; Ahmed, A.; Elbatal, I.; Kayid, M.\n2006\nWeighted Hellinger distance as an error criterion for bandwidth selection in kernel estimation.\u00a0Zbl\u00a01099.62034\n2006\nEfficient estimation of a semiparametric partially linear varying coefficient model.\u00a0Zbl\u00a01064.62043\nAhmad, Ibrahim; Leelahanon, Sittisak; Li, Qi\n2005\nFurther results involving the MIT order and the IMIT class.\u00a0Zbl\u00a01075.60010\nAhmad, I. A.; Kayid, M.; Pellerey, F.\n2005\nCharacterizations of the RHR and MIT orderings and the DRHR and IMIT classes of life distributions.\u00a0Zbl\u00a01336.60027\n2005\nNondifferentiable second order symmetric duality in multiobjective programming.\u00a0Zbl\u00a01075.90067\n2005\nMoment inequalities derived from comparing life with its equilibrium form.\u00a0Zbl\u00a01071.62093\n2005\nNondifferentiable second-order symmetric duality.\u00a0Zbl\u00a01141.90571\n2005\nBounds of moment generating functions of some life distributions.\u00a0Zbl\u00a01107.62013\n2005\nOn the mean inactivity time ordering with reliability applications.\u00a0Zbl\u00a01059.62105\n2004\nFurther moments inequalities of life distributions with hypothesis testing applications: The IFRA, NBUC and DMRL classes.\u00a0Zbl\u00a01034.60014\n2004\nOn nondifferentiable second order symmetric duality in mathematical programming.\u00a0Zbl\u00a01070.90105\n2004\nA bandwidth selection for kernel density estimation of functions of random variables.\u00a0Zbl\u00a01429.62132\n2004\nData based bandwidth selection in kernel density estimation with parametric start via kernel contrasts.\u00a0Zbl\u00a01062.62056\nAhmad, Ibrahim A.; Ran, Iris S.\n2004\nA simple and more efficient new approach to life testing.\u00a0Zbl\u00a01215.62105\n2004\nKernel contrasts: A data-based method of choosing smoothing parameters in nonparametric density estimation.\u00a0Zbl\u00a01049.62033\nAhmad, Ibrahim A.; Ran, Iris S.\n2004\nSome properties of classes of life distributions with unknown age.\u00a0Zbl\u00a01062.62020\n2004\nTesting normality using kernel methods.\u00a0Zbl\u00a01024.62018\n2003\nAnalysis of kernel density estimation of functions of random variables.\u00a0Zbl\u00a01054.62030\n2003\nOn moment inequalities of the supremum of empirical processes with applications to kernel estimation.\u00a0Zbl\u00a00996.62028\n2002\nMoments inequalities of aging families of distributions with hypotheses testing applications.\u00a0Zbl\u00a00971.60014\n2001\nMOL solvers for hyperbolic PDEs with source terms.\u00a0Zbl\u00a00986.65084\n2001\nOptimal bandwidths for kernel density estimators of functions of observations.\u00a0Zbl\u00a00965.62030\n2001\nA note on goodness-of-fit statistics with asymptotically normal distributions.\u00a0Zbl\u00a00982.62041\nAhmad, Ibrahim A.; Dorea, Chang C. Y.\n2001\nTesting exponentiality against positive ageing using kernel methods.\u00a0Zbl\u00a00972.62095\n2000\nA goodness-of-fit test for exponentiality based on the memoryless property.\u00a0Zbl\u00a00924.62039\nAhmad, Ibrahim A.; Alwasel, Ibrahim A.\n1999\nTesting new better than used classes of life distributions derived from a convex ordering using kernel methods.\u00a0Zbl\u00a00955.62099\nAhmad, I. A.; Hendi, M. I.; Al-Nachawati, H.\n1999\nNonparametric estimation of the expected duration of old age.\u00a0Zbl\u00a00939.62028\n1999\nTesting whether a survival distribution is new better than used of an unknown specified age.\u00a0Zbl\u00a00938.62111\n1998\nTesting independence by nonparametric kernel method.\u00a0Zbl\u00a00899.62049\n1997\nAn algorithm for ODEs from atmospheric dispersion problems.\u00a0Zbl\u00a00889.65085\n1997\nGoodness-of-fit statistics based on weighted $$L_ p$$-functionals.\u00a0Zbl\u00a00889.62036\n1997\nTesting symmetry of an unknown density function by kernel method.\u00a0Zbl\u00a00926.62032\n1996\nModification of some goodness of fit statistics. II: Two-sample and symmetry testing.\u00a0Zbl\u00a00893.62033\n1996\nOn multivariate kernel estimation for samples from weighted distributions.\u00a0Zbl\u00a00810.62050\n1995\nA class of statistics useful in testing increasing failure rate average and new better than used life distributions.\u00a0Zbl\u00a00804.62086\n1994\nNonparametric estimation of joint discrete-continuous probability densities with applications.\u00a0Zbl\u00a00803.62033\nAhmad, Ibrahim A.; Cerrito, Patricia B.\n1994\nModification of some goodness-of-fit statistics to yield asymptotically normal null distributions.\u00a0Zbl\u00a00817.62033\n1993\nGoodness of fit tests based on the $$L_2$$-norm of multivariate probability density functions.\u00a0Zbl\u00a01360.62206\nAhmad, Ibrahim A.; Cerrito, Patricia B.\n1993\nA new test for mean residual life times.\u00a0Zbl\u00a00751.62045\n1992\nResiduals density estimation in nonparametric regression.\u00a0Zbl\u00a00785.62035\n1992\nBivariate symmetry: definitions and basic properties.\u00a0Zbl\u00a01263.62013\nAhmad, Ibrahim A.; Cerrito, Patricia B.\n1991\nTesting whether F is more IFR than G.\u00a0Zbl\u00a00691.62046\nAhmad, I. A.; Kochar, S. C.\n1990\nTesting for dispersive ordering.\u00a0Zbl\u00a00662.62044\nAhmad, Ibrahim A.; Kochar, Subhash C.\n1988\nJackknife estimation for a family of life distributions.\u00a0Zbl\u00a00731.62149\n1988\nOn the Poisson approximation of multinomial probabilities.\u00a0Zbl\u00a00562.62013\n1985\nFitting a multiple regression function.\u00a0Zbl\u00a00537.62046\n1984\nOn $$L_ p$$-convergence rates for statistical functions with application to L-estimates.\u00a0Zbl\u00a00563.62013\n1983\nConsistency of a nonparametric estimation of a density functional.\u00a0Zbl\u00a00517.62043\n1983\nOn the normal approximation of an estimate of the mean residual life of a multicomponent system.\u00a0Zbl\u00a00509.62090\n1983\nA note on weak convergence of mean residual life of stationary mixing random variables.\u00a0Zbl\u00a00495.62045\n1983\nNonparametric estimation of the location and scale parameters based on density estimation.\u00a0Zbl\u00a00486.62038\n1982\nIntegrated mean square properties of density estimation by orthogonal series methods for dependent variables.\u00a0Zbl\u00a00493.62039\n1982\n$$L_p$$-consistency of multivariate density estimates.\u00a0Zbl\u00a00514.62061\n1982\nA note on nonparametric density estimation for dependent variables using a delta sequence.\u00a0Zbl\u00a00477.62022\n1981\nOn some asymptotic properties of U-statistics.\u00a0Zbl\u00a00468.62017\n1981\nThe exact order of normal approximation in bivariate renewal theory.\u00a0Zbl\u00a00463.60030\n1981\nConditioned rates of convergence in the CLT for sums and maximum sums.\u00a0Zbl\u00a00449.60017\n1981\nOn the Berry-Esseen theorem for random U-statistics.\u00a0Zbl\u00a00463.60028\n1980\nNonparametric estimation of an affinity measure between two absolutely continuous distributions with hypotheses testing applications.\u00a0Zbl\u00a00453.62033\n1980\nOn the Chernoff-Savage theorem for dependent sequences.\u00a0Zbl\u00a00457.62021\n1980\nNonparametric estimation of Matusita\u2019s measure of affinity between absolutely continuous distributions.\u00a0Zbl\u00a00458.62033\n1980\nAsymptotic joint distribution of sample quantiles and sample mean with applications.\u00a0Zbl\u00a00432.62012\nLin, Pi-Erh; Wu, Ke-Tsai; Ahmad, Ibrahim A.\n1980\nOn concentration functions of random sums of independent random variables.\u00a0Zbl\u00a00428.60063\n1980\nA remark on the SLLN for random partial sums.\u00a0Zbl\u00a00424.60031\n1980\nStrong consistency of density estimation by orthogonal series methods for dependent variables with applications.\u00a0Zbl\u00a00445.62053\n1979\nA note on rates of convergence in the multidimensional CLT for maximum partial sums.\u00a0Zbl\u00a00406.60021\n1979\nNonparametric estimation of a vector-valued bivariate failure rate.\u00a0Zbl\u00a00369.62041\n1977\nA Berry-Esseen type theorem.\u00a0Zbl\u00a00355.60025\n1977\nA nonparametric estimation of the entropy for absolutely continuous distributions.\u00a0Zbl\u00a00336.62001\n1976\nNonparametric sequential estimation of a multiple regression function.\u00a0Zbl\u00a00372.62026\n1976\nUniform strong convergence of a generalized failure rate estimate.\u00a0Zbl\u00a00367.62045\n1976\nOn asymptotic properties of an estimate of a functional of a probability density.\u00a0Zbl\u00a00354.62036\n1976\nA nonparametric test for the monotonicity of a failure rate function.\u00a0Zbl\u00a00349.62065\n1975\nA class of asymptotically distribution-free statistics similar to Student\u2019s t.\u00a0Zbl\u00a00319.62032\n1975\nall top 5","date":"2021-06-20 14:08:06","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5892138481140137, \"perplexity\": 2346.0927339146538}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623487662882.61\/warc\/CC-MAIN-20210620114611-20210620144611-00627.warc.gz\"}"}
| null | null |
Fabien Leclercq (born 19 October 1972 in Lille, France) is a French football player. He currently plays at Gap FC.
External links
1972 births
Living people
Footballers from Lille
French footballers
France under-21 international footballers
French expatriate footballers
Lille OSC players
Heart of Midlothian F.C. players
AS Cannes players
ASOA Valence players
FC Sète 34 players
Ligue 1 players
Ligue 2 players
Scottish Premier League players
Expatriate footballers in Scotland
Association football defenders
Competitors at the 1993 Mediterranean Games
Mediterranean Games bronze medalists for France
Mediterranean Games medalists in football
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{"url":"https:\/\/www.beatthegmat.com\/set-of-all-values-of-d-t276489.html","text":"\u2022 Get 300+ Practice Questions\n\nAvailable with Beat the GMAT members only code\n\n\u2022 Free Veritas GMAT Class\nExperience Lesson 1 Live Free\n\nAvailable with Beat the GMAT members only code\n\n\u2022 Free Trial & Practice Exam\nBEAT THE GMAT EXCLUSIVE\n\nAvailable with Beat the GMAT members only code\n\n\u2022 5 Day FREE Trial\nStudy Smarter, Not Harder\n\nAvailable with Beat the GMAT members only code\n\n\u2022 Magoosh\nStudy with Magoosh GMAT prep\n\nAvailable with Beat the GMAT members only code\n\n\u2022 Award-winning private GMAT tutoring\nRegister now and save up to $200 Available with Beat the GMAT members only code \u2022 Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code \u2022 FREE GMAT Exam Know how you'd score today for$0\n\nAvailable with Beat the GMAT members only code\n\n\u2022 1 Hour Free\nBEAT THE GMAT EXCLUSIVE\n\nAvailable with Beat the GMAT members only code\n\n\u2022 5-Day Free Trial\n5-day free, full-access trial TTP Quant\n\nAvailable with Beat the GMAT members only code\n\n## Set of all values of d\n\ntagged by: Brent@GMATPrepNow\n\nThis topic has 2 expert replies and 0 member replies\ngmattesttaker2 Legendary Member\nJoined\n14 Feb 2012\nPosted:\n641 messages\nFollowed by:\n8 members\n11\n\n#### Set of all values of d\n\nMon May 19, 2014 7:08 pm\nHello,\n\nWhich of the following inequalities indicates the set of all values of d for which the lengths of the three sides of a triangle can be 3,4, and d?\n\nA) 0 B) 0 C) 0 D) 1 E) 1\nOA: E\n\nThanks,\nSri\n\n### GMAT\/MBA Expert\n\nBrent@GMATPrepNow GMAT Instructor\nJoined\n08 Dec 2008\nPosted:\n11521 messages\nFollowed by:\n1229 members\n5254\nGMAT Score:\n770\nMon May 19, 2014 8:09 pm\ngmattesttaker2 wrote:\nWhich of the following inequalities indicates the set of all values of d for which the lengths of the three sides of a triangle can be 3,4, and d?\n\nA) 0 B) 0 C) 0 D) 1 E) 1\nIMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .\ndifference between sides A and B < third side < sum of sides A and B\n\nSo, 4 - 3 < d < 4 + 3\nSimplify: 1 < d < 7\n\nCheers,\nBrent\n\n_________________\nBrent Hanneson \u00e2\u20ac\u201c Founder of GMATPrepNow.com\nUse our video course along with\n\nCheck out the online reviews of our course\nCome see all of our free resources\n\nGMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT\u00e2\u20ac\u2122s FREE 60-Day Study Guide and reach your target score in 2 months!\n\n### GMAT\/MBA Expert\n\nRich.C@EMPOWERgmat.com Elite Legendary Member\nJoined\n23 Jun 2013\nPosted:\n9445 messages\nFollowed by:\n480 members\n2867\nGMAT Score:\n800\nMon May 19, 2014 8:40 pm\nHi Sri,\n\nThis question is actually written in such a way that if you know a bit about triangles, then you can logically eliminate all the wrong answers. Here's how.\n\nThe question does NOT state that the third side has to be an integer, so we have to keep an open mind about non-integers.\n\nNotice how three of the answers are 0 < d. These 3 answers imply that the missing side could be \"just above 0\"; for practical purposes, the ONLY type of triangles that allow for that possibility are isosceles triangles - the two sides that we're given would have to be the SAME LENGTH for this option to exist. With sides of 3 and 4, we CANNOT have a side that's \"just above 0.\" Eliminate A, B and C.\n\nWith the Pythagorean Theorem comes the \"Magic Pythagorean Triples\", one of which is the 3\/4\/5 right triangle. With sides of 3 and 4, the missing side COULD be a 5, so we need an answer that accounts for that possibility. Eliminate D.\n\nGMAT assassins aren't born, they're made,\nRich\n\n_________________\nContact Rich at Rich.C@empowergmat.com\n\n### Top First Responders*\n\n1 GMATGuruNY 70 first replies\n2 Rich.C@EMPOWERgma... 42 first replies\n3 Brent@GMATPrepNow 40 first replies\n4 Jay@ManhattanReview 24 first replies\n5 Terry@ThePrinceto... 10 first replies\n* Only counts replies to topics started in last 30 days\nSee More Top Beat The GMAT Members\n\n### Most Active Experts\n\n1 GMATGuruNY\n\nThe Princeton Review Teacher\n\n133 posts\n2 Scott@TargetTestPrep\n\nTarget Test Prep\n\n113 posts\n3 Rich.C@EMPOWERgma...\n\nEMPOWERgmat\n\n111 posts\n4 Jeff@TargetTestPrep\n\nTarget Test Prep\n\n111 posts\n5 Brent@GMATPrepNow\n\nGMAT Prep Now Teacher\n\n90 posts\nSee More Top Beat The GMAT Experts","date":"2018-04-26 21:08:18","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.35079720616340637, \"perplexity\": 5594.324561433587}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-17\/segments\/1524125948549.21\/warc\/CC-MAIN-20180426203132-20180426223132-00477.warc.gz\"}"}
| null | null |
Q: update database record in while loop php I am trying to develop a simple page in php to update attendance days.I have set the query to display the records from db and added a check box with data displayed from db.I want to update the specific record of db on which check box is checked.i want to update the the attendance column with 1 to existing value.for this i just tried written code to display the data from db and added a check box but dnt know to update the record where check box is checked on submit button.here is my initial code.any one help
<?php
require_once("../db/db_connect.php");
$db = new DB_CONNECT();
$sql = "SELECT cv_id, cd_id, cv_fomfeeback FROM candidateverification;";
$res = pg_query($sql) or die ($sql);
// output data of each row
while($row = pg_fetch_row($res)){
echo "cd id: " . $row[0]. " cv id: " . $row[1]. " atn: " . $row[2]. "<input type='checkbox' value='1'/> <br>";
}
?>
<html lang="en">
<head>
<body>
<input type="button" action="update" value="Submit"/>
</body>
</html>
I want to update cv_fomfeeback column with +1 if check box is checked.
A: First you need to name your checkbox. You must do this in a way, so that you get all the checkboxes (-> array) and know the row id of the checkes boxes (-> associative array).
Your checkbox could look like this:
echo "<input type=\"checkbox" name=\"boxes[{$row[0]}]\" value=\"1\">";
On the page that is called after submit has been done (see the comment of @TheNAkos) you will find all checked boxes in the associative array accessible via
$_POST["boxes"]
From there you need to loop through the array and update the rows accordingly.
I will not post a complete example, but those hints should help you find the solution by yourself.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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| 4,633
|
Adelaide Sophia Claxton (Londres, 10 de mayo de 1841 - 29 de agosto de 1927) fue una pintora, ilustradora e inventora británica. Fue una de las primeras mujeres artistas en ganarse la vida a través de la prensa comercial, vendiendo ilustraciones satíricas y cómicas a más de media docena de publicaciones periódicas.
Carrera
Estudió arte en Cary's School en el área de Bloomsbury de Londres, donde comenzó a centrarse en la pintura de figuras en acuarela.
Las pinturas de Claxton combinan escenas de la vida doméstica con elementos literarios o fantásticos como fantasmas y sueños. Comenzó a exhibir su trabajo a fines de la década de 1850 en la Society of Women Artists, expuso varias veces en la Royal Academy of Arts, la Royal Hibernian Academy y la Royal Society of British Artists, así como en la Sociedad de Mujeres Artistas. Una de sus obras, El sueño de una noche de verano en Hampton Court, fue tan popular que terminó pintando cinco copias; otra, Little Nell, la copió 13 veces. Wonderland, una pintura que muestra a una niña leyendo cuentos de los hermanos Grimm a la luz de las velas, está muy reproducida. El pintor inglés Walter Sickert basó su óleo She Was the Belle of the Ball (Después de Adelaide Claxton) en una de sus obras.
Claxton se ganaba la vida a través de sus pinturas y vendiendo ilustraciones cómicas y dibujos satíricos de la alta sociedad a revistas populares como Bow Bells, The Illustrated London News, London Society, Judy (donde fue una de las principales ilustradoras), y varios otros. Fue una de las primeras artistas británicas en trabajar con regularidad en el mercado de las revistas, donde le pagaban entre 2 y 7 libras esterlinas por ilustración. En 1859, el Illustrated Times presentó su pintura El abanderado en su portada.
También fue autora de dos libros ilustrados, A Shillingsworth of Sugar-Plums (1867) y Brainy Odds and Ends (1904; un compendio de lemas y similares).
El trabajo de Claxton está en la colección de Walker Art Gallery, Liverpool y otras instituciones artísticas.
Invenciones
En 1874, Claxton se casó con George Gordon Turner, un evento que terminó de manera efectiva con su carrera como ilustradora. Claxton centró su interés en inventar, y en la década de 1890 se registraron varias patentes bajo su nombre de casada de Adelaide Sophia Turner. Uno de ellos fue para una "Muleta para axilas para reposacabezas y respaldos de sillas". Otro fue para "Gorros para orejas sobresalientes" (es decir, orejas que sobresalían).
Referencias
Escritores de Londres
Artistas de Londres
Escritores del Reino Unido del siglo XIX
Científicos del siglo XIX
Inventoras
Pintores del Reino Unido del siglo XIX
Inventores del Reino Unido
Ilustradores del Reino Unido
Satíricos del Reino Unido
Pintoras de Reino Unido
Fallecidos en Londres
|
{
"redpajama_set_name": "RedPajamaWikipedia"
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| 3,279
|
How do I get a hard copy of my policy?
To download and print a copt of your policy, please log into your Evari Dashboard and follow the prompts to download your policy.
There are a number of factors that affect the price. This includes things like the nature of your business, the types of cover, limits and excesses selected and where you operate your business from.
Why does the quote system auto populate some values?
This information will then auto populate into the Evari quote system and you will be asked to confirm these values. It is at this stage that you can elect to change any of these values and confirm your changes.
My Cover limit says SET - how do I change the cover limit?
Once you move to the 'customise your quote page' you will see that the cover limits for Stock & Contents and Business Disruption (where selected) are SET.
To change the limits on these sections you will need to use the 'click to go back button' on the toolbar to go back to the previous page and alter the values.
The set cover limit for Business Disruption will default to 50% of your current annual revenue amount.
The set cover limit for Stock & Contents will default to the total of your stock and contents values.
Evari is unable to price match with any other insurers. We do however suggest that you review the cover types you have selected, against the covers offered by other insurers, as well as any limits, sub limited & excesses. Different policies may not be exactly alike, so understanding what you will and won't be cover for is important to help you decide what is the best cover for your business.
Why is the premium different to the other quotations I have obtained?
Evari's policy provides comprehensive cover which includes accidental damage and flood cover whereas some some insures may provide defined events only cover, so it is really important that you compare Evari's policy wordings with the other insurers policy wordings/PDS and select the best cover for your business.
Evari allows you to tailor the covers you elect to take out by turning sections on or off and increasing or reducing both cover limits and section excesses thus changing the premium payable.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,955
|
Why So Many Celebrities Keep Their Babies' Umbilical Cord Blood
Like flower crowns and vaginal steaming, umbilical cord banking is a hot trend among celebs like Kourtney Kardashian and Audrina Partridge—but this fad might actually do some good.
by Bethy Squires
Jul 27 2016, 5:00pm
Image by Juliette Toma
Back in April, Nick Carter let the world know that he had a private umbilical cord blood bank. Carter tagged the pic #notasponsoredpost, #stemcelltherapy, and #LOOKITUP. I did, in fact, #LOOKITUP; cord blood banking is the practice of storing your newborn's umbilical cord and placental blood in either a private or public bank for future medical use. The cord and the placenta both carry potentially life-saving stem cells.
Nick Carter is not the only celeb to extoll the virtues of holding on to gestational ephemera. Audrina Partridge went with ViaCord private banking services. In 2012, Giuliana Rancic was a paid spokesperson for Cord Blood Registry (CBR), a company that is also rumored to hold the cord blood of Tori Spelling's offspring, though I could not confirm this. Kourtney Kardashian was photographed with a collection kit from StemCyte. So why are all these celebrities storing their babies' blood? Is this a bizarre celebrity luxury like steaming your vagina, or asking to be excluded from the narrative? Or is cord blood banking actually useful?
Read More: How to Come Down From Too Much Caffeine
"Cord blood is currently used to treat blood cancers like leukemia, as well as lymphoma, neuroblastoma, and hemoglobin opathies like sickle cell," says Dr. Rebecca Haley of Bloodworks Northwest. "We have banked 11,000 cord blood units and shipped a thousand," she says.
Cord blood banking works in two ways. For those who use private banks, like Partridge and Rancic, the bank keeps their child's cord and placenta blood, so should their child become ill, their donations could be harvested for treatment purposes. With public blood banks, donors can deposit their baby's blood for free, with the understanding that they can't necessarily access their children's blood if they need it. Public cord blood banks are connected by an international registry; doctors can access blood from around the world to treat their patients.
Cord blood is the body's ultimate self-repair kit.
Cord blood contains a type of stem cell called a hematopoietic stem cell. These stem cells are the building blocks of our blood and immune system. When treating leukemia, for example, a cord blood transplant would take place after chemotherapy because chemo destroys the blood-producing cells in the bone marrow. The cord blood stem cells are introduced into the bone marrow of a patient, where they "fill the marrow, as it would naturally," Haley says. The healthy blood-producing cells replace the sick ones and help to keep the leukemia in remission.
A varied supply of public cord blood is important to medicine, as a child's own cord blood may not always be the most useful in treating a blood disorder. If your child has sickle cell anemia, for example, their cord blood will as well. "For a genetic disease, the cord blood would have the exact same disease," says Dr. Heather Brown. Brown is the vice president of scientific and medical affairs at CBR, the private bank where both Rancic and Spelling deposited their cord blood. However, she doesn't have any insight into the rise of celebrity cord blood banking. ("I didn't even know Audrina was pregnant," she says.)
For More Stories Like This, Sign Up for Our Newsletter
Private banking, unlike the public option, costs money. A Vogue article published in February of this year listed the average price of private cord blood banking at $2,000 for the initial banking, with a yearly storage fee of $150. What that buys you is guaranteed stem cells for your family. Stem cells need to match the human leukocyte antigen (HLA) profile of the donor. "Siblings have a 25 percent chance of having an exact HLA match," says Brown.
Private banks can also use cord blood for more unproven treatments, whereas public banks are FDA-mandated to only provide cord blood for FDA-approved treatments. There are whole worlds of regenerative therapies being explored currently by private banks. "We are funding clinical trials for the treatment of autism, cerebral palsy, other types of brain injuries like pediatric strokes, and even type 1 diabetes," Brown says.
"Cord blood is the body's ultimate self-repair kit," she explains. "By trying these stem cells on other diseases, the hope is that they'll kick start the body's self-repair system. We think that's what we're seeing with these initial studies." For these future cures, you may very well want your child's cord blood. But the research is still in the early stages. "At a recent conference someone presented their initial findings of a study where patients were treated with their own cord blood for their cerebral palsy," Brown says. "All of us are dying to get our hands on that data."
Merry Duffy of the National Marrow Donor Program is cautiously optimistic about the research being done on cord blood's regenerative properties. "It shows a lot of promise, but there's a lot more work to be done," Duffy says. She says that cord blood has already been approved by the FDA to treat "around 80 different diseases."
I asked Duffy if public cord blood banking had any celebrity endorsements, like the private sector. There is one: former Minnesota Twins first baseman Ron Carew. In 1995, Carew's daughter, Michelle, was diagnosed with Leukemia. She needed a bone marrow transplant and her Panamanian heritage complicated the matter. Ethnic minorities often have a hard time finding donors because their HLA profiles don't match the majority. Cord blood donations, however, don't need to be as exact a match because the stem cells are less mature and more malleable. The following year Michelle was able to receive a cord blood donation—a procedure that was rare at the time—but it was too late. "He brought a lot of attention to the need for minority donors," Duffy says.
Whether private of public, it turns out that cord blood banking is scientifically sound—and it could potentially save your life. I can't wait to find out I was wrong about cryofacials, too.
midrange editorial
Audrina Partridge
placenta blood banking
Broadly Health
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,620
|
'use strict';
var Promise = require('es6-promise').Promise;
var Block = require('./Block');
var isPromise = require('../util').isPromise;
require('./Then'); // extend Block with function then
require('./Listen'); // extend Block with function listen
/**
* Tell
* Send a message to the other peer.
* @param {* | Function} message A static message or callback function
* returning a message dynamically.
* When `message` is a function, it will be
* invoked as callback(message, context),
* where `message` is the output from the
* previous block in the chain, and `context` is
* an object where state can be stored during a
* conversation.
* @constructor
* @extends {Block}
*/
function Tell (message) {
if (!(this instanceof Tell)) {
throw new SyntaxError('Constructor must be called with the new operator');
}
this.message = message;
}
Tell.prototype = Object.create(Block.prototype);
Tell.prototype.constructor = Tell;
// type information
Tell.prototype.isTell = true;
/**
* Execute the block
* @param {Conversation} conversation
* @param {*} [message] A message is ignored by the Tell block
* @return {Promise.<{result: *, block: Block}, Error>} next
*/
Tell.prototype.execute = function (conversation, message) {
// resolve the message
var me = this;
var resolve;
if (typeof this.message === 'function') {
var result = this.message(message, conversation.context);
resolve = isPromise(result) ? result : Promise.resolve(result);
}
else {
resolve = Promise.resolve(this.message); // static string or value
}
return resolve
.then(function (result) {
var res = conversation.send(result);
var done = isPromise(res) ? res : Promise.resolve(res);
return done.then(function () {
return {
result: result,
block: me.next
};
});
});
};
/**
* Create a Tell block and chain it to the current block
* @param {* | Function} [message] A static message or callback function
* returning a message dynamically.
* When `message` is a function, it will be
* invoked as callback(message, context),
* where `message` is the output from the
* previous block in the chain, and `context` is
* an object where state can be stored during a
* conversation.
* @return {Block} Returns the appended block
*/
Block.prototype.tell = function (message) {
var block = new Tell(message);
return this.then(block);
};
/**
* Send a question, listen for a response.
* Creates two blocks: Tell and Listen.
* This is equivalent of doing `babble.tell(message).listen(callback)`
* @param {* | Function} message
* @param {Function} [callback] Invoked as callback(message, context),
* where `message` is the just received message,
* and `context` is an object where state can be
* stored during a conversation. This is equivalent
* of doing `listen().then(callback)`
* @return {Block} Returns the appended block
*/
Block.prototype.ask = function (message, callback) {
// FIXME: this doesn't work
return this
.tell(message)
.listen(callback);
};
module.exports = Tell;
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,286
|
{"url":"https:\/\/socratic.org\/questions\/what-is-the-unit-circle#562856","text":"# What is the unit circle?\n\nThe circumfrence of the unit circle is $2 \\pi$. An arc of the unit circle has the same length as the measure of the central angle that intercepts that arc. Also, because the radius of the unit circle is one, the trigonometric functions sine and cosine have special relevance for the unit circle.","date":"2022-05-17 15:07:05","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 1, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9064423441886902, \"perplexity\": 114.59493410021174}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652662517485.8\/warc\/CC-MAIN-20220517130706-20220517160706-00539.warc.gz\"}"}
| null | null |
\section{ Introduction and main results}
\setcounter{equation}{0}
\label{sec:5-1}
In this paper, we consider the following quasilinear Schr\"{o}dinger equation introduced in \cite{LiWa03,LiWW03}
\begin{equation}\label{eq.sch5-1}
i\partial_tz=-\Delta z+w(x)z-l(|z|^2)z-\kappa\Delta h(|z|^2)h'(|z|^2)z,\quad x\in{\mathbb{R}}^N,
\end{equation}
where $w(x)$ is a given potential, $\kappa>0$ is a constant, $N\geq3$.
$h,~l$ are real functions of essentially pure power form.
Eq.(\ref{eq.sch5-1}) comes from mathematical physics and was used to model some
physical phenomena.
If $\kappa=0$, Eq.(\ref{eq.sch5-1}) is a semilinear problem which has been extensively studied.
If $\kappa>0$, it is a quasilinear problem which has many applications in physics.
It is known that the case of $h(s)=s$ was used for the superfluid film equation in plasma physics by Kurihura in \cite{Kuri81}.
It also appears in plasma physics and fluid mechanics \cite{LiSe78}, in the theory of Heisenberg ferromagnetism and magnons \cite{KoIK90,QuCa82} in dissipative quantum mechanics \cite{Hass80} and in condensed matter theory \cite{MaFe84}.
If we consider solutions of the form
$z(x,t)=\exp(-iet)u(x)$, which are called standing waves,
we observe that this $z(x,t)$ satisfies Eq.(\ref{eq.sch5-1}) if and only
if the function $u(x)$ solves the equation
\begin{eqnarray}\label{eq.sch5-2}
-\Delta u+V(x)u-\kappa\alpha(\Delta(h(|u|^2)))h'(|u|)^{2}u
=l(|u|^2)u,\quad x\in{\mathbb{R}}^N,
\end{eqnarray}
where $V(x)=w(x)-e$ is the new potential function.
In recent years, the case $h(s)=s$ has been extensively studied under different conditions on the potential $V(x)\geq0$ and the nonlinear perturbation $l(u)$, one can refer to \cite{LiWW03,CoJe04,OMS07,OMS10} and some references therein.
The difficulty of Eq.(\ref{eq.sch5-2}) lies in the unbounded operator. In order to overcome this difficulty, Liu and Wang etc. in \cite{LiWW03} defined a change of variable and change the problem to a semilinear one. More precisely, they used the change of variable $v=f^{-1}(u)$ with $f$ defined by ODE: $f'(t)=(1+2f^2(t))^{-1/2}, ~t\in(0,+\infty)$ and $f(t)=-f(-t), ~t\in(-\infty,0)$. Then they proved the existence of positive solutions in an corresponding Orlicz space.
This method was widely used in the studies of such kind of problems thereafter, for examples \cite{CoJe04,OMS07,OMS10}. But in the latter literatures the working space is the usual Sobolev space $H^1(\mathbb{R}^N)$.
It is also interesting to study Eq.(\ref{eq.sch5-2}) with the nonlinearity $l(s)$ is at critical growth. In \cite{LiWa03}, Liu and Wang pointed out that the number $2(2^*)$ behaves like critical exponent for Eq.(\ref{eq.sch5-2}).
In \cite{SiVi10}, Silva and Vieira proved the existence of solutions of Eq.(\ref{eq.sch5-2}) with a general $l(|u|^2)u=K(x)u^{2(2^*)-1}+g(x,u)$.
To our knowledge, there are few literatures study more general problem $h(s)=s^{\alpha}$ with $\alpha>1/2$. We mention that in \cite{LiWa03}, the existence results are obtained through a constrained minimization argument for $l(u)$ at subcritical growth. In \cite{Moam06}, Moameni consider the problem for $l(u)$ at critical growth under radially symmetric conditions. But note that such assumptions enable the study to avoid the difficulty of losing compactness caused by Sobolev imbedding.
In \cite{LiZh13}, Li and Zhang studied the problem that $h(s)=s^{\alpha}$,
$l(s)=s^{(q-2)/2}+s^{(2^*-2)/2}$, where $\alpha>1/2,~2(2\alpha)\leq q<2^*(2\alpha)$, $2^*=2N/(N-2)$, and proved the existence of positive solution. Here and in the following, we always denote $2(2\alpha)=2\times2\alpha$, $2^*(2\alpha)=2^*\times2\alpha$.
Compare to \cite{LiZh13}, in this paper, we are interested in the problem with $h(s)=s^{\alpha}$,
$l(s)=s^{(q-2)/2}+s^{(2^*-2)/2}$, where $0<\alpha<1/2,~2\leq q<2^*$.
It was used to models the self-channeling of high-power ultrashort laser in matter \cite{BoGa93}.
Moreover, we consider problems that $V(x)<0$.
Denote
\[
X:= D^{1,2}({\mathbb{R}}^N)=\{u\in L^{2^*}({\mathbb{R}}^N):|\nabla u|\in L^2({\mathbb{R}}^N)\}
\]
equipped with the norm $\|u\|^2_X=\int_{{\mathbb{R}}^N}|\nabla u|^2\mbox{d}x$.
Let $\lambda c(x):=-V(x)>0,~\lambda\geq0$.
In this paper, we consider the following equation
\begin{eqnarray}\label{eq.sch5-3}
-\Delta u-\lambda c(x)u-\kappa\alpha(\Delta(|u|^{2\alpha}))|u|^{2\alpha-2}u
=|u|^{q-2}u+|u|^{2^*-2}u,\quad x\in{\mathbb{R}}^N.
\end{eqnarray}
Note that when $0<\alpha<1/2$, the operator of second order is singular in the equation, this cause one of the main difficulty of the study.
Another difficulty of the study is caused by the nonlinear term $|u|^{q-2}u$ in the equation since $D^{1,2}(\mathbb{R}^N)$ does not imbed into $L^{q}(\mathbb{R}^N)$.
Let $f(t)=|u|^{q-2}u+|u|^{2^*-2}u$, $2\leq q<2^*$.
We want to find weak solutions to Eq.(\ref{eq.sch5-3}). By {\it weak solution}, we mean a function $u$ in $X$ satisfying that,
for all $\varphi\in C_0^{\infty}({\mathbb{R}}^N)$, there holds
\begin{eqnarray}\label{def.I'}
\int_{{\mathbb{R}}^N}\nabla u\nabla\varphi-\lambda\int_{{\mathbb{R}}^N}c(x)u\varphi+\kappa\alpha\int_{{\mathbb{R}}^N}\nabla(|u|^{2\alpha})\nabla(|u|^{2\alpha-2}u\varphi)
=\int_{{\mathbb{R}}^N}f(u)\varphi.
\end{eqnarray}
According to the variational methods, the weak solutions of (\ref{eq.sch5-3}) corresponds the critical points
of the functional $I: X\to{\mathbb{R}}$ defined by
\begin{eqnarray}\label{def.I}
I(u)=\frac{1}{2}\int_{{\mathbb{R}}^N}(1+2\kappa\alpha^2|u|^{2(2\alpha-1)})|\nabla u|^2-\frac{\lambda}{2}\int_{{\mathbb{R}}^N}c(x)u^2
-\int_{{\mathbb{R}}^N}F(u),
\end{eqnarray}
where $F(t)=\int_0^uf(s)\mbox{d}s$. For $u\in X$, $I(u)$ is lower semicontinuous when $0<\alpha<1/2$, and not differentiable in all directions $\varphi\in X$. In order to use the classical critical point theorem, we will use a change of variable to reformulate functional $I$.
Let $\beta(t)=(1+2\kappa\alpha^2|t|^{2(2\alpha-1)})^{1/2}$, then $\beta(t)$ is monotone and decreasing in $t\in(0,+\infty)$. For $t_0>0$ sufficiently small,
we have
\[
\int_0^{t_0}\beta(s)ds\leq2\alpha\sqrt{\kappa}\int_0^{t_0}s^{2\alpha-1}ds=\sqrt{\kappa}t_0^{2\alpha}.
\]
This make it possible for us to define an invertible, odd, $C^1$ function $h:{\mathbb{R}}\to{\mathbb{R}}$ by
\begin{eqnarray}\label{def.h}
v=h^{-1}(u)=\int_0^u\beta(s)ds,
\end{eqnarray}
where $h^{-1}$ is the inverse function of $h$.
For simplicity of notation we may assume that $\kappa\alpha=1$.
Inserting $u=h(v)$ into (\ref{def.I}), we get another functional $J$ defined on $X$ given by
\begin{eqnarray}\label{def.J}
J(v)=I(h(v))=\frac{1}{2}\int_{{\mathbb{R}}^N}|\nabla v|^2
-\frac{\lambda}{2}\int_{{\mathbb{R}}^N}c(x)h(v)^2-\int_{{\mathbb{R}}^N}F(h(v)).
\end{eqnarray}
In Sect.\ref{sec:5-2} (see Proposition \ref{prop.J}) we prove that $J$ is well defined on $X$, and is continuous in $X$. Moreover, it is also G\^{a}teaux-differentiable, and for $\psi\in C_0^{\infty}({\mathbb{R}}^N)$,
\begin{eqnarray}\label{def.J'}
\langle J'(v),\psi\rangle=\int_{{\mathbb{R}}^N}\nabla v\nabla\psi
-\lambda\int_{{\mathbb{R}}^N}c(x)h(v)h'(v)\psi-\int_{{\mathbb{R}}^N}f(h(v))h'(v)\psi.
\end{eqnarray}
Since $u=h(v)$, we have $\nabla u=h'(v)\nabla v$. Moreover, from (\ref{def.h}), we have $\nabla v=\beta(u)\nabla u$. We get immediately
that $h'(v)=[\beta(u)]^{-1}=[\beta(h(v))]^{-1}$ and $\nabla u=[\beta(h(v))]^{-1}\nabla v$.
Now assume that $v\in X$, $v>0$ such that equality $\langle J'(v),\psi\rangle=0$ holds. We choose $\psi=\beta(h(v))\varphi$, then
$\nabla \psi=\beta(h(v))\nabla\varphi+\beta'(h(v))h'(v)\varphi\nabla v$. Let $u=h(v)$, then $u\in X$. Moreover, we have $h'(v)\psi=\varphi$ and
\begin{eqnarray*}
\nabla v\nabla\psi&=&\beta(h(v))\nabla v\nabla\varphi+\beta'(h(v))h'(v)\varphi|\nabla v|^2 \\
&=&\nabla u\nabla \varphi+\beta(u)\beta'(u)\varphi|\nabla u|^2.
\end{eqnarray*}
Thus from (\ref{def.J'}), we obtain that
\[
\int_{{\mathbb{R}}^N}\beta^2(u)\nabla u\nabla\varphi+\int_{{\mathbb{R}}^N}\beta(u)\beta'(u)\varphi|\nabla u|^2
-\lambda\int_{{\mathbb{R}}^N}c(x)u\varphi-\int_{{\mathbb{R}}^N}f(u)\varphi=0.
\]
This implies that $u$ such that (\ref{def.I'}) holds.
In summary, in order to find a weak solution to Eq.(\ref{eq.sch5-3}), it suffices to find a weak solution to the following equaiton
\begin{eqnarray}\label{eq.sch5-h}
-\Delta v-\lambda c(x)h(v)h'(v)=f(h(v))h'(v),\quad x\in{\mathbb{R}}^N.
\end{eqnarray}
We denote
\[
\tilde{r}=\left\{
\begin{array}{ll}
+\infty, & \hbox{$0<\alpha\leq\frac{1}{2^*}$;} \\
1+\frac{1}{2^*\alpha-1}, & \hbox{$\frac{1}{2^*}<\alpha<\frac{1}{2}$.}
\end{array}
\right.
\]
We assume that
\begin{description}
\item[(c)] the function $c(x)\in C({\mathbb{R}^N},{\mathbb{R}})$, $c(x)>0$ and there exists $r\in(\frac{N}{2},\tilde{r})$ such that $c(x)\in L^{r}(\mathbb{R}^N)$.
\item[(f)] assume that $q\in(2,2^*)$ and either \\
(i) $\frac{1}{4}<\alpha<\frac{1}{2}$, $q>\frac{4}{N-2}+4\alpha$ or \\
(ii) $0<\alpha\leq\frac{1}{4}$, $q>\frac{N+2}{N-2}$ holds.
\end{description}
Let $\lambda^*=2\alpha S\|c\|_{r}^{-1}$, where $S$ is the best constant for the Sobolev imbedding $H^1(\mathbb{R}^N)$ into $L^{2^*}(\mathbb{R}^N)$.
The following theorem is the main result of this paper.
\begin{thm}\label{thm.m1}
Assume that (c) and (f) hold,
then for $\lambda\in[0,\lambda^*)$, problem (\ref{eq.sch5-3}) has a positive weak solution $u\in X$.
Moreover, if $0<\alpha\leq {1}/{2^*}$, then $u\in H^1(\mathbb{R}^N)$.
\end{thm}
\begin{rem}\label{rem.m1-1}
We have $2^*-1<\frac{4}{N-2}+4\alpha<2^*$ for $\frac{1}{4}<\alpha<1/2$ and $\frac{N+2}{N-2}=2^*-1$.
\end{rem}
\begin{rem}\label{rem.m1-2}
Under the assumptions of Theorem \ref{thm.m1}, if $\|\lambda c\|_{r}< 2\alpha S$ for some $r\in(N/2,\tilde{r})$, then problem (\ref{eq.sch5-3}) has a positive solution in $X$.
\end{rem}
Let
\begin{eqnarray*}
&a_0=\frac{1+(2\alpha)^2}{1+2\alpha}\in(2\alpha,1),\quad\forall\alpha\in(0,1/2)\\
&a_1=\max\{a_0,2/2^*\},\quad \tilde{r}_1=2^*a_1/(2^*a_1-2).
\end{eqnarray*}
\begin{cor}\label{rem.m1-3}
Assume (f) holds and
\begin{description}
\item[(c)$'$] the function $c(x)\in C({\mathbb{R}^N},{\mathbb{R}})$, $c(x)>0$ and there exists $r\in(N/2,\tilde{r}_1)$ such that $c(x)\in L^{r}(\mathbb{R}^N)$,
\end{description}
then for $\lambda\in[0,S\|c\|_{r}^{-1})$, problem (\ref{eq.sch5-3}) has a positive solution.
\end{cor}
\begin{rem}\label{rem.m1-4}
By H\"{o}lder's inequality and Sobolev's inequality, we can prove that $\lambda^*=S\|c\|_{r}^{-1}\leq\lambda_1$, where $\lambda_1$ is the first eigenvalue of the following equation
\[
-\Delta u=\lambda c(x)u,\quad x\in{\mathbb{R}^N},
\]
that is,
\[
\lambda_1=\inf_{u\in X\setminus\{0\}}\frac{\int_{\mathbb{R}^N}|\nabla u|^{2}\mbox{d}x}{\int_{\mathbb{R}^N}c(x)u^2\mbox{d}x}.
\]
It is worthy of pointing out that computing the value $\lambda^*$ is much easier than obtaining $\lambda_1$.
Moreoer, the assumptions allow $c(x)$ to belong to a wide class of function space.
\end{rem}
The proof of Theorem \ref{thm.m1} is also applicable to problems at subcritical growth.
Let us consider the following equation
\begin{eqnarray}\label{eq.sch5-4}
-\Delta u-\lambda c(x)u-\kappa\alpha(\Delta(|u|^{2\alpha}))|u|^{2\alpha-2}u
=|u|^{q-2}u,\quad x\in{\mathbb{R}}^N.
\end{eqnarray}
\begin{thm}\label{thm.m3}
Assume that (c) holds,
then for $\lambda\in[0,\lambda^*)$, $q_0<q<2^*$, $q_0=\max\{2,2^*(2\alpha)\}$, problem (\ref{eq.sch5-4}) has a positive weak solution $u\in X$.
Moreover, if $0<\alpha\leq {1}/{2^*}$, then $u\in H^1(\mathbb{R}^N)$.
\end{thm}
In Sect.\ref{sec:5-2}, we first study the properties of the function $h$; then we prove that the functional $J$ is well defined on $X$, continuous in $X$ and G\^{a}teaux-differentiable in $X$, see Proposition \ref{prop.J}. These are crucial steps since we only have $D^{1,2}(\mathbb{R}^N)\hookrightarrow L^{2^*}(\mathbb{R}^N)$. To this end, we establish several imbedding results. In the end of the section, we show that $J$ has the mountain pass geometry.
In Sect.\ref{sec:5-3}, we prove that every Palais-Smale ((PS) in short) sequence $\{v_n\}$ of $J$ is bounded in $X$ and analyze the properties of (PS) sequence. In Sect.\ref{sec:5-4}, we employ the mountain pass theorem without Palais-Smale condition to prove the existence of positive solution to Eq.(\ref{eq.sch5-h}). This involving the computation of a mountain pass level $c\in(0,\frac{1}{N}S^{N/2})$.
In this paper, $\|\cdot\|_p$ denotes the norm of $L^p(\mathbb{R}^N)$; $C,~C_1,~C_2,\cdots$ denote positive constants.
\section{ Mountain pass geometry}
\setcounter{equation}{0}
\label{sec:5-2}
In this section, we will give some properties of the transformation $h$
and establish the geometric hypotheses of the mountain pass geometry.
\begin{lem}\label{lem.h}
The function $h(t)$ has the following properties,
\begin{description}
\item[(1)] $h(t)$ is odd, invertible, increasing and of class $C^1$ for $0<\alpha<1/2$, of class $C^2$ for $0<\alpha\leq1/4$;
\item[(2)] $|h'(t)|\leq1$ for all $t\in{\mathbb{R}}$;
\item[(3)] $|h(t)|\leq |t|$ for all $t\in{\mathbb{R}}$;
\item[(4)] $h^{2\alpha}(t)/t\to\sqrt{2/\kappa}$ as $t\to0^+$;
\item[(5)] $2\alpha h(t)\leq 2\alpha h'(t)t\leq h(t)$ for $t>0$;
\item[(6)] $h(t)/t\to1$ as $t\to+\infty$;
\item[(7)] $|h(t)|$ is convex;
\item[(8)] $h'(t)\leq (2\kappa\alpha^2)^{-\vartheta/2}|h(t)|^{(1-2\alpha)\vartheta}$ for all $\vartheta\in[0,1].$
\end{description}
\end{lem}
{\bf Proof}\quad
For part (1), $h(t)$ is odd and invertible by definition. Since $h'(t)=[\beta(h(t))]^{-1}\in(0,1)$, we have $h(t)$ is increasing and of class $C^1$
for $0<\alpha<1/2$. By direct computation, we have
\[
h''(t)=2\kappa\alpha^2(1-2\alpha)\frac{|h(t)|^{-4\alpha}h(t)}{\big(2\kappa\alpha^2+|h(t)|^{2(1-2\alpha)}\big)^2},
\]
so we have $h(t)$ is of class $C^2$ for $0<\alpha\leq1/4$.
Part (2) is obvious. For part (3), assume that $t>0$ and note that $\beta(h(t))>1$, we have
\begin{eqnarray*}\label{lem.h-1}
h(t)=\int_0^{h(t)}ds\leq \int_0^{h(t)}\beta(s)ds=t.
\end{eqnarray*}
Then part (3) follows since $h$ is odd.
For part (4), note that from part (3) we have $h(t)\to 0$ as $t\to 0$. Thus we can employ
L'Hospital's principle to prove that
\[
\lim_{t\to0^+}\frac{h^{2\alpha}(t)}{t}=\lim_{t\to0^+}2\alpha h^{2\alpha-1}(t)h'(t)=\sqrt{\frac{2}{\kappa}}.
\]
For part (5), we prove the right-hand side inequality. Let $H(t)=h(t)/h'(t)$ and $\tilde{H}(t)=H(t)-2\alpha t$. Then $\tilde{H}(0)=0$.
We prove that $\tilde{H}'(t)\geq0$, i.e. $H'(t)\geq 2\alpha$, and this implies the conclusion.
In fact, note that $h(t)$ has same sign of $t$, for $t=0$, by part (4) we have
\[
H'(0)=\lim_{t\to0}\frac{H(t)}{t}=\lim_{t\to0}\sqrt{\frac{2}{\kappa}}\frac{|H(t)|}{|h(t)|^{2\alpha}}=\sqrt{\frac{2}{\kappa}}\sqrt{2\kappa\alpha^2}=2\alpha.
\]
For $t\neq0$, we have
\begin{eqnarray*}
H'(t)&=&\bigg(\frac{h(t)\big(2\kappa\alpha^2+|h(t)|^{2(1-2\alpha)}\big)^{1/2}}{|h(t)|^{1-2\alpha}}\bigg)' \\
&\geq&\frac{|h(t)|^{2(1-2\alpha)}-(1-2\alpha)h(t)(2\kappa\alpha^2+|h(t)|^{2(1-2\alpha)})^{1/2}|h(t)|^{-1-2\alpha}h(t)h'(t)}{|h(t)|^{2(1-2\alpha)}} \\
&=&\frac{|h(t)|^{2(1-2\alpha)}-(1-2\alpha)|h(t)|^{2(1-2\alpha)}}{|h(t)|^{2(1-2\alpha)}} \\
&=&2\alpha.
\end{eqnarray*}
The left-hand side inequality can be proved similarly.
For part (6), we have $h'(t)>1/2$ for $t>0$ sufficiently large. So we conclude that $h(t)\to+\infty$ as $t\to+\infty$.
Thus by employing Hospital principle again, we have $\lim_{t\to+\infty}h(t)/t=\lim_{t\to+\infty}h'(t)=1$.
(7) Note that $h(t)$ is odd and $h(0)=0$, $h''(t)>0$ for $t>0$, we conclude that $|h(t)|$ is convex.
(8) For any $\vartheta\in[0,1]$, by the definition of $h'(t)$ and note that $0\leq h'(t)\leq1$, we have
\begin{eqnarray*}
h'(t)=h'(t)^{\vartheta}h'(t)^{1-\vartheta}
\leq h'(t)^{\vartheta}
\leq (2\kappa\alpha^2)^{-\vartheta/2}|h(t)|^{(1-2\alpha)\vartheta}.
\end{eqnarray*}
This ends the proof of the lemma.
$\quad\Box$
\begin{lem}\label{lem.h'-1}
For $t,~s\in{\mathbb{R}}$, we have
\[
|h'(t)-h'(s)|\leq 2^{1-\vartheta}(2\kappa\alpha^2)^{-\vartheta/2}|h(t)-h(s)|^{(1-2\alpha)\vartheta},\quad\forall~\vartheta\in[0,1].
\]
\end{lem}
{\bf Proof}\quad Consider $\eta(t):=t^{a},~t,~s>0,~a\in(0,1)$. We have
\begin{eqnarray}\label{lem.h'-1-1}
\eta(|t-s|)\geq|\eta(t)-\eta(s)|.
\end{eqnarray}
Now for $t,~s\in{\mathbb{R}}$, by direct computation and using (\ref{lem.h'-1-1}), we have
\begin{eqnarray*}\label{lem.h'-1-2}
H(t,s)&:=&|h'(t)-h'(s)| \\
&\leq&\frac{({2\kappa\alpha^2})^{1/2}||h(t)|^{1-2\alpha}-|h(s)|^{1-2\alpha}|}{(2\kappa\alpha^2+|h(t)|^{2(1-2\alpha)})^{1/2}(2\kappa\alpha^2+|h(s)|^{2(1-2\alpha)})^{1/2}}\\
&\leq& ({2\kappa\alpha^2})^{-1/2}|h(t)-h(s)|^{1-2\alpha}.
\end{eqnarray*}
Note that by (2) of Lemma \ref{lem.h}, we also have $H(t,s)\leq2$, we conclude that
\[
H(t,s)=H^{1-\vartheta}(t,s)H^{\vartheta}(t,s)\leq2^{1-\vartheta}(2\kappa\alpha^2)^{-\vartheta/2}|h(t)-h(s)|^{(1-2\alpha)\vartheta}
\]
for all $\vartheta\in[0,1]$.
$\quad\Box$
\begin{lem}\label{lem.embed-2}
If $v\in X$, then $h(v)\in L^r(\mathbb{R}^N),~r\in[2^*(2\alpha),2^*]$.
\end{lem}
{\bf Proof}\quad Let $v\in X$, then we have $\|\nabla v\|_2\leq C$ for some constant $C>0$.
For $a\in[2\alpha,1]$, we have
\begin{eqnarray}\label{lem.embed-2-0}
\nabla(|h(v)|^a)=a|h(v)|^{a-2}h(v)h'(v)\nabla v=\frac{a|h(v)|^{a-2}h(v)|h(v)|^{1-2\alpha}}{(2\alpha+|h(v)|^{2(1-2\alpha)})^{1/2}}\nabla v
\end{eqnarray}
In order to ensure that $\|\nabla(h(v)^a)\|_2\leq C$, it requires that
\[
0\leq (a-1)+(1-2\alpha)=a-2\alpha\leq 1-2\alpha,
\]
that is, $2\alpha\leq a\leq 1$. Since
\begin{eqnarray}\label{lem.embed-2-1}
|\nabla(|h(v)|^a)|^2\leq\frac{1}{2\alpha}|\nabla v|^2,\quad \forall a\in[2\alpha,1],
\end{eqnarray}
we obtain that $\|\nabla(|h(v)|^a)\|_2\leq C/(2\alpha)$ for all $a\in[2\alpha,1]$. Similar to the proof of Sobolev's inequality, we have
$|h(v)|^a\in L^{2^*}(\mathbb{R}^N)$, this gives that $h(v)\in L^{2^*a}(\mathbb{R}^N)$ for $a\in[2\alpha,1]$.
$\quad\Box$
\begin{lem}\label{lem.embed-3}
The map: $v\to h(v)$ from $X$ into $L^r({\mathbb{R}}^N)$ is continuous for $2^*(2\alpha)\leq r\leq 2^*$.
\end{lem}
{\bf Proof}\quad
For any $r\in[2^*(2\alpha),2^*]$, there exists $a\in[2\alpha,1]$ such that $r=2^*a$. Then for any sequence $\{v_n\}\subset X$ that converges strongly to $0$, by Sobolev's inequality and (\ref{lem.embed-2-1}), we have
\begin{eqnarray}\label{lem.embed-3-1}
\|h(v_n)\|_{r}^{2a}=\||h(v_n)|^a\|_{2^*}^{2}\leq S^{-1}\|\nabla |h(v_n)|^a\|_{2}^{2}\leq (2\alpha S)^{-1}\|v_n\|_X^2,
\end{eqnarray}
which tends to $0$ as $n\to\infty$.
Thus the map $v\to h(v)$ from $X$ into $L^{r}({\mathbb{R}}^N)$ is continuous.
$\quad\Box$
By using (2)-(3) of Lemma \ref{lem.h}, we can also prove that
\begin{lem}\label{lem.embed-1}
The map: $v\to h(v)$ from $H^1({\mathbb{R}}^N)$ into $L^p({\mathbb{R}}^N)$ is continuous for $2\leq p\leq 2^*$,
and is locally compact for $2\leq p<2^*$.
\end{lem}
{\bf Proof}\quad
The proof is similar to that for Lemma \ref{lem.embed-3}.
Firstly, assume that $\{v_n\}\subset H^1({\mathbb{R}}^N)$ converges strongly to $0$, then by part (3) of Lemma \ref{lem.h} and Sobolev's inequality, we have
\begin{eqnarray*}\label{lem.embed-1-1}
\|h(v_n)\|^2_{2^*}\leq \|v_n\|^2_{2^*}\leq S^{-1}\|v_n\|^2_X,
\end{eqnarray*}
which tends to $0$ as $n\to\infty$.
Thus the map $v\to h(v)$ from $H^1({\mathbb{R}}^N)$ into $L^{2^*}({\mathbb{R}}^N)$ is continuous. By interpolation inequality, we obtain that
the map $v\to h(v)$ from $H^1({\mathbb{R}}^N)$ into $L^{p}({\mathbb{R}}^N)$ is continuous for $2\leq p\leq2^*$.
Secondly, assume that $\{v_n\}$ is bounded in $H^1({\mathbb{R}}^N)$, exist a subsequence (we still denote it by $\{v_n\}$) and a $v\in H^1({\mathbb{R}}^N)$ such that
$v_n\to v$ locally in $L^{p}({\mathbb{R}}^N)$ for $2\leq p<2^*$.
By mean value theorem and (2)-(3) of Lemma \ref{lem.h}, we have
\begin{eqnarray}\label{lem.embed-1-2}
|h(v_n)-h(v)|\leq|h'(v+\theta(v_n-v))||v_n-v|\leq |v_n-v|,
\end{eqnarray}
where $\theta\in(0,1)$. Thus the map $v\to h(v)$ from $H^1({\mathbb{R}}^N)$ into $L^{p}({\mathbb{R}}^N)$ is locally compact for $2\leq p<2^*$.
$\quad\Box$
Noting that $H^1({\mathbb{R}}^N)\subset D^{1,2}({\mathbb{R}}^N)$ is dense, we thus can combine Lemma \ref{lem.embed-3} and Lemma \ref{lem.embed-1} to conclude that
\begin{cor}\label{lem.embed-4}
The map: $v\to h(v)$ from $H^1({\mathbb{R}}^N)$ into $L^p({\mathbb{R}}^N)$ is continuous for $2_{*}\leq p\leq 2^*$,
and is locally compact for $2_{*}\leq p<2^*$, where $2_{*}=\min\{2,2^*(2\alpha)\}$.
\end{cor}
{\bf Proof}\quad
If $2\leq 2^*(2\alpha)$, then the conclusions hold obviously. Now we assume that
$2^*(2\alpha)<2$ and $p\in[2^*(2\alpha),2)$. Then the first part of the corollary follows from (\ref{lem.embed-3-1}) and the fact that $\|v_n\|_X^2\leq\|v_n\|_{H^1(\mathbb{R}^N)}^2$. On the other hand, by H\"{o}lder's inequality, we have
\begin{eqnarray}\label{lem.embed-4-1}
\|h(v_n)-h(v)\|_{p}\leq\|h(v_n)-h(v)\|_{2^*(2\alpha)}^{\theta}\|h(v_n)-h(v)\|_{2}^{1-\theta}
\end{eqnarray}
for some $\theta\in[0,1]$. Then the second part of the corollary holds by Lemma \ref{lem.embed-1}.
$\quad\Box$
\begin{lem}\label{lem.embed-5}
The map: $v\to h(v)$ from $X$ into $L^r({\mathbb{R}}^N)$ is locally compact for $2^*(2\alpha)\leq r<2^*$.
\end{lem}
{\bf Proof}\quad
We should only prove that the conclusion holds for the case $2^*(2\alpha)<2$ and $r\in[2^*(2\alpha),2)$. If $2^*(2\alpha)\leq2$, by Lemma \ref{lem.embed-2}, for any $v\in X$, we have $h(v)\in L^2(\mathbb{R}^N)$, thus $h(v)\in H^1(\mathbb{R}^N)$.
Now assume that $\{v_n\}\subset X$ is bounded, by (\ref{lem.embed-2-1}), $\{h(v_n)\}\subset L^2(\mathbb{R}^N)$ is bounded uniformly in $n$.
Thus $\{h(v_n)\}$ is bounded in $H^1(\mathbb{R}^N)$. Then by Lemma \ref{lem.embed-1}, we conclude that $\{h(v_n)\}$ is locally compact in $L^2(\mathbb{R}^N)$. Finally, we obtain that the map $v\to h(v)$ from $X$ into $L^{r}({\mathbb{R}}^N)$ is locally compact for $r\in[2^*(2\alpha),2)$ by inequality (\ref{lem.embed-4-1}).
$\quad\Box$
If $0<\alpha\leq {1}/{2^*}$, then we have $2^*(2\alpha)\leq2$. Thus, according to the proof of Lemma \ref{lem.embed-5}, we have
\begin{thm}\label{thm.u-in-H1}
Assume that $0<\alpha\leq {1}/{2^*}$, then every solution for (\ref{eq.sch5-3}) belongs to $H^1(\mathbb{R}^N)$.
\end{thm}
Let $L^2(\mathbb{R}^N,c(x))$ be the weighted Lebesgue space defined by
\[
L^2(\mathbb{R}^N,c(x)):=\bigg\{u\in L^2(\mathbb{R}^N):\int_{\mathbb{R}^N}c(x)u^2\mbox{d}x<+\infty\bigg\},
\]
and endowed with the norm
\[
\|u\|_{2,c}:=\bigg(\int_{\mathbb{R}^N}c(x)u^2\mbox{d}x\bigg)^{1/2}.
\]
We have
\begin{lem}\label{lem.embed-Lc}
Assume hypothesis (c) holds, then the map $v\rightarrow h(v)$ from $X$ into $L^2(\mathbb{R}^N,c(x))$ is continuous and compact.
\end{lem}
{\bf Proof}\quad
Let $s>0$ satisfies that $\frac{2}{s}+\frac{1}{r}=1$, where $r\in(\frac{N}{2},\tilde{r})$ and $\tilde{r}$ is given by assumption (c).
By Lemma \ref{lem.embed-2}, we have $c(x)\in L^{r}({\mathbb{R}}^N)$ and $h(v)\in L^{s}({\mathbb{R}}^N)$.
Then for $v\in X$, by H\"{o}lder's inequality, we have
\begin{eqnarray}\label{lem.embed-Lc-1}
\int_{{\mathbb{R}}^N}c(x)h(v)^2\mbox{d}x\leq \|c\|_{r'}\|h(v)\|_{s}^2<+\infty.
\end{eqnarray}
By Lemma \ref{lem.embed-3}, we obtain that the the map $v\to h(v)$ from $X$ into $L^2(\mathbb{R}^N,c(x))$ is continuous.
Now assume that $\{v_n\}\subset X$ is bounded, then there exist a subsequence (still denoted by $\{v_n\}$), and a $v\in X$, such that $v_n\rightharpoonup v$ in $X$, $v_n\to v$ in $L_{\rm loc}^t({\mathbb{R}}^N),~1\leq t<2^*$.
On the other hand, since by (\ref{lem.embed-2-1}), $\{h(v_n)\}\subset X$ is also bounded, there exist a subsequence (still denoted by $\{h(v_n)\}$), and a $w\in X$, such that $h(v_n)\rightharpoonup w$ in $X$, $h(v_n)\to w$ in $L_{\rm loc}^t({\mathbb{R}}^N),~2^*(2\alpha)\leq t<2^*$.
We claim that $w=h(v)$ a.e. in ${\mathbb{R}}^N$. Indeed, for any $\delta>0$, there exists $R_\delta>0$ such that
$\int_{B_{R_\delta}^c}c(x)h(v)^2<\delta/3$ and $\int_{B_{R_\delta}^c}c(x)w^2<\delta/3$, where $B_{R_\delta}=\{x\in{\mathbb{R}}^N:|x|\leq R_\delta\}$ and $B_{R_\delta}^c={\mathbb{R}}^N\setminus B_{R_\delta}$. Thus, by (\ref{lem.embed-1-2}) and the locally compact imbedding, we have for $n$ sufficiently large,
\begin{eqnarray*}
0&\leq&\int_{{\mathbb{R}}^N}c(x)|h(v)-w|^2 \\
&=&\int_{B_{R_\delta}}c(x)|h(v)-w|^2+\int_{B_{R_\delta}^c}c(x)|h(v)-w|^2 \\
&\leq&\int_{B_{R_\delta}}c(x)|h(v_n)-h(v)|^2+\int_{B_{R_\delta}}c(x)|h(v_n)-w|^2 \\
&&+\int_{B_{R_\delta}^c}c(x)h(v)^2+\int_{B_{R_\delta}^c}c(x)w^2 \\
&<&\delta.
\end{eqnarray*}
This proves the claim.
Now for any $\varepsilon>0$, there exists $R_{\varepsilon}>0$ such that
\[
\int_{B_{R_\varepsilon}^c}|c(x)|^{r}\mbox{d}x\leq\bigg(\frac{\varepsilon}{4C}\bigg)^{r}
\]
where $C>0$ satisfies that $(2\alpha S)^{-1}\|v_n\|_{X}^2\leq C$. Thus by H\"{o}lder's inequality and (\ref{lem.embed-2-1}), we have
\[
\int_{B_{R_\varepsilon}^c}c(x)|h(v_n)-h(v)|^{2}\mbox{d}x
\leq\|c\|_{L^{r}(B_{R_\varepsilon}^c)}\|h(v_n)-h(v)\|^2_{L^{s}(B_{R_\varepsilon}^c)}\leq\frac{\varepsilon}{2}
\]
Since $X\hookrightarrow L^2(B_R)$ is compact, it follows that
there exists $n_0\in{\mathbb{N}}$ such that for $n\geq n_0$,
\[
\int_{B_{R_\varepsilon}}c(x)|h(v_n)-h(v)|^2\mbox{d}x\leq\frac{\varepsilon}{2}.
\]
Thus we obtain that
\[
\int_{{\mathbb{R}}^N}c(x)|h(v_n)-h(v)|^2\mbox{d}x\leq\bigg(\int_{B_{R_\varepsilon}}+\int_{B_{R_\varepsilon}^c}\bigg)c(x)|h(v_n)-h(v)|^2\mbox{d}x\leq{\varepsilon}.
\]
This implies that the map $v\rightarrow h(v)$ from $X$ into $L^2(\mathbb{R}^N,c(x))$ is compact.
$\quad\Box$
Now we come back to the discussion of functional $J$. We have
\begin{prop}\label{prop.J}
Under assumptions of Theorem \ref{thm.m1}, the functional $J$ has the following properties:$\\$
(1) $J$ is well defined on $X$. $\\$
(2) $J$ is continuous in $X$. $\\$
(3) $J$ is G\^{a}teaux-differentiable.
\end{prop}
{\bf Proof}\quad
(1) Firstly, for $v\in X$, by Lemma \ref{lem.embed-Lc}, we have $\int_{\mathbb{R}^N}c(x)h(v)^2\mbox{d}x<+\infty$.
Next, by assumptions of Theorem \ref{thm.m1}, for $\alpha\in(\frac{1}{4},\frac{1}{2})$, we have $q>\frac{4}{N-2}+4\alpha>2^*(2\alpha)$;
for $\alpha\in(0,\frac{1}{4}]$, we have $q>2^*-1> 2^*(2\alpha)$. Then Lemma \ref{lem.embed-3} implies that $\|h(v)\|_{q}^{q}<+\infty$.
Thus we have
\[
\int_{{\mathbb{R}}^N}F(x,h(v))\mbox{d}x\leq C(\|h(v)\|_{q}^{q}+\|h(v)\|_{2^*}^{2^*})<+\infty.
\]
These show that $J$ is well defined on $X$.
(2) Assume that $v_n\to v$ in $X$. By Sobolev's inequality, $\|v_n-v\|_{2^*}\to0$. By mean value theorem, (8) of Lemma \ref{lem.h} and H\"{o}lder's inequality, we have
\begin{eqnarray*}
&&\bigg|\int_{{\mathbb{R}}^N}c(x)[h(v_n)^2-h(v)^2]\mbox{d}x\bigg| \\
&&\quad =\bigg|\int_{{\mathbb{R}}^N}2c(x)h(v+\theta_n(v_n-v))h'(v+\theta_n(v_n-v))(v_n-v)\mbox{d}x\bigg| \\
&&\quad \leq 2(2\alpha)^{-\vartheta_r/2}\int_{{\mathbb{R}}^N}c(x)|h(v+\theta_n(v_n-v))|^{1+(1-2\alpha)\vartheta_r}|v_n-v|\mbox{d}x \\
&&\quad \leq 2(2\alpha)^{-\vartheta_r/2}\|c\|_r\|h(v+\theta_n(v_n-v))\|_{s}^{1+(1-2\alpha)\vartheta_r}\|v_n-v\|_{2^*}
\to0,
\end{eqnarray*}
where $\theta_n\in(0,1)$ and $s=[1+(1-2\alpha)\vartheta_r](1-\frac{1}{2^*}-\frac{1}{r})^{-1}$ with some $\vartheta_r\in[0,1]$ such that $s\in[2^*(2\alpha),2^*]$. Here, in the last inequality, we have used Lemma \ref{lem.embed-3} to obtain that $\|h(v+\theta_n(v_n-v))\|_{s}<+\infty$. Likewise, together with (2)-(3) of Lemma \ref{lem.h}, for $q\geq2^*(2\alpha)$,
\begin{eqnarray*}
&&\bigg|\int_{{\mathbb{R}}^N}[F(h(v_n))-F(h(v))]\mbox{d}x\bigg| \\
&&\quad \leq\int_{{\mathbb{R}}^N}\big|f(h(v+\theta_n(v_n-v)))h'(v+\theta_n(v_n-v))(v_n-v)\big|\mbox{d}x \\
&&\quad \leq\int_{{\mathbb{R}}^N}\big|h(v+\theta_n(v_n-v))\big|^{q-1}h'(v+\theta_n(v_n-v))\big|(v_n-v)\big|\mbox{d}x \\
&&\qquad +\int_{{\mathbb{R}}^N}\big|v+\theta_n(v_n-v)\big|^{2^*-1}\big|(v_n-v)\big|\mbox{d}x \\
&&\quad \leq (2\alpha)^{-\vartheta_q/2}\big(\|h(v+\theta_n(v_n-v))\|_{t}^{(q-1)+(1-2\alpha)\vartheta_q}\|v_n-v\|_{2^*}\big) \\
&&\qquad +2^{2^*-2}\big(\|v\|_{2^*}^{2^*-1}\|v_n-v\|_{2^*}+\|v_n-v\|_{2^*}^{2^*}\big)
\to0,
\end{eqnarray*}
where $t=[(q-1)+(1-2\alpha)\vartheta_q]2^*(2^*-1)^{-1}$ with some $\vartheta_q\in[0,1]$ such that $t\in[2^*(2\alpha),2^*]$.
Thus we have $J(v_n)\to J(v)$, that is, $J$ is continuous in $X$.
(3) Since $h\in C^1(\mathbb{R})$, for $v\in X$, $t>0$ and for any $\phi\in X$, by mean value theorem, we have
\[
\frac{1}{t}\int_{{\mathbb{R}}^N}c(x)\big[h(v+t\phi)^2-h(v)^2\big]\mbox{d}x=\int_{{\mathbb{R}}^N}2c(x)h(v+\theta t\phi)h'(v+\theta t\phi)\phi\mbox{d}x,
\]
where $\theta\in(0,1)$. By mean value theorem, we have
\begin{eqnarray*}
&& I:=\bigg|\int_{{\mathbb{R}}^N}c(x)h(v+\theta t\phi)h'(v+\theta t\phi)\phi\mbox{d}x-\int_{{\mathbb{R}}^N}c(x)h(v)h'(v)\phi\mbox{d}x\bigg| \\
&&\quad \leq\int_{{\mathbb{R}}^N}c(x)\big|h(v+\theta t\phi)-h(v)\big||h'(v+\theta t\phi)||\phi|\mbox{d}x \\
&&\qquad +\int_{{\mathbb{R}}^N}c(x)\big|h(v)\big|\big|h'(v+\theta t\phi)-h'(v)\big||\phi|\mbox{d}x \\
&&\quad \leq \theta t\int_{{\mathbb{R}}^N}c(x)\big|h'(v+\xi\theta t\phi)\big||h'(v+\theta t\phi)||\phi|^2\mbox{d}x \\
&&\qquad +\int_{{\mathbb{R}}^N}c(x)\big|h(v)\big|\big|h'(v+\theta t\phi)-h'(v)\big||\phi|\mbox{d}x
:=I_1+I_2,
\end{eqnarray*}
where $\theta,~\xi\in(0,1)$.
(i) We consider $I_1$.
If $r=\frac{N}{2}$, then by (2) of Lemma \ref{lem.h} and H\"{o}lder's inequality,
\[
I_1\leq \theta t\int_{{\mathbb{R}}^N}c(x)|\phi|^2\mbox{d}x \leq \theta t\|c\|_{N/2}\|\phi\|_{2^*}^2\to0,\quad t\to0.
\]
Otherwise, let us consider $s_1:=s_1(r)=(1-\frac{2}{2^*}-\frac{1}{r})^{-1}$ defined in $r\in(\frac{N}{2},\tilde{r})$. We have $s_1(r)$ is decreasing and $s_1\in(\frac{2^*\alpha}{1-2\alpha},+\infty)$ for $\alpha\in(\frac{1}{4},\frac{1}{2})$, $s_1\in(\frac{2^*}{2^*-2},+\infty)$ for $\alpha\in(0,\frac{1}{4}]$. Let $t_1:=t_1(s_1,\vartheta_1)=2s_1(1-2\alpha)\vartheta_{1}$. Note that for any ${r}\in(\frac{N}{2},\tilde{r})$, there exists $\vartheta_{1}:=\vartheta_1(r)\in[0,1]$ such that $t_1=2^*(2\alpha)$,
by the definition of $h'(t)$ and H\"{o}lder's inequality,
\begin{eqnarray*}
I_1\leq \theta t(2\alpha)^{-\vartheta_{1}}\|c\|_{r}\|h(v+\xi\theta t\phi)\|_{2^*(2\alpha)}^{(1-2\alpha)\vartheta_{1}}\|h(v+\theta t\phi)\|_{2^*(2\alpha)}^{(1-2\alpha)\vartheta_{1}}\|\phi\|_{2^*}^2
\to0,
\quad t\to0.
\end{eqnarray*}
(ii) We consider $I_2$. Firstly, for $\alpha\in(\frac{1}{2^*},\frac{1}{2})$, we have $2^*(2\alpha)\in(2,2^*)$. Let $s_2:=s_2(r)=(1-\frac{1}{2^*}-\frac{1}{r})^{-1}$,
then for $r\in[\frac{N}{2},\frac{2^*(2\alpha)}{(2^*-1)2\alpha-1}]$, we have $s_2\in[2^*(2\alpha),2^*]$.
By H\"{o}lder's inequality and Lebesgue's dominated convergence theorem,
\[
I_2\leq \|c\|_{r}\|h(v)\|_{s_2}\|(h'(v+\theta t\phi)-h'(v))\phi\|_{2^*}\to0,\quad t\to0;
\]
For $r\in(\frac{2^*(2\alpha)}{(2^*-1)2\alpha-1},\frac{2^*\alpha}{2^*\alpha-1})$, let $s_3:=s_3(r)=(1-\frac{1}{2^*}-\frac{1}{2^*(2\alpha)}-\frac{1}{r})^{-1}$. We have $s_3\in(\frac{2^*(2\alpha)}{1-2\alpha},+\infty)$.
Let $t_3:=t_3(s_3,\vartheta_3)=(1-2\alpha)\vartheta_3 s_3$, then for any $r\in(\frac{2^*(2\alpha)}{(2^*-1)2\alpha-1},\frac{2^*\alpha}{2^*\alpha-1})$,
there exists $\vartheta_3:=\vartheta_3(r)\in[0,1]$ such that $t_3=2^*(2\alpha)$. By Lemma \ref{lem.h'-1}, H\"{o}lder's inequality and Lebesgue's dominated convergence theorem,
\begin{eqnarray*}
I_2 \leq C\|c\|_{r}\|h(v)\|_{2^*(2\alpha)}\|h(v+\theta t\phi)-h(v)\|_{2^*(2\alpha)}^{(1-2\alpha)\vartheta_3}
\|\phi\|_{2^*}\to0,\quad t\to0;
\end{eqnarray*}
Secondly, for $\alpha\in(0,\frac{1}{2^*}]$, we have $2^*(2\alpha)\in(0,2]$. Let $s_4:=s_4(r)=(1-\frac{1}{2^*}-\frac{1}{r})^{-1}$, then
for $r\in[\frac{N}{2},+\infty)$, we have $s_4\in(\frac{2^*}{2^*-1},2^*]\subset(1,2^*]$. If $s_4\geq2^*(2\alpha)$,
then
\[
I_2\leq \|c\|_{r}\|h(v)\|_{s_4}\|(h'(v+\theta t\phi)-h'(v))\phi\|_{2^*}\to0,\quad t\to0;
\]
If $s_4<2^*(2\alpha)$,
we let $t_4:=t_4(s_4, \theta_4)=(1-2\alpha)\theta_4\frac{2^*(2\alpha)s_4}{2^*(2\alpha)-s_4}$, then $t_4$ is increasing in $s_4$ and
$t_4\in(2^*(2\alpha)\theta_4,(+\infty)\theta_4)$.
Note that there exists $\vartheta_4:=\vartheta_4(r)\in[0,1]$ such that $t_4=2^*(2\alpha)$, we have
\begin{eqnarray*}
I_2&\leq& \|c\|_{r}\|h(v)(h'(v+\theta t\phi)-h'(v))\|_{s_4}\|\phi\|_{2^*} \\
&\leq& C\|c\|_{r}\|h(v)\|_{2^*(2\alpha)}\|h(v+\theta t\phi)-h(v)\|_{2^*(2\alpha)}^{(1-2\alpha)\vartheta_4}\|\phi\|_{2^*}
\to0,\quad t\to0.
\end{eqnarray*}
In summary, from (i)-(ii), we conclude that $I\to0$. This means that
\[
\frac{1}{t}\int_{{\mathbb{R}}^N}c(x)\big[h(v+t\phi)^2-h(v)^2\big]\mbox{d}x\to\int_{{\mathbb{R}}^N}2c(x)h(v)h'(v)\phi\mbox{d}x.
\]
Likewise, for $q\geq2^*(2\alpha)$, we have
\[
\frac{1}{t}\int_{{\mathbb{R}}^N}\big[F(h(v+t\phi))-F(h(v))\big]\mbox{d}x\to\int_{{\mathbb{R}}^N}f(h(v))h'(v)\phi\mbox{d}x.
\]
These imply that $J$ is G\^{a}teaux-differentiable. This completes the proof.
$\quad\Box$
In the following, we consider the existence of positive solutions of Eq.(\ref{eq.sch5-h}). From variational methods, we will study the positive critical points of the following functional
\[
J^+(v)=\frac{1}{2}\int_{{\mathbb{R}}^N}|\nabla v|^2\mbox{d}x
-\frac{\lambda}{2}\int_{{\mathbb{R}}^N}c(x)h(v)^2\mbox{d}x-\int_{{\mathbb{R}}^N}F(h(v)^+)\mbox{d}x.
\]
To avoid cumbersome notations, in the rest of this paper, we still denote $J^+(v)$ and $F(h(v)^+)$ by $J(v)$ and $F(h(v))$ respectively.
\begin{lem}\label{lem.mp-1}
There exist $\rho_0,~a_0>0$ such that $J(v)\geq a_0$ for all $\|v\|_{X}=\rho_0$.
\end{lem}
{\bf Proof}\quad
Let $s>0$ satisfies that $\frac{2}{s}+\frac{1}{r}=1$, where $r\in(N/2,\tilde{r})$ and $\tilde{r}$ is given by assumption (c).
Note that $|h(v)|\leq |v|$, by Sobolev's inequality, we have
\begin{eqnarray}\label{lem.mp-1-1}
J(v)&=& \frac{1}{2}\int_{\mathbb{R}^N}|\nabla v|^2\mbox{d}x
-\frac{\lambda}{2}\int_{\mathbb{R}^N}c(x)h(v)^2\mbox{d}x
-\int_{\mathbb{R}^N}F(h(v))\mbox{d}x \nonumber\\
&\geq& \frac{1}{2}\|v\|_{X}^2-\frac{\lambda}{2}\|c\|_{r}\|h(v)\|_{s}^{2}
-\frac{1}{q}\|h(v)\|_{q}^{q}
-\frac{1}{2^*}\|h(v)\|_{2^*}^{2^*} \nonumber\\
&\geq& \frac{1}{2}(1-\lambda C_1S^{-1}\|c\|_{r})\|v\|_{X}^2-C_2(\|v\|_{X}^q+\|v\|_{X}^{2^*}),
\end{eqnarray}
where $C_1=1/(2\alpha)$ according to (\ref{lem.embed-2-1}). Let $\lambda^*=C_1S^{-1}\|c\|_{r}$. Note that $2^*>q>2$, then for $\lambda\in(0,\lambda^*)$, there exist $\rho>0$ and $a_0>0$ such that
$J(v)\geq a_0$ for all $\|v\|_{X}=\rho$.
$\quad\Box$
\begin{lem}\label{lem.mp-2}
There exists $v\in X$ such that $J(v)<0$.
\end{lem}
{\bf Proof}\quad
Given $\varphi\in C_0^{\infty}(\mathbb{R}^N,[0,1])$ with $\mbox{supt}(\varphi)=\overline{B}_2$ and $\varphi(x)=1$ for $x\in B_1$.
Note that $\lim\limits_{t\to+\infty}h(t\varphi)/t\varphi=1$, we have $F(h(t\varphi))\geq\frac{1}{2}F(t\varphi)$ for $t\in\mathbb{R}$ large enough.
Then we have
\begin{eqnarray*}
J(t\varphi)\leq\frac{t^2}{2}\int_{\mathbb{R}^N}|\nabla\varphi|^2
-\frac{\lambda t^2}{4}\int_{B_1}c(x)|\varphi|^2
-\frac{t^q}{2q}\int_{B_1}|\varphi|^q
-\frac{t^{2^*}}{22^*}\int_{B_1}|\varphi|^{2^*}.
\end{eqnarray*}
Let $v=t_0\varphi$ with $t_0>0$ sufficiently large, we have $J(v)<0$.
$\quad \Box$
\section{ Analysis of (PS) conditions}
\setcounter{equation}{0}
\label{sec:5-3}
As a consequence of Lemma \ref{lem.mp-1} and Lemma \ref{lem.mp-2}, there exists a Palais-Smale sequence $\{v_n\}$ of $J$ at level $c$ with
\begin{eqnarray}\label{def.c}
c=\inf_{\gamma\in\Gamma}\sup_{t\in[0,1]}J(\gamma(t))>0,
\end{eqnarray}
where $$\Gamma=\{\gamma\in C([0,1],X):\gamma(0)=0,\gamma(1)\neq0,J(\gamma(1))<0\}.$$
That is, $\{v_n\}$ satisfies $J(v_n)\to c,~J'(v_n)\to0$ as $n\to\infty$.
\begin{prop}\label{prop.ps-1}
Every Palais-Smale sequence $\{v_n\}$ for $J$ is bounded in $X$.
\end{prop}
{\bf Proof}\quad
Since $\{v_n\}\subset X$ is a Palais-Smale sequence, we have
\begin{eqnarray}\label{prop.ps-1-1}
J(v_n)=\frac{1}{2}\int_{\mathbb{R}^N}|\nabla v_n|^2dx
-\frac{\lambda}{2}\int_{\mathbb{R}^N}c(x)h(v_n)^2dx
-\int_{\mathbb{R}^N}F(h(v_n))dx\to c,
\end{eqnarray}
and for any $\psi\in C_0^{\infty}(\mathbb{R}^N)$,
\begin{eqnarray*}\label{prop.ps-1-2}
J'(v_n)\psi&=&\int_{\mathbb{R}^N}\Big[\nabla v_n\nabla\psi
-\lambda c(x)h(v_n)h'(v_n)\psi
-f(h(v_n))h'(v_n)\psi\Big]dx\nonumber\\
&=&o(1)\|\psi\|_X.
\end{eqnarray*}
Note that $h(t)/h'(t)\to0$ as $t\to0$, we have $h(t)/h'(t)\in X$ by direct computation. Moreover, since $C_0^{\infty}(\mathbb{R}^N)$ is dense in $X$, we can take $\psi=h(v_n)/h'(v_n)$ as test functions and get
\begin{eqnarray}\label{prop.ps-1-3}
\langle J'(v_n),\psi\rangle &=& \int_{{\mathbb{R}}^N}|\nabla v_n|^2-\lambda\int_{{\mathbb{R}}^N}c(x)h(v_n)^2-\int_{{\mathbb{R}}^N}f(h(v_n))h(v_n) \nonumber\\
&& -\int_{{\mathbb{R}}^N}\frac{2\alpha(1-2\alpha)}{2\alpha+|h(v_n)|^{2(1-2\alpha)}}|\nabla v_n|^2.
\end{eqnarray}
It follows that
\begin{eqnarray*}
c+o(1)\|v_n\|_{X} &=& J(v_n)-\frac{1}{q}\langle J'(v_n),\psi\rangle \\
&\geq& \bigg(\frac{1}{2}-\frac{1}{q}\bigg)\int_{{\mathbb{R}}^N}|\nabla v_n|^2
-\lambda\bigg(\frac{1}{2}-\frac{1}{q}\bigg)\int_{{\mathbb{R}}^N}c(x)h(v_n)^2.
\end{eqnarray*}
Similar to (\ref{lem.mp-1-1}), we obtain $\{v_n\}$ is bounded in $X$.
Note that $|\nabla h(v_n)|\leq|\nabla v_n|$, we conclude that $\{h(v_n)\}$ is also bounded in $X$.
$\quad\Box$
Since $v_n$ is a bounded Palais-Smale sequence, there exists $v\in X$ such that $v_n\rightharpoonup v$ in $X$. We show that there holds $J'(v)=0$. In fact, by Lemma \ref{lem.h}, Lemma \ref{lem.embed-3}, Lemma \ref{lem.embed-Lc} and Lebesgue Dominated Convergence Theorem, for any $\psi\in C_0^{\infty}({\mathbb{R}^N})$, we have
\begin{eqnarray*}
&&\langle J'(v_n)-J'(v),\psi\rangle\\
&=&\int_{{\mathbb{R}}^N}(\nabla v_n-\nabla v)\nabla\psi
-\lambda\int_{{\mathbb{R}}^N}c(x)(h(v_n)h'(v_n)-h(v)h'(v))\psi\\
&&-\int_{{\mathbb{R}}^N}(|h(v_n)|^{q-2}h(v_n)h'(v_n)-|h(v)|^{q-2}h(v)h'(v))\psi\\
&&-\int_{{\mathbb{R}}^N}(|h(v_n)|^{2^*-2}h(v_n)h'(v_n)-|h(v)|^{2^*-2}h(v)h'(v))\psi
\to0.
\end{eqnarray*}
Note that $\langle J'(v_n),\psi\rangle\to0$, we get $J'(v)=0$.
In order to prove that $v$ is a weak solution of (\ref{eq.sch5-3}), we must show that $v$ is nontrivial.
\begin{prop}\label{prop.ps-3}
Let $\{v_n\}$ be a Palais-Smale sequence for $J$ at level $c<\frac{1}{N}S^{N/2}$, assume that $v_n\rightharpoonup v$ in $X$, then $v\neq0$.
\end{prop}
{\bf Proof}\quad
We prove the proposition by contradiction. Assume that $v=0$. By Proposition \ref{prop.ps-1}, $\{h(v_n)\}$ is bounded in $X$.
Claim 1: $\{v_n\}$ is also a (PS) sequence for the functional $\tilde{J}: X\to{\mathbb{R}}$ defined by
\begin{eqnarray*}\label{def.J00}
\tilde{J}(v)=\frac{1}{2}\int_{{\mathbb{R}}^N}|\nabla v|^2\mbox{d}x-\frac{1}{q}\int_{{\mathbb{R}}^N}|h(v)|^q\mbox{d}x
-\frac{1}{2^*}\int_{{\mathbb{R}}^N}|h(v)|^{2^*}.
\end{eqnarray*}
Indeed, since the imbedding from $X$ into $L^2({\mathbb{R}^N},c(x))$ is compact, we have
\[
|J(v_n)-\tilde{J}(v_n)|=\frac{\lambda}{2}\int_{{\mathbb{R}}^N}c(x)h(v_n)^2\mbox{d}x\to0,
\]
and for any $\psi\in X$,
\[
|\langle J'(v_n)-\tilde{J}'(v_n),\psi\rangle|=\bigg|\lambda\int_{{\mathbb{R}}^N}c(x)h(v_n)h'(v_n)\psi\bigg|\to0.
\]
Claim 2: For all $R>0$,
\begin{eqnarray}\label{prop.ps-3-2}
\lim\limits_{n\to\infty}\sup\limits_{y\in{\mathbb{R}^N}}\int_{B_R(y)}|h(v_n)|^{q_0}\mbox{d}x=0,
\end{eqnarray}
cannot occur, where $q_0=\max\{2, 2^*(2\alpha)\}$.
Suppose by contradiction that (\ref{prop.ps-3-2}) occurs, that is, $\{v_n\}$ vanished; then by H\"{o}lder's inequality and Sobolev's inequality,
we have
\begin{eqnarray*}
\|h(v_n)\|_{L^s(B(y,R))}&\leq&\|h(v_n)\|_{L^{q_0}(B(y,R))}^{1-\theta}\|h(v_n)\|_{L^{2^*}(B(y,R))}^{\theta}\\
&\leq& C\|h(v_n)\|_{L^{q_0}(B(y,R))}^{1-\theta}\|\nabla h(v_n)\|_{2}^{\theta},
\end{eqnarray*}
where $\theta=\frac{s-q_0}{2^*-q_0}\frac{2^*}{s}$. Choosing $\theta=2/s$, we obtain
\[
\int_{B(y,R)}|h(v_n)|^s\mbox{d}x\leq C^s\|h(v_n)\|_{L^{q_0}(B(y,R))}^{(1-\theta)s}\int_{B(y,R)}|\nabla h(v_n)|^2\mbox{d}x.
\]
Now covering ${\mathbb{R}}^N$ by balls of radius $R$ in such a way that each point of ${\mathbb{R}}^N$ is contained in at most $N+1$ balls,
we find
\[
\int_{{\mathbb{R}}^N}|h(v_n)|^s\mbox{d}x\leq (N+1)C^s\sup\limits_{y\in{\mathbb{R}}^N}\bigg(\int_{B(y,R)}|h(v_n)|^{q_0}\mbox{d}x\bigg)^{(1-\theta)s/{q_0}}\int_{{\mathbb{R}}^N}|\nabla h(v_n)|^2\mbox{d}x,
\]
which implies that $h(v_n)\to0$ in $L^s({\mathbb{R}}^N)$.
Since $q_0<s<2^*$, by H\"{o}lder's inequality, we get
\begin{eqnarray}\label{prop.ps-3-3}
h(v_n)\to0 ~ in~ L^p({\mathbb{R}}^N),\quad for ~all~ q_0<p<2^*.
\end{eqnarray}
Especially, $h(v_n)\to0$ in $L^q({\mathbb{R}}^N)$.
Now let $\psi=h(v_n)/h'(v_n)$. Since by Lemma \ref{lem.embed-Lc}, $\lambda\int_{\mathbb{R}^N}c(x)h(v_n)^2\mbox{d}x\to0$, we have
\begin{eqnarray*}
o(1)&=&\langle J'(v_n),\psi\rangle\\
&\geq&\int_{{\mathbb{R}}^N}|\nabla h(v_n)|^2\mbox{d}x-\lambda\int_{{\mathbb{R}}^N}c(x)h(v_n)^2\mbox{d}x\\
&&-\int_{{\mathbb{R}}^N}|h(v_n)|^q\mbox{d}x-\int_{{\mathbb{R}}^N}|h(v_n)|^{2^*}\mbox{d}x\\
&\geq&\|h(v_n)\|_X^2-\|h(v_n)\|_{2^*}^{2^*}.
\end{eqnarray*}
By Sobolev's inequality,
\[
o(1)\geq\|h(v_n)\|_{X}^2(1-S^{-2^*/2}\|h(v_n)\|_{X}^{2^*-2}).
\]
If $\|h(v_n)\|_{X}\to0$, then by (5) of Lemma \ref{lem.h}, (\ref{lem.embed-Lc-1}) in Lemma \ref{lem.embed-Lc}, (\ref{prop.ps-3-3}) and Sobolev's inequality,
\begin{eqnarray*}
\int_{{\mathbb{R}}^N}|\nabla v_n|^2\mbox{d}x
&=&\langle J'(v_n),v_n\rangle +\lambda\int_{{\mathbb{R}}^N}c(x)h(v_n)h'(v_n)v_n\mbox{d}x\\
&&+\int_{{\mathbb{R}}^N}|h(v_n)|^{q-2}h(v_n)h'(v_n)v_n\mbox{d}x\\
&&+\int_{{\mathbb{R}}^N}|h(v_n)|^{2^*-2}h(v_n)h'(v_n)v_n\mbox{d}x\\
&\leq&\langle J'(v_n),v_n\rangle +\frac{\lambda}{2\alpha}\int_{{\mathbb{R}}^N}c(x)h(v_n)^2\mbox{d}x\\
&&+\frac{1}{2\alpha}\int_{{\mathbb{R}}^N}|h(v_n)|^{q}\mbox{d}x+\frac{1}{2\alpha}\int_{{\mathbb{R}}^N}|h(v_n)|^{2^*}\mbox{d}x\to0,
\end{eqnarray*}
we contradict $J(v_n)\to c>0$; therefore,
\[
\|h(v_n)\|_{2^*}^{2^*}\geq\|h(v_n)\|_{X}^2+o(1)\geq S^{N/2}+o(1).
\]
By (5) of Lemma \ref{lem.h}, we get
\begin{eqnarray*}
c&=&\lim\limits_{n\to\infty}\bigg\{J(v_n)-\frac{1}{2}\langle J'(v_n),v_n\rangle\bigg\}\\
&=&\lim\limits_{n\to\infty}\bigg\{\frac{\lambda}{2}\int_{{\mathbb{R}}^N}c(x)h(v_n)(h'(v_n)v_n-h(v_n))\mbox{d}x\\
&&+\int_{{\mathbb{R}}^N}|h(v_n)|^{q-2}\Big(\frac{1}{2}h'(v_n)v_n-\frac{1}{q}h(v_n)^2\Big)\mbox{d}x\\
&&+\int_{{\mathbb{R}}^N}|h(v_n)|^{2^*-2}\Big(\frac{1}{2}h'(v_n)v_n-\frac{1}{2^*}h(v_n)^2\Big)\mbox{d}x\bigg\}\\
&\geq&\lim\limits_{n\to\infty}\Big(\frac{1}{2}-\frac{1}{2^*}\Big)\int_{{\mathbb{R}}^N}|h(v_n)|^{2^*}\mbox{d}x\\
&\geq&\frac{1}{N}S^{N/2}
\end{eqnarray*}
which contradicts $c<\frac{1}{N}S^{N/2}$. Thus $\{v_n\}$ does not vanish and there exist $R>0$, $b>0$ and $\{y_n\}\subset{\mathbb{R}^N}$ such that
\[
\lim\limits_{n\to\infty}\int_{B(y,R)}|h(v_n)|^q\mbox{d}x\geq b>0.
\]
Define $\tilde{v}_n(x)=v_n(x+y_n)$. Since $\{v_n\}$ is a (PS) sequence for $\tilde{J}$, $\tilde{v}_n$ is also a (PS) sequence for $\tilde{J}$.
Arguing as in the case of $\{v_n\}$, we get $\tilde{v}_n\rightharpoonup\tilde{v}\in X$ with $\tilde{J}'(\tilde{v})=0$.
Since $\{\tilde{v}_n\}$ does not vanish, we have $\tilde{v}\neq0$. Therefore, by Fatau's lemma, we have
\begin{eqnarray*}
c&\geq&\liminf\limits_{n\to\infty}\bigg\{\tilde{J}(\tilde{v}_n)-\frac{1}{2}\langle\tilde{J}'(\tilde{v}_n),\tilde{v}_n\rangle\bigg\}\\
&=&\liminf\limits_{n\to\infty}\bigg\{\int_{{\mathbb{R}}^N}|h(v_n)|^{q-2}\Big(\frac{1}{2}h'(v_n)v_n-\frac{1}{q}h(v_n)^2\Big)\mbox{d}x\\
&&+\int_{{\mathbb{R}}^N}|h(v_n)|^{2^*-2}\Big(\frac{1}{2}h'(v_n)v_n-\frac{1}{2^*}h(v_n)^2\Big)\mbox{d}x\bigg\}\\
&\geq&\int_{{\mathbb{R}}^N}|h(v_n)|^{q-2}\Big(\frac{1}{2}h'(v)v-\frac{1}{q}h(v)^2\Big)\mbox{d}x\\
&&+\int_{{\mathbb{R}}^N}|h(v_n)|^{2^*-2}\Big(\frac{1}{2}h'(v)v-\frac{1}{2^*}h(v)^2\Big)\mbox{d}x\\
&=&\tilde{J}(\tilde{v})-\frac{1}{2}\langle\tilde{J}'(\tilde{v}),\tilde{v}\rangle.
\end{eqnarray*}
Thus $\tilde{v}\neq0$ is a critical point of $\tilde{J}$ with $\tilde{J}(\tilde{v})\leq c$.
Define
\[
\tilde{c}=\inf_{\gamma\in\tilde{\Gamma}}\sup_{t\in[0,L]}\tilde{J}(\gamma(t))>0,
\]
where $\tilde{\Gamma}=\{\gamma\in C([0,L],X):\gamma(0)=0,\gamma(L)\neq0,\tilde{J}(\gamma(L))<0\}$ for some $L>1$.
Now we construct a path $\gamma(t):[0,L]\to X$ like \cite{JeTa03} such that
\begin{eqnarray*}
\left\{
\begin{array}{ll}
\gamma(0)=0, \tilde{J}(\gamma(L))<0, & \hbox{$v\in \gamma([0,L])$;} \\
\gamma(t)(x)>0, & \hbox{$\forall x\in{\mathbb{R}^N},t\in[0,L]$;} \\
\max\limits_{t\in[0,L]}\tilde{J}(\gamma(t))=\tilde{J}(\tilde{v}). & \hbox{}
\end{array}
\right.
\end{eqnarray*}
Setting
\begin{eqnarray}\label{prop.ps-3-4}
\gamma(t)(x)=\left\{
\begin{array}{ll}
\tilde{v}(x/t), & \hbox{$t>0$;} \\
0, & \hbox{$t=0$.}
\end{array}
\right.
\end{eqnarray}
We see that $\gamma(t)(x)\in\tilde{\Gamma}$ and
\begin{eqnarray*}
&\|\nabla \gamma(t)\|_2^2=t^{N-2}\|\nabla \tilde{v}\|_2^2,\\
&\|h(\gamma(t))\|_q^q=t^{N}\|h(\tilde{v})\|_q^q,\\
&\|h(\gamma(t))\|_{2^*}^{2^*}=t^{N}\|h(\tilde{v})\|_{2^*}^{2^*}.
\end{eqnarray*}
Thus
\[
\tilde{J}(\gamma(t))=\frac{1}{2}t^{N-2}\|\nabla \tilde{v}\|_2^2-t^{N}\Big(\frac{1}{q}\|h(\tilde{v})\|_q^q+\frac{1}{2^*}\|h(\tilde{v})\|_{2^*}^{2^*}\Big).
\]
$\tilde{J}'(\tilde{v})=0$ implies that $\gamma(1)$ is a critical point of $\tilde{J}(\gamma(t))$. Thus $\frac{\mbox{d}}{\mbox{d}t}\Big|_{t=1}\tilde{J}(\gamma(t))=0$. It follows that
\[
\frac{N-2}{2N}\int_{{\mathbb{R}}^N}|\nabla \tilde{v}|^2\mbox{d}x=\frac{1}{q}\int_{{\mathbb{R}}^N}|h(\tilde{v})|^q\mbox{d}x
+\frac{1}{2^*}\int_{{\mathbb{R}}^N}|h(\tilde{v})|^{2^*}\mbox{d}x.
\]
Then
\begin{eqnarray*}
\frac{\mbox{d}}{\mbox{d}t}\tilde{J}(\gamma(t))&=&\frac{N-2}{2}t^{N-3}\int_{{\mathbb{R}}^N}|\nabla \tilde{v}|^2\mbox{d}x\\
&&-Nt^{N-1}\bigg(\frac{1}{q}\int_{{\mathbb{R}}^N}|h(\tilde{v})|^q\mbox{d}x
+\frac{1}{2^*}\int_{{\mathbb{R}}^N}|h(\tilde{v})|^{2^*}\mbox{d}x\bigg)\\
&=&\frac{N-2}{2}t^{N-3}\int_{{\mathbb{R}}^N}|\nabla \tilde{v}|^2\mbox{d}x-\frac{N-2}{2}t^{N-1}\int_{{\mathbb{R}}^N}|\nabla \tilde{v}|^2\mbox{d}x\\
&=&\frac{N-2}{2}t^{N-3}(1-t^2)\int_{{\mathbb{R}}^N}|\nabla \tilde{v}|^2\mbox{d}x.
\end{eqnarray*}
We conclude that $\frac{\mbox{d}}{\mbox{d}t}\tilde{J}(\gamma(t))>0$ for $t\in(0,1)$ and $\frac{\mbox{d}}{\mbox{d}t}\tilde{J}(\gamma(t))<0$ for $t\in(1,L)$. Thus we get the desired path.
If $\lambda=0$, we have proved the proposition. For $\lambda>0$, since the path $\gamma$ given by (\ref{prop.ps-3-4}) belongs to $\tilde{\Gamma}\subset\Gamma$ after scaling, we obtain
\[
c\leq\max\limits_{t\in[0,L]}J(\gamma(t))=J(\gamma(\overline{t}))<\tilde{J}(\gamma(\overline{t}))
\leq\max\limits_{t\in[0,L]}\tilde{J}(\gamma(t))=\tilde{J}(\tilde{v})\leq c,
\]
which is a contradiction. Therefore, $v$ is nontrivial.
$\quad\Box$
\section{Proof of main theorems}
\setcounter{equation}{0}
\label{sec:5-4}
In this section, we will study the properties of the functional $J$ and prove the main theorem, this include the construction of a path that has a maximum level $c<\frac{1}{N}S^{N/2}$.
\begin{lem}\label{lem.h-2*-1}
There exists $d_0>0$ such that
\[
\lim\limits_{t\to+\infty}(t-h(t))\geq d_0.
\]
\end{lem}
{\bf Proof}\quad
Assume that $t>0$. By Lemma \ref{lem.h} we have $h(t)\leq t$ and $h(t)\leq h'(t)t$. Thus we have
\begin{eqnarray*}
t-h(t)&\geq&t(1-h'(t))\\
&=&t\frac{(2\kappa\alpha^2+h(t)^{2(1-2\alpha)})^{1/2}-h(t)^{1-2\alpha}}
{(2\kappa\alpha^2+h(t)^{2(1-2\alpha)})^{1/2}}\\
&\geq&\frac{\kappa\alpha^2t}{2\kappa\alpha^2+h(t)^{2(1-2\alpha)}}\\
&\geq&\frac{\kappa\alpha^2t}{2h(t)^{2(1-2\alpha)}}\quad\mbox{for $t$ large}\\
&:=&d(\alpha,t).
\end{eqnarray*}
Case 1. If $\frac{1}{4}<\alpha<\frac{1}{2}$, then $0<1-2\alpha<\frac{1}{2}$ and thus $d(\alpha,t)\to+\infty$ as $t\to+\infty$.
Case 2. If $\alpha=\frac{1}{4}$, then $1-2\alpha=1$ and thus $d(\alpha,t)\to\frac{\kappa\alpha^2}{2}$ as $t\to+\infty$.
Case 3. If $0<\alpha<\frac{1}{4}$, we claim that $t-h(t)\to0$ is impossible.
Assume on the contrary. Note that $4\alpha<1$ and $h(t)^{4\alpha-1}\to0$ as $t\to+\infty$, by L'Hospital's Principle, we have
\begin{eqnarray*}
0&\leq&\lim\limits_{t\to+\infty}\frac{t-h(t)}{h(t)^{4\alpha-1}}\\
&=&\lim\limits_{t\to+\infty}\frac{1-h'(t)}{(4\alpha-1)h(t)^{4\alpha-2}h'(t)}\\
&=&\lim\limits_{t\to+\infty}\frac{h(t)^{1-2\alpha}}{4\alpha-1}
[(2\kappa\alpha^2+h(t)^{2(1-2\alpha)})^{1/2}-h(t)^{1-2\alpha}]\\
&=&\frac{\kappa\alpha^2}{4\alpha-1}<0,
\end{eqnarray*}
a contradiction.
In summation, for all $0<\alpha<1/2$, there exists $d_0>0$ such that the conclusion of the lemma holds.
$\quad\Box$
\begin{lem}\label{lem.h-2*-2}
For $h(t)$ defined in (\ref{def.h}), we have
(i) If $\frac{1}{4}<\alpha<\frac{1}{2}$, then
\[
\lim\limits_{t\to+\infty}\frac{t-h(t)}{t^{4\alpha-1}}=\frac{\kappa\alpha^2}{4\alpha-1};
\]
(ii) If $0<\alpha\leq\frac{1}{4}$, then
\[
\lim\limits_{t\to+\infty}\frac{t-h(t)}{\log h(t)}
\leq\left\{
\begin{array}{ll}
\frac{\kappa}{16}, & \hbox{$\alpha=\frac{1}{4}$;} \\
0, & \hbox{$0<\alpha<\frac{1}{4}$.}
\end{array}
\right.
\]
\end{lem}
{\bf Proof}\quad
(i) Assume that $t>0$. By the proof of Lemma \ref{lem.h-2*-1}, when $\frac{1}{4}<\alpha<\frac{1}{2}$, we have $t-h(t)\to+\infty$ as $t\to+\infty$, then we can use L'Hospital's Principle to compute that
\begin{eqnarray*}
\lim\limits_{t\to+\infty}\frac{t-h(t)}{t^{4\alpha-1}}
=\lim\limits_{t\to+\infty}\frac{1-h'(t)}{(4\alpha-1)t^{4\alpha-2}}
=\frac{\kappa\alpha^2}{4\alpha-1}
\end{eqnarray*}
(ii) When $0<\alpha\leq\frac{1}{4}$ and if there exists a constant $C>0$ such that $t-h(t)\leq C$, then the conclusion holds. Otherwise, we may assume that $t-h(t)\to+\infty$ as $t\to+\infty$. Then again by L'Hospital's Principle, we have
\begin{eqnarray*}
A&:=&\lim\limits_{t\to+\infty}\frac{t-h(t)}{\log h(t)}\\
&=&\lim\limits_{t\to+\infty}h(t)\bigg(\frac{1}{h'(t)}-1\bigg)\\
&=&\lim\limits_{t\to+\infty}\frac{2\kappa\alpha^2h(t)^{2\alpha}}
{(2\kappa\alpha^2+h(t)^{2(1-2\alpha)})^{1/2}+h(t)^{1-2\alpha}}.
\end{eqnarray*}
Thus $A=\frac{\kappa}{16}$ when $\alpha=\frac{1}{4}$ and $A=0$ when $0<\alpha<\frac{1}{4}$.
This completes the proof.
$\quad\Box$
To finish the proof of Theorem \ref{thm.m1}, we construct a path which minimax level less than $\frac{1}{N}S^{N/2}$.
\begin{prop}\label{prop.mp-1}
The minimax level $c$ defined in (\ref{def.c}) satisfies
\[
c<\frac{1}{N}S^{N/2}.
\]
\end{prop}
{\bf Proof}\quad
We follow the strategy used in \cite{BrNi93}. Let
\[
v^*=\frac{[N(N-2)\varepsilon^2]^{(N-2)/4}}{(\varepsilon^2+|x|^2)^{(N-2)/2}}
\]
be the solution of $-\Delta u=u^{2^*-1}$ in $\mathbb{R}^N$. Then
\begin{eqnarray*}
\int_{{\mathbb{R}}^N}|\nabla v^*|^2=\int_{{\mathbb{R}}^N}|v^*|^{2^*}=S^{N/2},
\end{eqnarray*}
Let $\eta_\varepsilon(x)\in C_0^\infty({\mathbb{R}^N},[0,1])$ be a cut-off function with
$\eta_\varepsilon(x)=1$ in $B_\varepsilon=\{x\in{\mathbb{R}^N}:|x|\leq\varepsilon\}$ and
$\eta_\varepsilon(x)=0$ in $B^c_{2\varepsilon}={\mathbb{R}^N}\setminus B_{2\varepsilon}$.
Let $v_\varepsilon=\eta_\varepsilon v^*$.
For all $\varepsilon>0$, there exists $t^\varepsilon>0$ such that $J(t^\varepsilon v_\varepsilon)<0$ for all $t>t^\varepsilon$. Define the class of paths
\begin{eqnarray*}
\Gamma_\varepsilon=\{\gamma\in C([0,1],X):\gamma(0)=0,\gamma(1)=t^\varepsilon v_\varepsilon\}
\end{eqnarray*}
and the minimax level
\begin{eqnarray*}
c_\varepsilon=\inf_{\gamma\in\Gamma_\varepsilon}\max_{t\in[0,1]}J(\gamma(t))
\end{eqnarray*}
Let $t_\varepsilon$ be such that
\[
J(t_\varepsilon v_\varepsilon)=\max_{t\geq0}J(tv_\varepsilon)
\]
Note that the sequence $\{v_\varepsilon\}$ is uniformly bounded in $X$, we conclude that $\{t_\varepsilon\}$ is upper and lower bounded by two positive constants. In fact, if $t_\varepsilon\to0$, we have $J(t_\varepsilon v_\varepsilon)\to0$; otherwise, if $t_\varepsilon\to+\infty$, we have $J(t_\varepsilon v_\varepsilon)\to-\infty$. In both cases we get contradictions according to Lemma \ref{lem.mp-1}. This proved the conclusion.
According to \cite{BrNi93}, we have, as $\varepsilon\to0$,
\begin{eqnarray}\label{prop.v-1}
\|\nabla v_\varepsilon\|^2_{2}=S^{N/2}+O(\varepsilon^{N-2}),\quad
\|v_\varepsilon\|^{2^*}_{{2^*}}=S^{N/2}+O(\varepsilon^N).
\end{eqnarray}
Define
\begin{eqnarray*}
H(t_\varepsilon v_\varepsilon)
=-\frac{\lambda}{2}\int_{\mathbb{R}^N}c(x)h(t_\varepsilon v_\varepsilon)
-\frac{1}{q}\int_{\mathbb{R}^N}h(t_\varepsilon v_\varepsilon)^q
+\frac{1}{2^*}\int_{\mathbb{R}^N}[(t_\varepsilon v_\varepsilon)^{2^*}
-h(t_\varepsilon v_\varepsilon)^{2^*}]
\end{eqnarray*}
By the definition of $v_\varepsilon$, for $x\in B_\varepsilon$, there exist two constants $c_2\geq c_1>0$ such that for $\varepsilon$ small enough, we have
\[
c_1\varepsilon^{-(N-2)/2}\leq v_\varepsilon(x)\leq c_2\varepsilon^{-(N-2)/2}
\]
and
\[
c_1\varepsilon^{-(N-2)/2}\leq h(v_\varepsilon(x))\leq c_2\varepsilon^{-(N-2)/2}.
\]
Note that $t_\varepsilon$ is upper and lower bounded, $c(x)$ is continuous in $\overline{B}_\varepsilon$, there exist constants $C_1>0, C_2>0$ such that
\begin{eqnarray}\label{prop.mp-1-2}
\int_{B_\varepsilon}c(x)h^2(t_\varepsilon v_\varepsilon)\geq C_1\varepsilon^{2} =C_1\varepsilon^{(\frac{2^*}{2}-1)(N-2)}
\end{eqnarray}
and
\begin{eqnarray}\label{prop.mp-1-3}
\int_{B_\varepsilon}h^q(t_\varepsilon v_\varepsilon)\geq C_2\varepsilon^{N-q\frac{N-2}{2}} =C_2\varepsilon^{(\frac{2^*}{2}-\frac{q}{2})(N-2)}.
\end{eqnarray}
Moreover, note that $h(t_\varepsilon v_\varepsilon)\leq t_\varepsilon v_\varepsilon$ and $2^*>2$, by H\"{o}lder's inequality, we have
\begin{eqnarray*}
R_\varepsilon&:=&
\frac{1}{2^*}\int_{B_\varepsilon}[(t_\varepsilon v_\varepsilon)^{2^*}-h^{2^*}(t_\varepsilon v_\varepsilon)]\\
&\leq& \int_{B_\varepsilon}(t_\varepsilon v_\varepsilon)^{2^*-1}(t_\varepsilon v_\varepsilon-h(t_\varepsilon v_\varepsilon))\\
&\leq&\bigg(\int_{B_\varepsilon}(t_\varepsilon v_\varepsilon)^{2^*}\bigg)^{\frac{2^*-1}{2^*}} \bigg(\int_{B_\varepsilon}(t_\varepsilon v_\varepsilon-h(t_\varepsilon v_\varepsilon))^{2^*}\bigg)^{\frac{1}{2^*}}.
\end{eqnarray*}
According to Lemma \ref{lem.h-2*-2}, there exist $C_3>0$ such that for $\frac{1}{4}<\alpha<\frac{1}{2}$,
\begin{eqnarray}\label{prop.mp-1-4}
R_\varepsilon\leq C_3\bigg(\int_{B_\varepsilon}(t_\varepsilon v_\varepsilon)^{2^*(4\alpha-1)}\bigg)^{\frac{1}{2^*}}
\leq C_3\varepsilon^{(1-2\alpha)(N-2)},
\end{eqnarray}
while for $0<\alpha<\frac{1}{4}$, there exists a constant $\delta\in(0,1)$ such that
\begin{eqnarray}\label{prop.mp-1-5}
R_\varepsilon\leq C_3\bigg(\int_{B_\varepsilon}(t_\varepsilon v_\varepsilon)^{2^*\delta}\bigg)^{\frac{1}{2^*}}
\leq C_3\varepsilon^{\frac{1}{2}(1-\delta)(N-2)}.
\end{eqnarray}
From the above estimations (\ref{prop.mp-1-2})-(\ref{prop.mp-1-5}), we get
\begin{eqnarray}\label{prop.mp-1-6}
H(t_\varepsilon v_\varepsilon)\leq -C_1\varepsilon^{(\frac{2^*}{2}-1)(N-2)} -C_2\varepsilon^{(\frac{2^*}{2}-\frac{q}{2})(N-2)} +C_3\varepsilon^{(1-2\alpha)(N-2)}
\end{eqnarray}
when $\frac{1}{4}<\alpha<\frac{1}{2}$ and
\begin{eqnarray}\label{prop.mp-1-7}
H(t_\varepsilon v_\varepsilon)\leq -C_1\varepsilon^{(\frac{2^*}{2}-1)(N-2)} -C_2\varepsilon^{(\frac{2^*}{2}-\frac{q}{2})(N-2)}
+C_3\varepsilon^{\frac{1}{2}(1-\delta)(N-2)}
\end{eqnarray}
when $0<\alpha<\frac{1}{4}$.
Now we have
\begin{eqnarray}\label{prop.mp-1-1}
J(t_\varepsilon v_\varepsilon)=\frac{t_\varepsilon^2}{2}\int_{\mathbb{R}^N}|\nabla v_\varepsilon|^2-\frac{t_\varepsilon^{2^*}}{2^*}\int_{\mathbb{R}^N}|v_\varepsilon|^{2^*} +H(t_\varepsilon v_\varepsilon).
\end{eqnarray}
Since the function $\xi(t)=\frac{1}{2}t^2-\frac{1}{2^*}t^{2^*}$ achieve its maximum $\frac{1}{N}$ at point $t_0=1$, by using (\ref{prop.v-1}), we derive from (\ref{prop.mp-1-1}) that
\begin{eqnarray}\label{prop.mp-1-8}
J(t_\varepsilon v_\varepsilon)\leq \frac{1}{N}S^{N/2}+H(t_\varepsilon v_\varepsilon)+O(\varepsilon^{N-2}).
\end{eqnarray}
Combining (\ref{prop.mp-1-6}), (\ref{prop.mp-1-7}) and (\ref{prop.mp-1-8}), we conclude that
(i) for $\frac{1}{4}<\alpha<\frac{1}{2}$ and $q>\frac{4}{N-2}+4\alpha$, we have $(\frac{2^*}{2}-\frac{q}{2})(N-2)<(1-2\alpha)(N-2)$;
(ii) for $0<\alpha<\frac{1}{4}$ and $q>\frac{N+2}{N-2}$, we have $(\frac{2^*}{2}-\frac{q}{2})(N-2)<\frac{1}{2}(1-\delta)(N-2)$ for $\delta>0$ small enough.
Therefore, conclusions (i)-(ii) give that
\begin{eqnarray}\label{prop.mp-1-9}
c_\varepsilon=J(t_\varepsilon v_\varepsilon)< \frac{1}{N}S^{N/2}.
\end{eqnarray}
Finally, since $\Gamma_\varepsilon\subset\Gamma$, we have
\[
c\leq c_\varepsilon<\frac{1}{N}S^{N/2}.
\]
This proved the proposition.
$\quad\Box$
{\bf Proof of Theorem \ref{thm.m1}}\quad
Firstly, by Lemma \ref{lem.mp-1}-\ref{lem.mp-2}, the functional $J$ has the Mountain Pass Geometry. Then there exists a Palais-Smale sequence $\{v_n\}$ at level $c$ given in (\ref{def.c}). Secondly, by Proposition \ref{prop.ps-1}, the Palais-Smale sequence $\{v_n\}$ is bounded in $X$. By Proposition \ref{prop.ps-3}, if $c<\frac{1}{N}S^{N/2}$, then the weak limit $v$ of $\{v_n\}$ in $X$ is nonzero and it is a critical point of $J$. Finally, by Proposition \ref{prop.mp-1}, there indeed exists a mountain pass which maximum level $c_\varepsilon$ is strictly less than $\frac{1}{N}S^{N/2}$. This implies that the level $c<\frac{1}{N}S^{N/2}$ and $v$ is a nontrivial weak solution of Eq.(\ref{eq.sch5-h}). Then $u=h(v)$ is a weak solution of Eq.(\ref{eq.sch5-3}).
$\quad\Box$
{\bf Proof of Corollary \ref{rem.m1-3}}\quad
According to (\ref{lem.embed-2-0}), we have
\[
|\nabla (|h(v)|^a)|^2\leq\frac{a^2|h(v)|^{2(a-2\alpha)}}{2\alpha+|h(v)|^{2(1-2\alpha)}}|\nabla v|^2.
\]
Let
\[
\eta(s)=\frac{s^{2(a-2\alpha)}}{2\alpha+s^{2(1-2\alpha)}},\quad s\in(0,+\infty),
\]
then $\eta(s)$ has a unique maximum point $s_0$ satisfies $s_0^{2(1-2\alpha)}=\frac{2\alpha(a-2\alpha)}{(1-a)}$.
Assume that $s_0\geq1$, that is, $a_0=\frac{1+(2\alpha)^2}{1+2\alpha}\leq a\leq1$, then we have
\[
\eta(s_0)=\frac{s_0^{2(a-2\alpha)}}{2\alpha+s_0^{2(1-2\alpha)}}\leq\frac{s_0^{2(1-2\alpha)}}{2\alpha+s_0^{2(1-2\alpha)}}\leq1.
\]
This implies $|\nabla (|h(v)|^a)|^2\leq|\nabla v|^2$, thus the constant $C_1=1$ in (\ref{lem.mp-1-1}). Then conclusion follows from Theorem \ref{thm.m1}.
$\quad\Box$
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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{"url":"http:\/\/cms.math.ca\/cmb\/msc\/13F25?fromjnl=cmb&jnl=CMB","text":"location:\u00a0 Publications \u2192 journals\nSearch results\n\nSearch: MSC category 13F25 ( Formal power series rings [See also 13J05] )\n\n Expand all \u00a0\u00a0\u00a0\u00a0 \u00a0 Collapse all Results 1 - 2 of 2\n\n1. CMB Online first\n\nChang, Gyu Whan\n Power series rings over Prufer $v$-multiplication domains, II Let $D$ be an integral domain, $X^1(D)$ be the set of height-one prime ideals of $D$, $\\{X_{\\beta}\\}$ and $\\{X_{\\alpha}\\}$ be two disjoint nonempty sets of indeterminates over $D$, $D[\\{X_{\\beta}\\}]$ be the polynomial ring over $D$, and $D[\\{X_{\\beta}\\}][\\![\\{X_{\\alpha}\\}]\\!]_1$ be the first type power series ring over $D[\\{X_{\\beta}\\}]$. Assume that $D$ is a Pr\u00c3\u00bcfer $v$-multiplication domain (P$v$MD) in which each proper integral $t$-ideal has only finitely many minimal prime ideals (e.g., $t$-SFT P$v$MDs, valuation domains, rings of Krull type). Among other things, we show that if $X^1(D) = \\emptyset$ or $D_P$ is a DVR for all $P \\in X^1(D)$, then ${D[\\{X_{\\beta}\\}][\\![\\{X_{\\alpha}\\}]\\!]_1}_{D - \\{0\\}}$ is a Krull domain. We also prove that if $D$ is a $t$-SFT P$v$MD, then the complete integral closure of $D$ is a Krull domain and ht$(M[\\{X_{\\beta}\\}][\\![\\{X_{\\alpha}\\}]\\!]_1)$ = $1$ for every height-one maximal $t$-ideal $M$ of $D$. Keywords:Krull domain, P$v$MD, multiplicatively closed set of ideals, power series ringCategories:13A15, 13F05, 13F25\n\n2. CMB 1998 (vol 41 pp. 3)\n\nAnderson, David F.; Dobbs, David E.\n Root closure in Integral Domains, III {If A is a subring of a commutative ring B and if n is a positive integer, a number of sufficient conditions are given for A[[X]]is n-root closed in B[[X]]'' to be equivalent to A is n-root closed in B.'' In addition, it is shown that if S is a multiplicative submonoid of the positive integers ${\\bbd P}$ which is generated by primes, then there exists a one-dimensional quasilocal integral domain A (resp., a von Neumann regular ring A) such that $S = \\{ n \\in {\\bbd P}\\mid A$ is $n$-root closed$\\}$ (resp., $S = \\{n \\in {\\bbd P}\\mid A[[X]]$ is $n$-rootclosed$\\}$). Categories:13G05, 13F25, 13C15, 13F45, 13B99, 12D99\n top of page | contact us | privacy | site map |","date":"2016-10-22 01:49:00","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8626426458358765, \"perplexity\": 830.2677848147262}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-44\/segments\/1476988718423.28\/warc\/CC-MAIN-20161020183838-00459-ip-10-171-6-4.ec2.internal.warc.gz\"}"}
| null | null |
\section{Introduction}\label{intro}
Targeted maximum likelihood estimation \cite[TMLE,][]{vanderLaan&Rubin06,
vanderLaanRose11} is a general template for
estimation in semiparametric or nonparametric models.
The key to each update step of TMLE is to specify and fit a parametric submodel with certain properties, described in detail below.
(A parametric submodel is defined as a parametric model that is contained in the overall model.) Throughout this paper, the overall model is a nonparametric model.
Therefore, many choices are available for the form of the parametric submodel.
We investigate the performance of TMLE
when the parametric submodel is chosen to be from an exponential
family. A computational advantage of this choice is that because the parametrization as well
as the parameter space of an exponential family are always convex
\citep{boyd2004}, standard methods for optimization can be applied to solve this
problem. Another advantage of this approach is that it can be applied to a wide variety of estimation problems.
Specifically, it can be used to estimate any smooth parameter defined in the nonparametric model, under conditions described below.
We demonstrate how to implement TMLE using exponential families
in the following three estimation problems:
\begin{enumerate}
\item Estimating the mean of an outcome missing at random, where covariates are observed for the entire sample.
\item Estimating a nonparametric extension of the parameter in a median regression model.
\iffalse
We consider an extension
of this parameter to the nonparametric model
given by $\beta_0\equiv \arg\min_\beta E|Y-g(X,\beta)|$, where we
assume that this minimizer is unique. This parameter $\beta_0$ is
well defined even when the median regression model $g$ is incorrectly specified, but equals the median regression
parameter when the model is correctly specified.
\fi
\item Estimating the causal effect of a continuous-valued exposure.
\iffalse
Originally studied
in \cite{Diaz12}, we revisit a situation in which the effect of $\gamma$ additional units of
of a
continuous exposure is estimated. Specifically, we present a
method to estimate the parameter $E\{E(Y|A+\gamma, W)\}$, where $A$ is
a continuous exposure, $W$ is a set of sufficient covariates,
$Y$ is the outcome, and $\gamma$ is a user-given value.
Under certain causal assumptions, this
parameter can be interpreted as the expected outcome in a hypothetical
population in which the conditional distribution of $A$ has been
shifted by $\gamma$ units. An
exponential family is used in this problem as a parametric
submodel for the conditional density of $A$ given $W$.
\fi
\end{enumerate}
We conduct a simulation study comparing different choices for the parametric submodel, focusing on the first of these problems.
We next present an overview of the TMLE template, and illustrate the implementation of TMLE for each of the
three problems above. We conclude with a
discussion of practical issues and directions for future research.
\section{Targeted maximum likelihood template}\label{tmle}
Let the random vector representing what is observed on an experimental unit be denoted by $O$, with sample space $\mathcal{O}$.
Let $\{O_1,\ldots,O_n\}$ be an independent, identically distributed sample
of observations $O$, each drawn from the unknown, true distribution $\mbox{$P_0$}$. We assume that $\mbox{$P_0$}\in \mathcal M$, where
$\mathcal M$ is the nonparametric model, defined as the class of all distributions having a continuous density with respect to
a dominating measure $\nu$.
Let $\mathcal{M}'$ denote the class of all densities corresponding to a distribution in $\mathcal{M}$, and let $p_0$ denote the density corresponding to $\mbox{$P_0$}$.
Let $\Psi(p)$ denote a $d$-dimensional Euclidean parameter with known
efficient influence function $D(\mbox{$p_0$},O)$. That is, $\Psi$ is a mapping from $\mathcal{M}$ to $\mathbb{R}^d$ for which
$D(\mbox{$p_0$},O)$ is the pathwise derivative, as defined, e.g., in \citet{Bickel97}. We refer to such a parameter as a smooth parameter.
Many commonly used parameters are smooth, including all those in this paper. The efficient influence function, by definition, satisfies
\begin{equation}
\int D(p,o)p(o)d\nu(o)=0 \mbox{ for all } p \in\mathcal{M}'. \label{effic_property}
\end{equation}
Denote the true value $\Psi(\mbox{$p_0$})$ by $\psi_0$. The template for a
targeted maximum likelihood estimator is defined by the following steps:
\begin{enumerate}
\item Construct an initial estimator $p^0$
of the true, unknown density $\mbox{$p_0$}$;
\item Construct a sequence of updated density estimates $p^k$, $k=1,2,\dots$. Given the current density estimate $p^k$, the updated density $p^{k+1}$ is constructed by specifying
a regular parametric submodel $\{p_\epsilon^k:\epsilon \in R\}$ of $\mathcal{M}$, where $R$ is an open subset of $\mathbb{R}^d$.
The submodel is required to satisfy two properties. First, it must equal the current density estimate $p^k$ at
$\epsilon=0$, i.e., $p_0^k = p^k$. Second, the score of $p_\epsilon^k$ at $\epsilon=0$ must equal the efficient
influence function for $\Psi$ at $p^k$, i.e.,
\begin{equation}
D(p^k,o) = \frac{d}{d
\epsilon}\left[\log p_\epsilon^k(o)\right]\bigg|_{\epsilon=0}, \mbox{ for all possible values of } o \in \mathcal{O}.\label{score}
\end{equation}
The parameter $\epsilon$ of the submodel $\{p_\epsilon^k:\epsilon \in R\}$ is fit using maximum likelihood estimation, i.e.,
\begin{equation}
\hat\epsilon=\arg\max_\epsilon\sum_{i=1}^n\log p^k_\epsilon(O_i), \label{mle}
\end{equation}
and
the updated density $p^{k+1}$ is defined to be the density in the parametric submodel\\ $\{p_\epsilon^k:\epsilon \in \mathbb{R}^d\}$ corresponding to $\hat\epsilon$, i.e.,
$p^{k+1}=p^k_{\hat\epsilon}$.
\item Iterate the previous step until convergence, i.e., until $\hat\epsilon\approx 0$. Denote the last step of the procedure by $k=k^*$.
\item Define the TMLE of $\psi_0$ to be
the substitution estimator
$\hat\psi\equiv \Psi(p^{k^*})$.
\end{enumerate}
The TMLE algorithm above can be generalized in the following ways: one
can let each $p^k$ represent an estimate of only certain components
of the density $p$ (typically those components relevant to estimation
of the parameter $\Psi$ for a specific problem); the parametric
submodel may satisfy a relaxed score condition, in that the efficient
influence function need only be contained in the linear span of the
score at $\epsilon=0$; or another loss function may be used in place
of the log-likelihood for estimating $\epsilon$ in (\ref{mle}). We
discuss the latter generalization in more detail in Section~\ref{second_onestep}.
\iffalse
With these elements defined, a general TMLE is given by the following iterative procedure:
\begin{enumerate}
\item Initialize $k=0$,
\item Estimate $\epsilon$ as $\hat\epsilon=\arg\max_\epsilon\sum_{i=1}^n\log p^k_\epsilon(O_i)$,
\item Update $p$ as $p^{k+1}=p^k_{\hat\epsilon}$,
\item Update $k=k+1$ and iterate steps 2 through 4 until convergence
($\hat\epsilon\approx 0$).
\end{enumerate}
\fi
The result of the above TMLE procedure is that at the final density estimate $p^{k^*}$, we have
\begin{equation}
\sum_{i=1}^n D(p^{k^*},O_i) \approx 0, \label{eifee}
\end{equation}
i.e., the final density estimate is a solution to the efficient influence function estimating equation.
This property, combined with the estimator being a substitution
estimator $\hat\psi\equiv \Psi(p^{k^*})$ and the smoothness of the parameter, is fundamental to proving
that TMLE has desirable properties. For example, it is
asymptotically linear with influence function equal
to the efficient influence function under certain assumptions, as described by \cite{vanderLaan&Rubin06}.
We give a heuristic argument for (\ref{eifee}), which is rigorously
justified under regularity conditions given in Result 1 of \cite{vanderLaan&Rubin06}.
Assume that at the final iteration of TMLE, i.e., the iteration where
$p^{k^*}$ is defined, we have $\hat{\epsilon}=0$. Then by equation (\ref{mle}),
the penultimate density $p^{k^*-1}$ must satisfy
\begin{equation}
0 = \hat\epsilon=\arg\max_\epsilon\sum_{i=1}^n\log p^{k^*-1}_\epsilon(O_i). \label{mle1}
\end{equation}
If $\log p^{k^*-1}_\epsilon$ is strictly convex in $\epsilon$, then the derivative at $\epsilon=0$ of the right side of (\ref{mle1}) equals $0$, which implies
\begin{eqnarray}
0 & = &\sum_{i=1}^n \frac{d}{d \epsilon} \log p^{k^*-1}_\epsilon(O_i)\bigg|_{\epsilon=\mathbf{0}} = \sum_{i=1}^n D(p^{k^*-1},O_i) = \sum_{i=1}^n D(p^{k^*},O_i), \label{used_pass_through_at_epsilon_0_property}
\end{eqnarray}
where the second equality follows from the score condition (\ref{score}) and third equality follows since by construction in step 2 we have
$p^{k^*}=p^{k^*-1}_{\hat\epsilon} = p^{k^*-1}_{0} = p^{k^*-1}$. This completes the heuristic argument for (\ref{eifee}).
\section{Implementing TMLE using an exponential family}
The key step in the TMLE algorithm is step 2, which requires a choice of the parametric submodel at each iteration $k$.
Let $p^k$ denote the density at the current iteration $k$, and consider construction of the parametric model in step 2.
One option is to use a submodel from an
exponential family, represented as
\begin{equation} p_\epsilon^k(O) = c(\epsilon, p^k)\exp\{\epsilon
D(p^k,O)\}p^k(O),\label{expfam1}
\end{equation}
where the normalizing constant $c(\epsilon, p^k) = \left[ \int \exp\{\epsilon
D(p^k,o)\}p^k(o) d\nu(o)\right]^{-1}$. The model is defined for all $\epsilon \in \mathbb{R}^d$ for which the integral in $c(\epsilon, p^k)$ is finite.
A key feature of parametric models of the form (\ref{expfam1}) is that they automatically satisfy the two conditions in step 2 of the TMLE algorithm.
First, by (\ref{expfam1}), we have at $\epsilon=0$ that $p_\epsilon^k = p^k$. Second, the score condition (\ref{score}) holds
since we have, for all possible values of $o \in \mathcal{O}$,
\begin{eqnarray}
\frac{d}{d\epsilon} \left\{\log p_\epsilon^k (o)\right\}\bigg|_{\epsilon =0} & = &
\frac{d}{d\epsilon} \left[ \log
\exp\left\{\epsilon
D(p^k,o)\right\} \right] \bigg|_{\epsilon =0}+ \frac{d}{d\epsilon} \left\{ \log c(\epsilon, p^k)\right\} \bigg|_{\epsilon =0} \nonumber \\
& = &
D(p^k,o) -
\left[ c(\epsilon, p^k)\int D(p^k,o')\exp\{\epsilon D(p^k,o')\}p^k(o')d\nu(o')\right]\bigg|_{\epsilon =0} \nonumber \\
&=&
D(p^k,o) -
c(0, p^k) \int D(p^k,o')p^k(o')d\nu(o')\nonumber \\
&=&
D(p^k,o), \nonumber
\end{eqnarray}
where the second equality follows from exchanging the order of differentiation and integration (justified under smoothness conditions by Fubini's Theorem), and the last equality follows from
$\int D(p^k,o)p^k(o)d\nu(o)=0$ by (\ref{effic_property}).
An advantage of using (\ref{expfam1}) as a submodel is that maximum likelihood
estimation of $\epsilon$ in an exponential family is a convex
optimization problem, which is computationally tractable. In particular, we take advantage of
the various R functions available to solve convex optimization
problems.
In Section~\ref{simula}, we illustrate a different implementation of TMLE that uses parametric
submodels given by
\begin{equation}
p_\epsilon^k(O)= c'(\epsilon, p^k)\{1 + \exp[-2\epsilon D(p^k,O)]\}^{-1}p^k(O), \label{ivan_submodel}
\end{equation}
for $c'(\epsilon, p^k)$ a normalizing constant, and which also has a convex log-likelihood function.
In Sections~\ref{ex1}-\ref{ex3}, we describe three estimation problems that can be solved with TMLE. The first problem,
estimating the mean of a variable missing at random, is an example where there exists a TMLE implementation that requires a single iteration and
that can be solved through a logistic regression of the outcome on a
so called ``clever covariate.'' In contrast, the examples in Sections~\ref{ex2}-\ref{ex3} generally require multiple iterations,
and cannot be solved using a clever covariate.
\section{Example 1: The mean of a variable missing at
random}\label{ex1}
\subsection{Problem Definition}\label{sec_prob_defn_1}
Assume we observe $n$ independent, identically distributed draws $O_1,\ldots,O_n$, each
having the observed data structure $O=(X,M,MY)\sim\mbox{$P_0$}$, where
$X$ is a vector of baseline random variables,
$M$ is an indicator of the outcome being observed, and $Y$ is the binary outcome.
For participants with $M=0$, we do not observe their outcome $Y$ (since we only observe $MY$, which equals zero for such participants); however, these participants do contribute baseline variables.
The only assumptions we make on the joint distribution
of $(X,M,Y)$ are that $Y$ is missing at random conditioned on $X$,
i.e., $M\mbox{$\perp\!\!\!\perp$} Y|X$, and that $P(M=1|X)>0$ with probability 1.
Define the outcome regression $\mu(X) \equiv E_P(Y|M=1,X)$, the propensity score $p_M(X)\equiv P(M=1|X)$, and
the marginal density $p_X(X)$ of the baseline variables $X$. All of these components of the density $p$ are assumed unknown.
The parameter of interest is $E_{P}(Y)$, which by the missing at random assumption equals
$E_{p_X}(\mu(X))$. This parameter only depends on the components $p_X$ and $\mu$ of the joint distribution $P$.
We denote the parameter of interest as
$\Psi(\mu, p_X)=E_{P}(Y)\equiv E_{p_X}(\mu(X))$, where $E_{p_X}$ denotes the expectation with respect to the marginal distribution of $X$.
Note that in general
$E_{p_X}(\mu(X)) \neq E_{P}(Y|M=1)$ (since the latter equals $E_{p_{X|M=1}}(\mu(X))$, i.e., the expectation of $\mu(X)$ with respect to the distribution of $X$ given $M=1$)
except in the special case
called missing completely at random, where $M$ and $X$ are marginally independent.
Denote the true mean of $Y$ by $\psi_0$. Identification and
estimation of $\psi_0$ is a widely studied problem
\cite[e.g.,][]{Robins97R,Kang&Shafer07}. The estimation problem
becomes particularly challenging when the dimension of $X$ is large,
since nonparametric estimators using empirical means suffer from the
curse of dimensionality. It is a challenging problem even when $X$ consists of a few, continuous-valued, baseline variables, as shown by \cite{Robins97R}.
Below, we contrast four TMLE implementations
for the above estimation problem. The purpose is to compare multiple options for the parametric submodel, in this simple problem. Also, we
demonstrate the general approach of using the exponential family
(\ref{expfam1}) as parametric submodel, in this relatively
well-studied problem, before applying it to more challenging problems
in Sections~\ref{ex2} and \ref{ex3}.
In Section~\ref{sec_onestep} we present an implementation of TMLE from
\citet{vanderLaan&Rubin06}, which requires only a single iteration. A
variation of this estimator that uses weighted logistic
regression is presented in Section~\ref{second_onestep}.
\iffalse
uses independent parametric submodels for each component of the likelihood $p_M$,
$p_X$, and $\mu$. Taking advantage of the fact that the corresponding
component of the efficient influence function does not depend on
$\mu$, the initial estimator $\mu^0$ is fluctuated based on
an exponential family that uses a clever covariate to obtain an
estimate that requires running a single logistic regression model, and
does not require the iterative procedure of the previous section.
\fi
In Section \ref{ex1_exp_family_implementation}, we describe a TMLE implementation using the
exponential family (\ref{expfam1}) as a submodel; we also present a fourth implementation using the submodel (\ref{ff2}).
Under the conditions described in Theorem~\ref{Theo} of Appendix~\ref{theorem}, the
asymptotic distribution of the TMLE estimator
is not sensitive to the choice of submodel when each of the initial estimators $p_M^0$
and $\mu^0$ converges to its true value at a rate faster than
$n^{1/4}$. However, the choice of submodel may impact finite sample performance.
Also, when one of the estimators $p_M^0$ and $\mu^0$ does not converge to
the true value, the submodel choice may even affect performance asymptotically.
To shed light on this, we perform a simulation study in Section~\ref{simula}.
In general, TMLE implementations require that one has derived the
efficient influence function of the parameter of interest with respect
to the assumed model (which is the nonparametric model throughout this
paper). For the parameter in this section, the efficient influence
function is given by \cite{Bang05}
\begin{equation}
D(p,O)=\frac{M}{p_M(X)}\{Y-\mu(X)\} + \mu(X) - \Psi(\mu, p_X).\label{eicEY}
\end{equation}
We will also
denote $D(p, O)$ by $D(\mu, p_M, p_{X},O)$, using the fact that the density $p$
can be decomposed into the components $\mu, p_M, p_{X}$ defined
above.
\subsection{First TMLE implementation for the mean of an outcome missing at random} \label{sec_onestep}
The first TMLE implementation has been extensively discussed in the literature
\cite[e.g.,][]{vanderLaan&Rubin06, vanderLaanRose11}, and we only provide
a brief recap. Following the template from Section~\ref{tmle},
we first define initial estimators $\mu^0$ and $p_M^0$ of
$\mu$ and $p_M$, respectively. These could obtained, e.g., by fitting logistic
regression models or by machine learning methods. We set the initial
estimator $p_{X}^0$ of $p_{X}$ to be the empirical distribution of
the baseline variables $X$, i.e., the distribution placing mass $1/n$
on each observation of $X$. The TMLE presented next is equivalent to
the estimator presented in page 1141 of \cite{Scharfstein1999R} when
$\mu^0$ is a logistic regression model fit. A detailed discussion of the
similarities between the TMLE template and the estimators that stem
from \cite{Scharfstein1999R} is presented in Appendix 2 of
\cite{Rosenblum2010T}. We now show the construction of a parametric
submodel for this problem.
\paragraph{Construction of the parametric submodel}
In this implementation of TMLE, the components $p_X$, $p_M$, and $\mu$
are each updated separately, such that they solve the corresponding part of the efficient influence function
estimating equation. Consider the $k$-th step of the TMLE algorithm
described in Section~\ref{tmle}. For the conditional expectation of $Y$ given
$X$ among individuals with $M=1$, and an estimator $\mu^k$, we define the logistic model
\begin{equation}
\logit \mu_\epsilon^k(X) = \logit \mu^k(X) + \epsilon
H_Y(X),\label{expFMAR}
\end{equation}
where $H_Y(X)=1/p_M^0(X)$. For the marginal distribution of $X$ we define the exponential model
\[p_{X,\theta}^k(X) \propto \exp\{\log p_{X}^k(X) + \theta H_X^k(X)\},\]
where $H_X^k(X)= \mu^k(X) - E_{p_X^k}\mu^k(X)$. The
variable $H_Y(X)$ has often been referred to as the ``clever
covariate''. The initial estimator of $p_M$ is not modified.
It is straightforward to show that the efficient influence
function $D(p^k,O)$ is a linear combination of the scores of this joint
parametric model for the distribution of $O$.
We now describe the TMLE implementation based on the submodel construction above.
For this case, this procedure involves
only one iteration. In the first iteration we have
\[\hat \theta=\arg\max_{\theta}\frac{1}{n} \sum_{i=1}^n \log p_{X,\theta}^0(X_i)=0.\] This is because
the MLE of $p_{X}$ in the nonparametric model is precisely
the empirical $p_X^0$. An estimate $\hat\epsilon$ of the parameter in the model
\[
\logit \mu_\epsilon^0(X) = \logit \mu^0(X) + \epsilon
H_Y(X),
\]
may obtained by running a logistic regression of $Y$ among individuals with $M=1$ on $H_Y(X)$ without intercept and including an
offset variable $\logit \mu^0(X)$. We now compute the updated estimate
of $\mu_0$ as \[\mu^1(X)=\expit \{\logit \mu^0(X) +
\hat\epsilon/p_M^0(X)\}.\] The score equation corresponding to this logistic regression model is
\begin{equation}
\sum_{i=1}^n \frac{M_i}{p_M^0(X_i)}(Y_i - \mu^1(X_i))=0.\label{esteqTMLE1}
\end{equation}
Note that this matches the first component of the efficient influence function (\ref{eicEY}).
Proceeding to the second iteration, we
estimate the parameter $\epsilon$ in the model
\[\mu_\epsilon^1(X)=\expit \{\logit \mu^1(X) +
\epsilon /p_M^0(X)\},\]
by running a logistic regression of $Y$ on $H_Y(X)$ with offset $\mu^1(X)$
and without intercept among participants with $M=1$. This is equivalent to solving the score
equation
\[\sum_{i=1}^n \frac{M_i}{p_M^0(X_i)}(Y_i - \expit \{\logit \mu^1(X_i) +
\epsilon /p_M^0(X_i)\})=0\]
in $\epsilon$. By convexity and (\ref{esteqTMLE1}), the solution $\epsilon$ to the score equation in the above display
is equal to zero, and so the algorithm is terminates in the second iteration. The TMLE $\hat\psi$ is thus defined as
$\hat\psi=\frac{1}{n}\sum_{i=1}^n\mu^1(X_i)$. Confidence intervals may be constructed using
the non-parametric bootstrap. For a more detailed discussion of the
asymptotic properties of this estimator, as well as simulations, see \cite{vanderLaan&Rubin06}.
\subsection{Second TMLE implementation for the mean of an outcome missing at random} \label{second_onestep}
Consider the following $k$-th iteration parametric submodel for the
expectation of $Y$ conditional on $X$ among participants with $M=1$
\begin{equation}
\logit \mu_\epsilon^k(X) = \logit \mu^k(X) + \epsilon\label{expFMARweights}.
\end{equation}
Let $\hat \epsilon$ be the first-step estimator of the intercept term
in a weighted logistic regression with weights $1/p_M^0(X)$ and offset
variable $\logit\mu^k(X)$. Let the updated estimator of $\mu_0$ be defined
as
\[\mu^1(X)=\expit \{\logit \mu^0(X) + \hat\epsilon\}.\]
By a similar argument as in the previous section, the estimate of
$\epsilon$ in the following iteration is equal to zero, and the TMLE
of $\psi$, defined as $\hat\psi=\frac{1}{n}\sum_{i=1}^n\mu^1(X_i)$,
converges in one step. Note that this implementation of the TMLE also
satisfies the score equation (\ref{esteqTMLE1}).
In addition, note that $\hat\epsilon$ in this section does not correspond to the
MLE of a parametric submodel. As a consequence, $\hat\psi$ is
not a targeted maximum likelihood estimator as defined in
Section~\ref{tmle}. Instead, it is part of a broader class of
estimators referred to as targeted minimum loss-based estimators, also
abbreviated as TMLE \cite{vanderLaanRose11}. These estimators generalize the TMLE framework of
Section~\ref{tmle} by allowing the use of general loss functions in
estimation of the parameter $\epsilon$ in the parametric submodel. In
the example of this section the loss function used is the weighted
least squares loss function.
This TMLE implementation is analogous to the estimator of Marshall
Joffe discussed in \cite{Robins2007} when $\mu^0$ is a parametric
model. The Joffe estimator is presented in \cite{Robins2007} as a
doubly robust alternative to the augmented IPW estimators when the
weights $1/p_M^0(X)$ are highly variable, i.e., when there are
empirical violations to the positivity
assumption; we simulate such scenarios in Section~\ref{simula}.
To the best of our knowledge, the above TMLE implementation was first
discussed by \citet{Stitelman2012} in the context of longitudinal
studies.
\subsection{Third and fourth TMLE implementations for the mean of an outcome missing at random} \label{ex1_exp_family_implementation}
We next give implementations of TMLE based on the following two types of submodel for $p$:
\begin{align}
p_\epsilon^k(O)&= c(\epsilon, p^k)\exp\{\epsilon D(p^k,O)\}p^k(O);\label{ff1}\\
p_\epsilon^k(O)&= c'(\epsilon, p^k)\{1 + \exp[-2\epsilon D(p^k,O)]\}^{-1}p^k(O).\label{ff2}
\end{align}
Here $c(\epsilon, p^k), c'(\epsilon, p^k)$ are the corresponding
normalizing constants, and $D(p^k,O)$ is the efficient influence
function given in (\ref{eicEY}). Model (\ref{ff1}) is the general
exponential family introduced in (\ref{expfam1}), while (\ref{ff2}) is
an alternative submodel.
The third and fourth TMLE implementations for estimating $E(Y)$ are defined by the following iterative procedure:
\begin{enumerate}
\item Construct initial estimators $p_M^0$, $p_X^0$, and $\mu^0$ for $p_M$, $p_X$, and $\mu$, respectively. We use the same initial estimators as in Section~\ref{sec_onestep}.
\item Construct
a sequence of updated density estimates $p^k$, $k=1,2,\dots$, where at each iteration $k$ we construct $p^{k+1}$ as follows:
estimate $\epsilon$ as
\[\hat\epsilon=\arg\max_{\epsilon} \sum_{i=1}^n \log p_\epsilon^k(X_i,M_i,Y_i),\]
where $p_\epsilon$ is given by (\ref{ff1}) or (\ref{ff2}), for the third or fourth implementation, respectively.
Computation of $p_\epsilon^k(X_i,M_i,Y_i)$ requires evaluation of
$D(p^k,O)$, which in turn requires $p_M^k$, $p_X^k$, and $\mu^k$.
Define $p^{k+1}=p_{\hat\epsilon}^k$, and define $p_M^{k+1}$,
$p_X^{k+1}$, $\mu^{k+1}$ to be the corresponding components of $p^{k+1}$.
\item The previous step is iterated until convergence, i.e., until $\hat\epsilon\approx 0$. Denote the last step of the procedure by $k=k^*$.
\item The TMLE of $\psi_0$ is defined as the substitution estimator
$\hat\psi\equiv \Psi(p^{k^*}) = E_{p_X^*}\{\mu^*(X)\}$, for
$p_X^*$ and $\mu^*$ the corresponding components of $p^{k^*}$.
\end{enumerate}
If the initial estimator $p_X^0$ is the empirical distribution, then
$p_X^*$ is a density (with respect to counting measure) with positive mass only at the observed
values $X_i$. This is an important computational characteristic when computing the normalizing constant $c(\epsilon, p^*)$, since
integrals over $p_X^*$ become weighted sums over the sample. The
optimization in each iteration of step 2 is carried out using the BFGS
\cite{Broyden1970,Fletcher1970,Goldfarb1970,Shanno1970}
algorithm as implemented in the $R$ function {\texttt optim()}. The
optimization problem is convex in $\epsilon$, so that under regularity
conditions we expect the algorithm to converge to the global optimum.
\paragraph{Motivation for TMLE implementation with submodel
(\ref{ff2}).} Submodel (\ref{ff1}) is not necessarily well define
for an unbounded efficient influence function $D(p^k,O)$. However, submodel
(\ref{ff2}) is always bounded and can be used with any
$D(p^k,O)$. An example of an unbounded efficient influence function is
given by (\ref{eicEY}) under empirical violations of the assumption
$P(p_M(X)>0)=1$. This problem has been extensively discussed,
particularly in the context of continuous outcomes
\cite[e.g.,][]{Bang05,Robins2007,Gruber2010t}. A TMLE with
submodel (\ref{ff2}) as presented in this section may provide an
alternative solution to those presented in the literature.
\subsection{Evaluating sensitivity of the TMLE to the choice of
parametric submodel}\label{simula}
We perform a simulation study to explore the sensitivity of the TMLE to
the above four different choices of parametric submodels from
Sections~\ref{sec_onestep}-~\ref{ex1_exp_family_implementation}.
We generate data satisfying the missing at random assumption defined in Section~\ref{sec_prob_defn_1}.
\paragraph{Data generating mechanism for simulations}
The observed data on each participant is the vector $(X,M,MY)$, where $X=(X_1,X_2)$.
The following defines the joint distribution of the variables $(X,Y)$:
\begin{align*}
X_1 & \sim N(0,1/2),\\
X_2|X_1 & \sim N(X_1,1),\\
Y|X_1,X_2 & \sim Ber(\logit(X_2-X_2^2)),
\end{align*}
where $Ber(p)$ denotes the Bernoulli distribution with probability $p$ of $1$ and probability $1-p$ of $0$.
We consider the following three missing outcome distributions, which are referred to as missingness mechanisms, and are depicted in Figure~\ref{Missing}:
\begin{align}
M|X_1,X_2 & \sim Ber(\logit(1+2X_2)),\label{D1}\\
M|X_1,X_2 & \sim Ber(\logit(-1+2X_2)),\label{D2}\\
M|X_1,X_2 & \sim Ber(\logit(-6+2X_2+2X_2^2)).\label{D3}
\end{align}
\begin{figure}[!htb]
\caption{Different missingness mechanisms $p_M(X)$ considered.}
\centering
\includegraphics[scale = 0.4]{D.pdf}\label{Missing}
\end{figure}
We refer to these missingness mechanisms as D1, D2, and D3 respectively.
A practical violation of the positivity assumption is said to occur if
for some values of $(X_1,X_2)$, we have $P(M=1|X_1,X_2) \approx 0$.
Practical positivity violations are moderate under D2 and severe under D3.
We consider these three missingness mechanisms to assess the
performance of each TMLE implementation under different practical
violations to the positivity assumption, a scenario of high interest
since many doubly robust estimators can perform
poorly \cite{Robins2007}. A large fraction of small
probabilities as in D3 may be unlikely in a
missing data application. However, it is very common in survey sample
estimation, a field in which inverse probability weighted
estimators are the rule. For reference, the minimum missingness
probability in D3 is $0.0015$, and the median is $0.0047$. This is
consistent with survey weights found in the literature \cite[e.g.,][]{Rudolph14}.
Various studies have investigated the
performance of different estimators under violations to the positivity
assumption \cite[e.g.,][]{Kang&Shafer07, Porter2011}. We focus
on TMLEs, assessing the impact of the choice of submodel. Each
missingness mechanism, combined with the joint distribution of $(X,Y)$
defined above, determines the joint distribution of the observed data
$(X,M,MY)$.
We simulated 10000 samples of sizes 200, 500, 1000, and 10000,
respectively. This was done for each missingness mechanism.
We implemented the four types of TMLE described
in this paper, using four different sets of working models for $\mu$ and
$p_M$: (i) correctly specified models for both, (ii)
correct model for $\mu$ and incorrect model for $p_M$, (iii) incorrect
model for $\mu$ and correct model for $p_M$, (iv) incorrect models
for both $\mu$ and $p_M$.
Misspecification of the working model for $\mu$ consisted of using a logistic regression of $Y$ on $(X_1,X_1^2)$ among individuals with
$M=1$; misspecification of the working model for $p_M$ consisted of running
logistic regressions of $M$ on $(X_1, X_1^2)$. The
TMLE iteration was stopped whenever $\hat\epsilon < 10^{-4}$.
\paragraph{Simulation results}
Table \ref{msetable} shows the relative efficiency (using as reference
the analytically computed efficiency bound) of the four
estimators for different sample sizes under each working model
specification. The efficiency bounds for distributions D1, D2, and D3
are 0.34, 1.05, and 55.23, respectively.
The estimators with model specification (i) would be expected to have
asymptotic relative efficiency equal to 1, which they approximately do at sample size
10000. The MSE of all estimators under severe positivity violations
(missingness mechanism D3) and model specifications (i), (ii), and (iii) is
smaller than the efficiency bound for sample sizes 200 and 500. This fact does not contradict
theory; it is expected since the TMLE is a substitution
estimator and therefore has variance bounded between zero and one,
even when the efficiency bound divided by the sample size falls outside of this interval. A
similar observation is true for model specification (ii) for all sample
sizes. In this case, misspecification of the missingness model causes
a substantial reduction in variability of the inverse probability
weights, which results in smaller finite sample
variance. However, we note that the relative efficiency gets closer to
its theoretical value of one as the sample size increases. In the
extreme case of D3 a sample size of 10000 was not large enough to observe
the properties predicted by asymptotic theory.
It was not expected that under D1, the TMLE estimators are approximately semiparametric efficient
for models (ii) and (iii). This may be a particularity of this
data generating mechanism, perhaps due to the low dimension of
the problem and the smoothness of this data generating
mechanism. As expected, the bias of the estimators
times square root of $n$ does not converge for model specification
(iv), since asymptotic theory dictates that in general at least one
of the working models must be correctly specified to imply
consistency of the TMLE.
Table~\ref{pcbiastable} shows the percent bias associated with each
estimator. The second TMLE implementation 2 performs better than its competitors in
finite samples under severe violations to the positivity assumption
(D3), particularly when the missingness model is
correctly specified (model specifications (i) and (iii)). However, under moderate positivity violation
(D2) and misspecification of the outcome mechanism (model specification (iii)) in large samples ($n=10000$), TMLE
implementation 2 performed worse than all of its competitors (MSE 1.63 vs
1.06). Implementations 3 and 4 did not perform particularly better
than the best of implementations 1 and 2 for any scenario under consideration.
\begin{table}[!htb]
\caption{Relative performance of the estimators ($n$ times MSE divided by the
efficiency bound). $\hat\psi_1$, $\hat\psi_2$, $\hat\psi_3$ and
$\hat\psi_4$ correspond to TMLE implementations 1, 2, 3, and 4,
respectively. Data generating mechanisms D1, D2, and D3 correspond to
expressions (\ref{D1}), (\ref{D2}), and (\ref{D3}), respectively. Model specification
(i) is correctly specified for $\mu$ and $p_M$, (ii) is correct
for $\mu$ and incorrect for $p_M$. (iii) is incorrect for $\mu$ and
correct for $p_M$, and (iv) is incorrect for both.}
\centering\scriptsize
\begin{tabular}{rc|cccc|cccc|cccc}\hline
\multirow{3}{*}{$n$} & & \multicolumn{12}{c}{Missingness Mechanism} \\
& Working & \multicolumn{4}{c}{D1} & \multicolumn{4}{c}{D2} & \multicolumn{4}{c}{D3} \\
& model &
$\hat\psi_1$ & $\hat\psi_2$ & $\hat\psi_3$
& $\hat\psi_4$ & $\hat\psi_1$ &
$\hat\psi_2$ & $\hat\psi_3$ & $\hat\psi_4$ &$\hat\psi_1$ & $\hat\psi_2$ & $\hat\psi_3$ & $\hat\psi_4$ \\\hline
\multirow{4}{*}{200} & (i) & 1.09 & 1.03 & 1.07 & 1.05 & 1.49 & 1.21 & 1.36 & 1.38 & 0.48 & 0.34 & 0.39 & 0.42 \\
& (ii) & 1.11 & 1.14 & 1.11 & 1.11 & 1.28 & 1.29 & 1.27 & 1.25 & 0.25 & 0.25 & 0.26 & 0.27 \\
& (iii) & 1.07 & 1.17 & 1.10 & 1.08 & 1.82 & 1.56 & 1.73 & 1.86 & 0.58 & 0.35 & 0.44 & 0.47 \\
& (iv) & 2.98 & 2.98 & 2.97 & 2.97 & 2.85 & 2.84 & 2.24 & 2.23 & 1.17 & 1.17 & 1.18 & 1.18 \\ \hline
\multirow{4}{*}{500} & (i) & 1.02 & 1.00 & 1.01 & 1.00 & 1.26 & 1.03 & 1.17 & 1.12 & 0.83 & 0.58 & 0.69 & 0.70 \\
& (ii) & 1.03 & 1.04 & 1.03 & 1.03 & 1.12 & 1.17 & 1.12 & 1.11 & 0.31 & 0.31 & 0.31 & 0.32 \\
& (iii) & 1.07 & 1.18 & 1.09 & 1.08 & 1.43 & 1.54 & 1.48 & 1.45 & 0.94 & 0.59 & 0.77 & 0.76 \\
& (iv) & 5.50 & 5.51 & 5.50 & 5.50 & 5.34 & 5.34 & 3.78 & 3.77 & 2.74 & 2.74 & 2.75 & 2.75 \\ \hline
\multirow{4}{*}{1000} & (i) & 1.01 & 1.00 & 1.01 & 1.00 & 1.19 & 1.05 & 1.14 & 1.07 & 1.09 & 0.79 & 0.94 & 0.93 \\
& (ii) & 1.06 & 1.07 & 1.06 & 1.06 & 1.11 & 1.16 & 1.10 & 1.10 & 0.37 & 0.37 & 0.37 & 0.38 \\
& (iii) & 1.01 & 1.11 & 1.02 & 1.02 & 1.18 & 1.56 & 1.29 & 1.18 & 1.25 & 0.86 & 1.10 & 1.07 \\
& (iv) & 9.89 & 9.89 & 9.89 & 9.89 & 9.74 & 9.74 & 6.29 & 6.29 & 5.27 & 5.26 & 5.27 & 5.27 \\\hline
\multirow{4}{*}{10000} & (i) & 0.99 & 0.99 & 0.99 & 0.99 & 1.04 & 0.99 & 1.01 & 0.99 & 1.07 & 1.00 & 1.04 & 1.07 \\
& (ii) & 1.05 & 1.06 & 1.06 & 1.06 & 1.06 & 1.11 & 1.06 & 1.06 & 0.54 & 0.53 & 0.54 & 0.54 \\
& (iii) & 1.01 & 1.10 & 1.01 & 1.01 & 1.06 & 1.63 & 1.03 & 1.03 & 1.36 & 1.31 & 1.53 & 1.24 \\
& (iv) & 87.40 & 87.40 & 87.40 & 87.40 & 87.26 & 87.25 & 53.14 & 53.14 & 52.11 & 52.11 & 52.10 & 52.10 \\\hline
\end{tabular}
\label{msetable}
\end{table}
\begin{table}[!htb]
\caption{Percent bias of each estimator. The true value of the
parameter is 0.36. $\hat\psi_1$, $\hat\psi_2$, $\hat\psi_3$ and
$\hat\psi_4$ correspond to TMLE implementations 1, 2, 3, and 4,
respectively. Data generating mechanisms D1, D2, and D3 correspond to
expressions (\ref{D1}), (\ref{D2}), and (\ref{D3}), respectively. Model specification
(i) is correctly specified for $\mu$ and $p_M$, (ii) is correct
for $\mu$ and incorrect for $p_M$. (iii) is incorrect for $\mu$ and
correct for $p_M$, and (iv) is incorrect for both.}
\centering\scriptsize
\begin{tabular}{rc|cccc|cccc|cccc}\hline
\multirow{3}{*}{$n$} & & \multicolumn{12}{c}{Missingness Mechanism} \\
& Working & \multicolumn{4}{c}{D1} & \multicolumn{4}{c}{D2} & \multicolumn{4}{c}{D3} \\
& model &
$\hat\psi_1$ & $\hat\psi_2$ & $\hat\psi_3$
& $\hat\psi_4$ & $\hat\psi_1$ &
$\hat\psi_2$ & $\hat\psi_3$ & $\hat\psi_4$ &$\hat\psi_1$ & $\hat\psi_2$ & $\hat\psi_3$ & $\hat\psi_4$ \\\hline
\multirow{4}{*}{200} & (i) & 0.40 & 0.00 & 0.20 & 0.10 & 3.40 & 0.80 & 1.90 & 1.70 & 25.00 & 5.50 & 3.00 & 9.50 \\
& (ii) & 0.20 & 0.20 & 0.10 & 0.10 & 1.50 & 0.90 & 1.30 & 0.80 & 18.20 & 17.90 & 17.90 & 17.30 \\
& (iii) & 0.10 & 1.30 & 0.60 & 0.20 & 5.30 & 6.80 & 6.70 & 6.00 & 39.30 & 8.00 & 11.30 & 22.50 \\
& (iv) & 15.20 & 15.20 & 15.20 & 15.20 & 21.50 & 21.40 & 21.50 & 21.50 & 33.10 & 33.90 & 33.20 & 33.10 \\ \hline
\multirow{4}{*}{500} & (i) & 0.10 & 0.00 & 0.10 & 0.00 & 1.20 & 0.00 & 0.60 & 0.20 & 20.10 & 2.90 & 8.40 & 10.80 \\
& (ii) & 0.10 & 0.10 & 0.10 & 0.10 & 0.80 & 0.60 & 0.70 & 0.60 & 17.50 & 17.50 & 17.40 & 17.30 \\
& (iii) & 0.10 & 0.60 & 0.40 & 0.10 & 1.40 & 3.20 & 2.60 & 1.70 & 31.00 & 2.70 & 20.90 & 27.40 \\
& (iv) & 15.10 & 15.10 & 15.10 & 15.10 & 21.10 & 21.10 & 21.10 & 21.10 & 33.30 & 33.80 & 33.30 & 33.30 \\ \hline
\multirow{4}{*}{1000} & (i) & 0.00 & 0.10 & 0.10 & 0.10 & 0.70 & 0.00 & 0.30 & 0.10 & 8.80 & 3.40 & 4.00 & 5.60 \\
& (ii) & 0.00 & 0.00 & 0.00 & 0.00 & 0.30 & 0.30 & 0.30 & 0.20 & 14.40 & 14.50 & 14.30 & 14.30 \\
& (iii) & 0.00 & 0.30 & 0.30 & 0.10 & 0.30 & 1.70 & 1.30 & 0.50 & 21.50 & 0.40 & 17.70 & 21.70 \\
& (iv) & 15.30 & 15.30 & 15.30 & 15.30 & 20.80 & 20.80 & 20.80 & 20.80 & 32.80 & 33.30 & 32.90 & 32.90 \\\hline
\multirow{4}{*}{10000} & (i) & 0.00 & 0.00 & 0.00 & 0.00 & 0.10 & 0.00 & 0.00 & 0.00 & 0.10 & 0.30 & 0.20 & 0.10 \\
& (ii) & 0.00 & 0.00 & 0.00 & 0.00 & 0.10 & 0.10 & 0.00 & 0.00 & 3.40 & 3.40 & 3.10 & 3.10 \\
& (iii) & 0.00 & 0.00 & 0.20 & 0.00 & 0.00 & 0.20 & 0.40 & 0.10 & 2.40 & 0.20 & 4.70 & 0.70 \\
& (iv) & 15.20 & 15.20 & 15.20 & 15.20 & 20.80 & 20.80 & 20.80 & 20.80 & 32.30 & 32.80 & 32.40 & 32.30 \\\hline
\end{tabular}
\label{pcbiastable}
\end{table}
\newpage
Another important question to ask when deciding on a parametric
submodel is the computational efficiency of the estimators.
Our simulations are in accordance to what we have observed in practice for this and other parameters, in that TMLE typically requires 6 or fewer iterations.
In the above simulations, the time required to compute the TMLE for a single data set
was typically less than a second.
\section{Example 2: Median regression}\label{ex2}
Consider the median regression model:
\begin{equation}
Y = g(X,\beta) + \delta \label{med_regr_model1},
\end{equation}
where $g(X,\beta)$ is a known, smooth function in $\beta$,
and where the conditional median of $\delta$ given $X$ is $0$ a.s.
This last condition is equivalent to having with probability 1 that
\begin{equation}
P(\delta \geq 0|X) \geq1/2 \mbox{ and } P(\delta \leq 0|X) \geq 1/2. \label{med_regr_model2}
\end{equation}
We let $\lambda(x,y)$ denote a dominating measure for the
distributions $P$ we consider, and denote by $p$ the density of
$P$. We say the above median regression model is correctly specified
if at the true data generating distribution $\mbox{$P_0$}$, we have for some
$\beta_0$ that the conditional median under $\mbox{$P_0$}$ of $Y - g(X,\beta_0)$ given $X$ is
$0$, with probability 1. Throughout, we do not assume the median regression model is correctly specified.
Define the following nonparametric extension of $\beta$ (which maps each density $p$ to a value
$\beta^\ast(p)$ in $\mathbb{R}^d$):
\begin{equation}
\beta^\ast(p) \equiv \arg \min_\beta E_p |Y -
g(X,\beta)|. \label{parameter_defn}
\end{equation}
We assume there is a unique minimizer in $\beta$
of $E_p |Y - g(X,\beta)|$. Under this assumption, if the median regression model
(\ref{med_regr_model1},\ref{med_regr_model2}) is correctly specified,
then this unique minimizer equals $\beta^\ast(p)$. However, even
when (\ref{med_regr_model1},\ref{med_regr_model2}) is misspecified,
the parameter in (\ref{parameter_defn}) is well defined as long as
there is a unique minimizer of $E_p |Y - g(X,\beta)|$. To simplify the notation, we denote $\beta^\ast(p)$ by $\beta(p)$ and
$\beta(\mbox{$p_0$})$ by $\beta_0$. The goal is to estimate $\beta_0$ based on $n$ i.i.d. draws
$O_i = (X_i,Y_i)$ from an unknown data generating distribution
$\mbox{$P_0$}$.
The nonparametric estimator of $\beta_0$ is the minimizer in $\beta$ of $\frac{1}{n}\sum_{i=1}^n
|Y_i - g(X_i,\beta)|$. \citet{Koenker1996} proposed a solution to this
optimization problem based on linear programming. Their methods are
implemented in the \texttt{quantreg} \cite{quantreg} R package. We develop a TMLE for $\beta_0$, in order to demonstrate it is a general methodology that can be applied to a variety of estimation problems, and to compare its performance versus the estimator of \citet{Koenker1996} that is explicitly tailored to the problem in this section.
The efficient influence function for the parameter
(\ref{parameter_defn}) in the nonparametric model, at distribution $P$, is
(up to a normalizing constant which we suppress in what follows):
\begin{eqnarray}
D(p,X,Y) \equiv -\left.\frac{d}{d\beta}g(X,\beta)\right|_{\beta =
\beta(p)}\mbox{sign}\{Y-g(X,\beta(p))\}. \label{eif}
\end{eqnarray}
In particular, we have
\begin{equation}
E_pD(p,X,Y) = 0, \label{score_property}
\end{equation}
for all sufficiently smooth $p$.
\paragraph{Construction of parametric submodel}
Given the estimate $p^k$ of $p_0$ at iteration $k$ of the TMLE algorithm, we construct
a regular, parametric model $\{p_\epsilon^k:\epsilon\}$
satisfying: (i) $p_0^k=p^k$ and (ii) $\frac{d}{d\epsilon}\log p_\epsilon^k(x,y)|_{\epsilon=0}=D(p^k,x,y)$ for each $x \in \mathcal{X}, y\in\mathcal{Y}$. We again use an exponential submodel as in (\ref{expfam1}), which in this case is
\begin{equation}
p_\epsilon^k(x,y) = p^k(x,y)\exp(\epsilon D(p^k,x,y))c(\epsilon,p^k), \label{submodel}
\end{equation}
where the normalization constant
$c(\epsilon,p) = \left[\int p(x,y)\exp(\epsilon D(p,x,y))d\lambda(x,y)\right]^{-1}$.
This parametric model is well-defined, regular, equals $p^k$ at $\epsilon=0$, and has score:
\begin{equation}
\frac{d}{d\epsilon}\left[\log p_\epsilon^k (x,y)\right] = D(p^k,x,y) -
c(\epsilon, p^k)\int D(p^k,x,y)\exp\{\epsilon D(p^k,x,y)\}p^k(x,y)d\lambda(x,y), \label{score1}
\end{equation}
under smoothness and integrability conditions that allow the interchange of the order of differentiation and
integration. It follows from
(\ref{score_property}) and (\ref{score1}) that the
score equals $D(p^k,x,y)$ at $\epsilon=0$, and therefore satisfies the conditions
(i) and (ii) described above.
\paragraph{Implementation of Targeted Maximum Likelihood Estimator}
We present an implementation of the TMLE applying the parametric submodel (\ref{submodel}). First, we
construct an initial density estimator $p^0(x,y)$. We let $p^0(x)$ be
the empirical distribution of $X$. We
fit a linear regression model for $Y$
given $X$ with main terms only, and let $p^0(y|X=x)$ be a normal
distribution with conditional mean as given in the linear regression
fit, and with conditional variance 1. We then define $p^0(x,y) \equiv
p^0(y|x)p^0(x).$ A more flexible method can be
used to construct the initial fit for the density of $Y$ given
$X$. Here we use this simple model to examine how well the
TMLE can recover from a poor choice for the initial density estimate.
Initializing $k=0$, the iterative procedure defining the TMLE involves the following
computations, at each iteration $k$ (where $a \leftarrow b$ represents setting $a$ to take value $b$):
\begin{eqnarray}
\beta^k & \leftarrow &\arg \min_\beta E_{p^k} |Y - g(X,\beta)|; \label{alg_step1} \\
D(p^k,X,Y) & \leftarrow & -\left.\frac{d}{d\beta}g(X, \beta)\right|_{\beta = \beta(p^k)}\mbox{sign}(Y-g(X,\beta(p^k))); \label{alg_step2} \\
p_\epsilon^k(x,y) & \leftarrow & p^k(x,y)\exp(\epsilon D(p^k,x,y))c(\epsilon,p^k); \label{submodel_again} \\
\hat\epsilon & \leftarrow &\arg \max_\epsilon \sum_{i=1}^n \log
p^k(X_i,Y_i)\exp\{\epsilon
D(p^k,X_i,Y_i)\}c(\epsilon,p^k); \label{alg_step3} \\
p^{k+1} & \leftarrow & p^k_{\hat\epsilon}.
\end{eqnarray}
The value of $\beta^k$ in (\ref{alg_step1}) is approximated by
grid search over $\beta$, where for each value of $\beta$ considered,
the expectation on the right hand side of (\ref{alg_step1}) is
approximated by Monte Carlo integration (based on generating 10000
independent realizations from the density $p^k$ and taking the empirical
mean over these realizations). The value of $\hat\epsilon$ in
(\ref{alg_step3}) is approximated by applying the Newton-Raphson
algorithm to the summation on the right side of
(\ref{alg_step3}), where we use the analytically derived gradient and Hessian
in the Newton-Raphson algorithm. The above process is
iterated over $k$ until convergence (we used $\hat\epsilon < 10^{-4}$
as stopping rule).
The density at the final iteration is denoted by
$p^\ast$, and the TMLE of $\beta_0$ is defined as $\beta_n\equiv
\beta(p^\ast)$. If the initial estimator of
$\mbox{$p_0$}(Y|X)$ is consistent, it is possible to use standard arguments for the analysis of
targeted maximum likelihood estimators \cite{vanderLaanRose11} to show
that this estimator is asymptotically linear with influence function
equal to the efficient influence function $D(\mbox{$p_0$},X,Y)$.
\paragraph{Simulation} We draw 10000 samples, each of
size 1000, of a two dimensional covariate $X=(X_1,X_2)$ by drawing $X_1\sim
U(0,1)$ and $X_2\sim U(0,1)$, with $X_1,X_2$ independent. We consider
two different outcome distributions for $Y$ given $X$; the outcomes
under each distribution are denoted by $Y_1,Y_2$, respectively.
The first outcome involves drawing $\delta_1\sim Exp(3)$, and setting
\begin{equation}
Y_1=-\frac{\ln(2)}{3} +
\expit(1.5X_1 + 2.5X_2) + \delta_1,\label{DR1}
\end{equation} where $\expit$ is the inverse of the
$\logit$ function $\logit(x)=\log(x/(1-x))$. This represents a case in which the error
distribution is skewed. The constant $\ln(2)/3$ was selected since it is the median of $Exp(3)$, which implies the median $Y_1$ given $X$ equals
$\expit(1.5X_1 + 2.5X_2)$.
The second outcome distribution involves drawing
$\delta_2\sim N(0,1)$ and setting
\begin{equation}
Y_2=\exp(X_1 + 2X_2) + \delta_2.\label{DR2}
\end{equation}
Note that we used $\exp$ in the above display instead of $\expit$.
We denote the first outcome distribution
(\ref{DR1}) by $D1$, and the second (\ref{DR2}) by $D2$.
We are interested in estimating the parameters
\begin{eqnarray}
\beta_0^{(1)} &=& \arg\min_\beta E|Y_1 - g(X,\beta)| \label{Y_1_param} \\
\beta_0^{(2)} &=& \arg\min_\beta E|Y_2 - g(X,\beta)|, \label{Y_2_param}
\end{eqnarray}
where $g(X,\beta)=\expit(\beta' X)$. The true value of $\beta_0^{(1)}$
is $(1.5, 2.5)$, whereas the true value of $\beta_0^{(2)}$ is
approximately $(2.1, 9.2)$ (obtained using Monte Carlo simulation).
The median regression model $g(X,\beta)=\expit(\beta' X)$
is a correctly specified model under the first outcome distribution, but is
incorrectly specified for the second outcome distribution.
However, the minimizers $\beta_0^{(1)}$ and
$\beta_0^{(2)}$ of the right sides of (\ref{Y_1_param}) and (\ref{Y_2_param}), respectively, are both well defined.
For each of the 10000 samples we computed the estimator described
above. The marginal distribution of $X$ was estimated by the empirical distribution in the given sample. The conditional distribution of $Y$ given
$X$ was misspecified by running a linear regression of $Y$ on
$(X_1,X_2)$ with main terms only,
and assuming that $Y$ is normally distributed with conditional
variance equal to one. This was done in order to assess how the TMLE
can recover from a poor fit of the initial densities resulting from a
distribution that is commonly used in statistical practice. We then computed
the MSE across the 10000 estimates as $E(||\hat \beta - \beta_0||^2)$,
where $||\cdot||$ represents the Euclidean norm. The results are
presented in Table \ref{tabMedReg}. For comparison, we
computed the same results for two other estimators: the quantile
regression function \texttt{nlrq()} implemented in the R package
\texttt{quantreg}, and a substitution estimator (SE) that is the
result of optimizing (\ref{alg_step1}) in the first iteration with
$p^k$ set to $p^0$.
\begin{table}[ht]
\caption{Square root of mean squared error (MSE) for estimators of
parameters (\ref{Y_1_param}) and (\ref{Y_2_param}). }\label{tabMedReg}
\centering
\begin{tabular}{rrr|rrr}
\hline
\multicolumn{3}{c|}{$\beta_0^{(1)}$} & \multicolumn{3}{c}{$\beta_0^{(2)}$}\\\hline
TMLE & \texttt{nlrq()} & SE & TMLE & \texttt{nlrq()} & SE\\
\hline
0.37 & 0.38 & 3.99 & 7.15 & 8.50 & 6.76 \\
\hline
\end{tabular}
\end{table}
The TMLE and the estimator of \citet{Koenker1996} perform
similarly for $\beta_0^{(1)}$, i.e., when the median regression model is correct.
The TMLE and SE perform better for estimating $\beta_0^{(2)}$, i.e., when
the median regression model is incorrectly specified. This is not
surprising since the estimator of \citet{Koenker1996} is designed for
the case where the median regression model is correctly specified.
\section{Example 3: The causal effect of a continuous exposure} \label{ex3}
We explore the use of an exponential family as a
parametric submodel only for certain components of the likelihood. Consider
a continuous exposure $A$, a binary outcome $Y$, and a set of covariates
$W$. For a user-given value $\gamma$ we are interested in estimating
the expectation of $Y$ under an intervention that causes a shift of
$\gamma$ units in the distribution of $A$ conditional on $W$. Formally, consider an i.i.d. sample of $n$ draws of the random variable $O=(W,A,Y)\sim \mbox{$P_0$}$. Denote
$\mu_0(A,W)\equiv E_{\mbox{$p_0$}}(Y|A,W)$, $p_{W,0}(W)$ the marginal
density of $W$ and $p_{A,0}(A|W)$ the conditional density of $A$
given $W$. We assume that these data were generated by a nonparametric
structural equation model \cite[NPSEM,][]{Pearl00}:
\[ W=f_W(U_W);\quad
A=f_A(W, U_A);\quad
Y=f_Y(A,W,U_Y),
\]
where $f_W$, $f_A$, and $f_Y$ are unknown but fixed functions, and
$U_W$, $U_A$, and $U_Y$ are exogenous random variables satisfying the
randomization assumption $U_A\mbox{$\perp\!\!\!\perp$} U_Y|W$. We are interested in the
causal effect on $Y$ of a shift of $\gamma$ units in $A$. Consider the following intervened NPSEM
\[ W=f_W(U_W);\quad
A_\gamma=f_A(W, U_A)+\gamma;\quad
Y_\gamma=f_Y(A_\gamma,W,U_Y).
\]
This intervened NPSEM represents the random variables that would have
been observed in a hypothetical world in which every participant
received $\gamma$ additional units of exposure $A$. \citet{Diaz12} proved that
\[E(Y_\gamma)=E_0\{\mu_0(A+\gamma, W)\}.\]
For each density $p$, define the parameter
\[\Psi(p)\equiv E_{p_W, p_A}\{\mu(A+\gamma, W)\},\]
where $\mu$, $p_A$, and $p_W$ are the outcome conditional
expectation, exposure mechanism, and
covariate marginal density corresponding to $p$,
respectively. We also use the notation $\Psi(\mu, p_A, p_W)$ to
refer to $\Psi(p)$. We are interested in estimating the true value of the parameter
$\psi_0\equiv \Psi(\mbox{$p_0$})$.
The efficient influence function of $\Psi(p)$ at $p$ is given by \cite{Diaz12} as:
\[D(p,O)\equiv \frac{p_A(A-\gamma|W)}{p_A(A|W)}\{Y-\mu(A, W)\} +
\mu(A+\gamma, W) - \Psi(p).\]
\paragraph{Construction of the parametric submodel}
Consider initial estimators $\mu^0(A, W)$ and $p_A^0(A|W)$, which can be
obtained, for example, through machine learning methods. We estimate
the marginal density of $W$ with its empirical
counterpart denoted $p_W^0$, and construct a sequence of parametric submodels for
$p_0$ by specifying each component as:
\begin{align*}
\logit \mu_\epsilon^k(A,W)&= \logit \mu^k (A, W) + \epsilon
H_Y^k(A, W)\\
p_{A,\epsilon}^k(A|W) & = c_1(\epsilon, W)p_A^k(A|W)\exp\{\epsilon H_A^k(A,W)\}\\
p_{W, \theta}^k(W) & = c_2(\theta, W)p_W^k(W)\exp\{\theta H_W^k(W)\},
\end{align*}
where
\begin{align*}
H_Y^k(A,W)&=\frac{p_A^k(A-\gamma|W)}{p_A^k(A|W)}\\
H_A^k(A,W)&=\mu^k(A+\gamma, W) - E_{p^k}\{\mu^k(A+\gamma, W)|W\}\\
H_W^k(W) & = E_{p^k}\{\mu^k(A+\gamma, W)|W\} - \Psi(p^k),
\end{align*}
and $c_1$, $c_2$ are the corresponding normalizing constants. The sum of the scores of these models at $\epsilon=0,\theta=0$ equals the
efficient influence function $D(p^k,O)$.
\paragraph{Implementation of Targeted Maximum Likelihood Estimator}
Following the TMLE template of Section \ref{tmle}, we have (where
the MLE of $\theta$ is $0$, due to the initial estimator of $p_W$ being the empirical distribution):
\begin{enumerate}
\item Compute initial estimators $\mu^0(A, W)$ and $p_A^0(A|W)$. For
example, $\mu^0$ and $p_A^0$ may be obtained through a stacked
predictor such as super learning \cite{vanderLaan&Polley&Hubbard07}. Super learners rely on a
user-supplied library of prediction algorithms to build a convex
combination with weights that minimize the cross-validated empirical
risk. In particular, the authors in the original paper \cite{Diaz12}
use a library containing various specifications of generalized linear models (GLMs), generalized
additive models, and Bayesian GLMs for $\mu^0$. The conditional
density $p_A^0$ is estimated using super learning in a library of
histogram-like density estimators, as proposed in
\cite{Diaz11}. Here we emphasize a particularly appealing feature of TMLE:
it allows the integration of machine learning methods with
semiparametric efficient estimation.
\item Construct
a sequence of updated density estimates $p^k$, $k=1,2,\dots$, where at each iteration $k$ we
estimate the maximizer of the relevant parts of
the log likelihood: \[\hat\epsilon =
\arg\max_{\epsilon}\sum_{i=1}^n\{Y_i\log\mu^k_\epsilon(A_i,W_i) +
(1-Y_i)\log(1-\mu^k_\epsilon(A_i,W_i)) + \log p_{A,\epsilon}^k(A_i,W_i)\}.\]
Define $p^{k+1}=p^{k}(\hat\epsilon)$
\item The previous step is iterated until convergence, i.e., until $\hat\epsilon\approx 0$. Denote the last step of the procedure by $k=k^*$.
\item The TMLE of $\psi_0$ is defined as the substitution estimator
$\hat\psi\equiv \Psi(p^{k^*})$.
\end{enumerate}
Optimization of the likelihood in step 2 is a convex optimization
problem that may be solved, for example, based on the Newton-Raphson
algorithm. Another option, implemented in the original paper using the R function \texttt{uniroot()}, is to
solve the estimating equation $S^k(\epsilon)=0$, where
\begin{multline}
S^k(\epsilon) = \sum_{i=1}^n\bigg\{[Y_i - \mu^k(A_i,W_i) -
\epsilon_1H_Y^k(O_i)]H_Y^k(O_i) + H_A^k(O_i) -
\\\frac{\int H_A^k(a, W_i)\
\exp\{\epsilon H_A^k(a, W_i)\}\
p_A^k(a|W_i)da}{\int \exp\{\epsilon
H_A^k(a, W_i)\}\ p_A^k(a|W_i)da}\bigg\}.
\end{multline}
In practice, the iteration process is carried out until
convergence in the values of $\hat\epsilon$ to approximately $0$ is
achieved. We denote
$\mu^\ast$ and $g_n^\ast$ the last values of the iteration, and
define the TMLE of $\psi_0$ as
$\psi_{n}\equiv \Psi(\mu^\ast, p_A^\ast, p_W^0)$. The variance
of $\psi_{n}$ can be estimated by the empirical variance of
$D(\mu^*,p_A^*, p_W^0,O)$. This is a consistent estimator of the
variance if both $p_A^0$ and $\mu^0$ are consistent. Simulations
studying the properties of this estimator were performed in the
original paper. The results of those simulations confirm the double
robustness of the TMLE (robustness to misspecification of one of the
estimates $\mu^0$ or $p_A^0$), it asymptotic efficiency, and its
superiority when compared to the inverse probability weighted
estimator. For more extensive discussion of the properties of this estimator we refer the
reader to \cite{Diaz12}.
\section{Discussion}
We presented several implementations of TMLE using parametric families
with convex log-likelihood in three examples. Since reliable and efficient algorithms exist for
convex optimization, parametric submodels with
convex log-likelihood may lead to computationally advantageous implementations of TMLE.
An important choice in any TMLE implementation is which
parametric submodel to use. We showed a simulation in which this choice
has a substantial impact on the performance of the targeted
maximum likelihood estimator, even at very large sample sizes. It is important to
consider the characteristics of each submodel before choosing an
estimator.
An additional consideration for the choice
of parametric family is ease of implementation. For example, for estimation of the mean
of a binary outcome missing at random, the TMLE using a logistic parametric submodel
from Section \ref{sec_onestep} converges in one step and is generally
faster and easier to implement than the alternatives we considered. However, under
severe violations of the positivity assumption, the
implementation of a TMLE presented in Section~\ref{second_onestep} may be more appealing than
the alternatives we considered, based on the results of our simulation.
Various estimators with desirable properties have been
proposed for some of the examples in this paper. Notably,
estimation of the expectation of an outcome missing at random has been
widely studied (see, e.g., \citet{Kang&Shafer07} for a review). Also, \citet{Haneuse2013} propose an estimator
of $\psi_0$ in Example 3 that relies on the correct specification of a
parametric model for the outcome expectation and
the conditional density of the exposure. TMLE, on the other hand, is
a general estimation template that allows the construction of
estimators for a considerable class of statistical problems, allowing
integration with data-adaptive estimation methods.
\section*{Acknowledgements}
We would like to thank Mark van der Laan for helpful discussions
that greatly improved this manuscript.
|
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}
| 6,559
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Get your expert high-quality articles on Godwins Removals published on multiple partner sites.
Godwins Removals Fonolive.com, #1 Social Classifieds.
Godwins Removals offers experienced and professional removal service to individuals and businesses looking to relocate their goods and furniture within London, the UK and Europe. With fully experienced and trained removal specialists, they have become the top choice for homeowners and businesses nationwide.
Share your Godwins Removals, London experience.
|
{
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| 315
|
{"url":"https:\/\/www.albert.io\/ie\/ap-physics-1-and-2\/graph-of-current-v-voltage","text":"Free Version\nModerate\n\n# Graph of Current v Voltage\n\nAPPH12-YTG39B\n\nA student connects a single resistor to a variable voltage source, then uses an ammeter to measure the current through the resistor at increasing voltages. The student\u2019s data is shown in the graph above.\n\nWhich of the following values is the resistance of the resistor?\n\nA\n\n$0.045 \\space \\Omega$\n\nB\n\n$22 \\space \\Omega$\n\nC\n\n$7.0 \\space \\Omega$\n\nD\n\n$1.6 \\space \\Omega$","date":"2017-03-23 18:22:33","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.35122230648994446, \"perplexity\": 938.7977098417164}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-13\/segments\/1490218187193.40\/warc\/CC-MAIN-20170322212947-00007-ip-10-233-31-227.ec2.internal.warc.gz\"}"}
| null | null |
Welcome to Onikewide's Blog
News,Entertainment, Lifestyle, Trend, Fashion, Inspiration and yes... Gossip! *Wink*
Mega Posts
NIGERIA GOSSIPS
About ONIKEWIDE
World Bank ranks Nigeria as one of the best places to do business
onikewide
onikewide 04:32:00 No comments:
Nigeria has moved up several places on the World Bank's Ease of Doing Business ranking..
Nigeria has made some progress on the World Bank's 'Ease of Doing Business' ranking.
The Ease of Doing Business is an index published periodically by the World Bank.
It is an aggregate figure that includes different parameters. These parameters indicate how easy or difficult it is to conduct business in a country.
The Ease of Doing Business compares business regulations in 190 countries across the world.
What is Nigeria's position now?
In the latest index from the World Bank, Nigeria is ranked 131 globally, moving up 15 places from its last ranking.
The World Bank office in the US (World Bank)
Enforcement of contracts entered was a key factor in Nigeria's ascent on the table. Wide ranging reforms by the federal government was also cited as a significant factor.
According to the Bretton Woods Institution: "Nigeria conducted reforms impacting six indicators, including making the enforcement of contracts easier, which placed the 200-million-person economy among the world's top improvers.
"Only two Sub-Saharan African economies rank in the top 50 on the ease of doing business rankings while most of the bottom 20 economies in the global rankings are from the region."
Not so good in Africa
Africa got a few knocks too, no thanks to poor infrastructure, bureaucratic bottlenecks and logistic concerns.
"Compared to other parts of the world, Sub-Saharan Africa still underperforms in several areas. In getting electricity, for example, businesses must pay more than 3,100% percent of income per capita to connect to the grid, compared to just over 400% in the Middle East and North Africa or 272% per cent in Europe and Central Asia.
When it comes to trading across borders and paying taxes, businesses spend about 96 hours to comply with documentary requirements to import, versus 3.4 hours in OECD high-income economies, and small and medium-sized businesses in their second year of operation need to pay taxes more than 36 times a year, compared to an average of 23 times globally," the World Bank wrote.
How Nigeria fared in the past
Nigeria was last ranked 146 among 190 economies.
In 2017, Nigeria was ranked 145.
The Ease of Doing Business in Nigeria averaged 145.09 from 2008 to 2018, reaching an all time high of 170 in 2014 and a record low of 120 in 2008.
The Nigerian presidency operates the Presidential Enabling Business Environment Council (PEBEC) overseen by Vice President Yemi Osinbajo.
PEBEC's main assignment is to initiate and implement reforms in Nigeria's business environment and in government processes.
Pop Star Pedi welcomes baby Girl with Girlfriend, Aviva
Pedi has welcomed his first Daughter with his Adorable
How to detect real Hennessy from fake. Cognac "Hennessy VSOP"
Consumption of brandy is growing from year To year, This
BREAKING- Actor 'The Rock' Finally Marries His Long-Time Girlfriend, Lauren Hashian
Hollywood actor, Dwayne Johnson popularly known as 'The
BBNaija: Mercy, Mike, Seyi, Gedoni, four other housemates up for eviction
Seven Big Brother Naija, BBNaija housemates, have been
BREAKING - "I Killed Him In Self Defence" - Corps Member Reveals Why She Hacked Man To Death In Akwa Ibom
Upon being interrogated by the police after being arrested, the
UPDATE - Nengi Reacts As Gov Diri Removes Her As Face Of Bayelsa, Appoints First Class Law Graduate
Governor Diri removed the Big Brother Naija star and
{PHOTO} Lady Breaks Up With Her Man After He Refused to Do 'Yahoo Yahoo'
A Nigerian man has revealed how he lost his girlfriend after
{VIDEO} Woman Recounts How She Was R*ped By The Man Hacked To Death By Corps Member In Akwa Ibom
A young lady identified as Effiong Laurel Scott has made
UPDATE - LASU Shuts Hostel As Three Students Test Positive For COVID-19
The hostel facilities were immediately closed for
BREAKING - 14 Reported Dead As Ikorodu Cult Clash Enters Day 3
Following the on-going cult clash between rival cult groups in
{PHOTO} Prophet Performing Money Ritual On Suspected Yahoo Boys In A River
In the viral video, the prophet was seen spraying money
Copyright 2016 © Welcome to Onikewide's Blog. Designed by Hung Wei-lee. Distributed by Newsprel.
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 9,954
|
Q: Gutenberg RichText multiline list with pre-formatted text control inputs? Is something like this even possible? Building a plugin and looking for guidance in building a block a list element with child elements. I want the user to be able to hit enter to create a new line (LI), but I want each line to include its own inputs/formatting (four inputs total: description, price, add on description, add on price) contained in their own tags, like a DIV or even B/STRONG. Help!
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,308
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import lombok.Data;
class DataOnLocalClass1 {
public static void main(String[] args) {
@Data class Local {
final int x;
String name;
}
}
}
class DataOnLocalClass2 {
{
@Data class Local {
final int x;
@Data class InnerLocal {
@lombok.NonNull String name;
}
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,593
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The men's 1500 metres at the 2015 World Championships in Athletics was held at the Beijing National Stadium on 27, 28 and 30 August.
Summary
The process of running rounds in the 1500 tends to select strategic experts because nobody would want to run hard three times in four days as this schedule would require. Since 2008 (excepting that bad race at the 2012 Olympics), the expert in this has been two-time defending champion Asbel Kiprop. But in case anybody wanted to run fast, Kiprop also left a message at the fastest race of the year in Monaco, where he blew away many of the members of this field by almost 2 seconds in his near miss of the world record. What makes Kiprop so dangerous is his ability to accelerate from the back of the field and in the final that is exactly where he went. Was he hiding or just waiting to pounce? With three other Kenyan teammates making it to the final, there was talk about a potential sweep. Timothy Cheruiyot and Elijah Motonei Manangoi took the race through an honest first two laps in 1:58.62. Only Aman Wote ran aggressively with them at the front, the other tacticians lining themselves up for the finish. Matthew Centrowitz, Jr. was the first to move forward as they came through for the bell. With 300 metres to go, Olympic champion Taoufik Makhloufi made his move, identical to the Olympics, Kiprop near the back of the pack beating only two Americans and boxed by Wote. Over the next 100 metres, Makhloufi opened a lead chase by Abdalaati Iguider. Kiprop slowed down to get out of the box, then ran around Wote out to lane 3. The tall Kenyan was now clearly moving faster than the rest of the field he was passing on the outside. As Kiprop swept past the field after the North African duo, only Silas Kiplagat came with him, these four breaking from the rest. As Kiprop caught Iguider, he reacted and ran even with Kiprop up to Makhloufi. With 50 metres to go, it was three abreast across the track with Kiplagat chasing Kiprop on the outside less than two metres back. Kiprop broke past the two North Africans and ran on to victory, while Iguider edged ahead of a spent Makhloufi. Out of nowhere (actually a distant fifth place) came sprinting Manangoi, faster than any of the leaders, drifting out to lane 3 for clear sailing. Passing three people in the last 10 metres, Manangoi crossed the finish line just ahead of a desperately diving Iguider to take silver, Iguider doing a full face plant to the track across the finish line holding on to bronze.
Records
Prior to the competition, the records were as follows:
Qualification standards
Schedule
Results
Heats
Qualification: First 6 in each heat (Q) and the next 6 fastest (q) advanced to the semifinals.
Semifinals
Qualification: First 5 in each heat (Q) and the next 2 fastest (q) advanced to the final.
Final
The final was held on 30 August at 19:45.
References
1500
1500 metres at the World Athletics Championships
|
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| 5,331
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{"url":"https:\/\/www.physicsforums.com\/threads\/deriving-equation-from-3d-euler-equations.643152\/","text":"# Deriving equation from 3D Euler Equations.\n\n## Homework Statement\n\nI've got the 3D Euler equations\n$\\frac{\\delta u}{\\delta t} + (u\\cdot \\nabla)u = -\\nabla p$\n$\\nabla \\cdot u = 0$\n\nI've been given that the impulse is\n$\\gamma = u + \\nabla\\phi$\n\n## Homework Equations\n\nAnd I need to derive\n$\\frac{D\\gamma}{Dt} = -(\\nabla u)^T \\gamma + \\nabla \\lambda$\n$\\frac{D\\phi}{Dt} = p - \\frac{\\left|u\\right|^2}{2} + \\lambda$\n\n## The Attempt at a Solution\n\nI've subbed the impulse equation into the first equation but don't really know where to go from there?","date":"2021-06-22 06:47:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7891795039176941, \"perplexity\": 1588.2347749827195}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623488512243.88\/warc\/CC-MAIN-20210622063335-20210622093335-00490.warc.gz\"}"}
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In the year to end October 2017 new build house prices rose on average by 5.0% across the UK which is down on last year's figure of 6.0%. If Greater London is taken out of the calculation and we take a crude average of the remaining regions, then the average house price growth is 4.2% which is slightly down on last year's figure of 4.6%. The latest Mortgage Market commentary from UK Finance says that housing market activity has been growing modestly since the start of the year. They note a shift in activity away from London and the South East towards the North and Wales and Scotland.
But overall sales volumes seem to be holding steady at present and the budget may yet stimulate the market.
|
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"redpajama_set_name": "RedPajamaC4"
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| 4,065
|
{"url":"https:\/\/nbviewer.ipython.org\/github\/davidrpugh\/numerical-methods\/blob\/master\/labs\/lab-1\/lab-1%20HW.ipynb","text":"# Numerical Methods for Economists: Lab Assignment The Solow (1956) Model\u00b6\n\nIn this lab assignment you will analyze a version of the Solow model with a constant elasticity of substituion (CES) production function and attempt to \"explain\" observed patterns in capital's share in the U.S. between 1950-2011.\n\nA CES production function looks as follows...\n\n$$Y(t) = \\bigg[\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\tag{1.2}$$\n\nwhere $0 < \\alpha < 1$ and $-\\infty < \\rho < 1$. The parameter $\\rho = \\frac{\\sigma - 1}{\\sigma}$ where $\\sigma$ is the elasticity of substitution between factors of production. The CES production technology is popular because it nests several interesing special cases. In particular, if factors of production are perfect substitutes (i.e., $\\sigma = +\\infty \\implies \\rho = 1$), then output is just a linear combination of the inputs.\n\n$$\\lim_{\\rho \\rightarrow 1} Y(t) = \\alpha K(t) + (1-\\alpha)A(t)L(t) \\tag{1.3}$$\n\nOn the other hand, if factors of production are perfect complements (i.e., $\\sigma = 0 \\implies \\rho = -\\infty$), then we recover the Leontief production function.\n\n$$\\lim_{\\rho \\rightarrow -\\infty} Y(t) = \\min\\left\\{\\alpha K(t), (1-\\alpha) A(t)L(t)\\right\\} \\tag{1.4}$$\n\nFinally, if the elasticity of substitution is unitary (i.e., $\\sigma=1 \\implies \\rho=0$), then output is Cobb-Douglas.\n\n$$\\lim_{\\rho \\rightarrow 0} Y(t) = K(t)^{\\alpha}(A(t)L(t))^{1-\\alpha} \\tag{1.5}$$\nIn\u00a0[\u00a0]:\nimport numpy as np\nimport pandas as pd\nfrom scipy import integrate, linalg, optimize\nimport matplotlib as mpl\nimport matplotlib.pyplot as plt\n\n# for the first few labs we will be working with models of growth\nimport growth\nimport pwt\n\n\n### (5 points) Part a)\u00b6\n\nShow that the CES production function as defined by equation 1.2 exhibits constant returns to scale.\n\nIn\u00a0[\u00a0]:\n\n\n\n### (10 points) Part b)\u00b6\n\nDerive the intensive forms for both the general CES production function as defined by equation 1.2 and for its Cobb-Douglas special case defined by equation 1.5. Show that both of these intensive production functions are concave.\n\nIn\u00a0[\u00a0]:\n\n\n\n### (5 points) Part c)\u00b6\n\nUsing your results from part b, complete the Python function below which defines output (per person\/effective person) in terms of capital (per person\/effective person) and model parameters.\n\nIn\u00a0[\u00a0]:\ndef ces_output(t, k, params):\n\"\"\"\nIntensive form for a CES production\nfunction.\n\nArguments:\n\nt: (array-like) Time.\nk: (array-like) Capital (per person\/effective person).\nparams: (dict) Dictionary of parameter values.\n\nReturns:\n\ny: (array-like) Output (per person\/ effective person)\n\n\"\"\"\n# extract params\nalpha = params['alpha']\nsigma = params['sigma']\nrho = # INSERT CODE HERE DEFINING RHO IN TERMS OF SIGMA!\n\n# nest Cobb-Douglas technology as special case\nif rho == 0:\ny = # INSERT CODE HERE!\nelse:\ny = # INSERT CODE HERE!\n\nreturn y\n\n\n### (5 points) Part d)\u00b6\n\nUsing your results from part b, complete the Python function below which defines the marginal product of capital (per person\/effective person) in terms of capital (per person\/effective person) and model parameters.\n\nIn\u00a0[\u00a0]:\ndef marginal_product_capital(t, k, params):\n\"\"\"\nMarginal product of capital with CES production function.\n\nArguments:\n\nt: (array-like) Time.\nk: (array-like) Capital (per person\/effective person).\nparams: (dict) Dictionary of parameter values.\n\nReturns:\n\nmpk: (array-like) Derivative of output with respect to capital, k.\n\n\"\"\"\n# extract params\nalpha = params['alpha']\nsigma = params['sigma']\nrho = # INSERT CODE HERE DEFINING RHO IN TERMS OF SIGMA!\n\n# nest Cobb-Douglas technology as special case\nif rho == 0:\nmpk = # INSERT CODE HERE!\nelse:\nmpk = # INSERT CODE HERE!\n\nreturn mpk\n\n\n### (5 points) Part e)\u00b6\n\nDerive the equation of motion for capital per effective worker when the general CES production function defined by equation 1.2 and for the Cobb-Douglas special case defined by equation 1.5.\n\nIn\u00a0[\u00a0]:\n\n\n\n### (5 points) Part f)\u00b6\n\nUsing your results from parts d) and e) and the Python function defining the equation of motion for capital (per person\/effective person) complete the Python function which defines the Jacobian for the Solow model.\n\nIn\u00a0[\u00a0]:\ndef equation_of_motion_capital(t, k, params):\n\"\"\"\nEquation of motion for capital (per person\/effective person).\n\nArguments:\n\nt: (array-like) Time.\nk: (array-like) Capital (per person\/effective person).\nparams: (dict) Dictionary of parameter values.\n\nReturns:\n\nk_dot: (array-like) Time-derivative of capital (per person\/effective\nperson).\n\n\"\"\"\n# extract params\ns = params['s']\nn = params['n']\ng = params['g']\ndelta = params['delta']\n\ny = ces_output(t, k, params)\n\nk_dot = s * y - (n + g + delta) * k\n\nreturn k_dot\n\nIn\u00a0[\u00a0]:\ndef solow_jacobian(t, k, params):\n\"\"\"\nThe Jacobian of the Solow model.\n\nArguments:\n\nt: (array-like) Time.\nk: (array-like) Capital (per person\/effective person).\nparams: (dict) Dictionary of parameter values.\n\nReturns:\n\njac: (array-like) Value of the derivative of the equation of\nmotion for capital (per worker\/effective worker) with\nrespect to k.\n\n\"\"\"\n# extract params\ns = params['s']\nn = params['n']\ng = params['g']\ndelta = params['delta']\n\nmpk = #INSERT YOUR CODE HERE\n\nk_dot = s * mpk - (n + g + delta)\n\nreturn k_dot\n\n\n### (5 points) Part g)\u00b6\n\nIn the cell below, create a Python dictionary called default_params using the following values: $\\alpha$ = 0.33, $\\delta$ = 0.04, $\\sigma$ = 1.0, $g$ = 0.02, $n$ = 0.01, $s$ = 0.15, $L(0)$=1.0, $A(0)$=1.0.\n\nIn\u00a0[\u00a0]:\n# INSERT CODE HERE!\n\n\n### (5 points) Part h)\u00b6\n\nIn the cell below, create instance of the SolowModel class called model using the results from parts c), d), f) and g).\n\nIn\u00a0[\u00a0]:\n# INSERT CODE HERE!\n\n\n### (10 points) Part i)\u00b6\n\nDerive an analytic expression for the steady state value of capital (per person\/effective person) using your result from part e) and use your result to complete the Python function in the cell below defining the analytic steady state value for $k$ as a function of model parameters.\n\nIn\u00a0[\u00a0]:\ndef analytic_k_star(params):\n\"\"\"Steady-state level of capital (per person\/effective person).\"\"\"\n# extract params\ns = params['s']\nn = params['n']\ng = params['g']\nalpha = params['alpha']\ndelta = params['delta']\nsigma = params['sigma']\nrho = # INSERT CODE HERE DEFINING RHO IN TERMS OF SIGMA!\n\n# nest Cobb-Douglas technology as special case\nif rho == 0:\nk_star = # INSERT CODE HERE!\nelse:\nk_star = # INSERT CODE HERE!\n\nreturn k_star\n\n\n### (5 points) Part j)\u00b6\n\nUsing the code from the lab session as a guide, create a Python dictionary called solow_steady_state_funcs containing your result from part i) and add it to the model.\n\nIn\u00a0[\u00a0]:\n# INSERT YOUR CODE HERE!!\n\n\nExecute the code in the cell below to calibrate the model for the U.S. using data from the Penn World Tables.\n\nIn\u00a0[\u00a0]:\n# calibrate the model!\ngrowth.calibrate_ces(model, 'USA', x0=[0.5, 0.5], bounds=None)\n\n# display the parameters...\nmodel.params\n\n\n### (5 points) Part k)\u00b6\n\nUsing the code examples from the lab as a guide, generate a plot of the Solow diagram demonstrating how the output, actual investment, and breakeven investment curves shift as a result of a 50% increase in $\\sigma$ (i.e., the elasticity of substitution between capital and effective labor). Explain why, and in which direction, each curve shifts. Discuss the impact on the steady state levels of capital, output, and consumption per effective person.\n\nIn\u00a0[\u00a0]:\n# INSERT YOUR CODE HERE!\n\n\n### (5 points) Part l)\u00b6\n\nUsing code from the lab as a guide, generate impulse response functions (IRFs) in for the Solow model following a 50% increase in the elasticity of substitution between capital and effective labor, $\\sigma$. Discuss the resulting IRFS.\n\nIn\u00a0[\u00a0]:\n# INSERT YOUR CODE HERE!\n\n\n### (5 points) Part m:\u00b6\n\nUsing your results from part b), derive an expression for the elasticity of output per effective person with respect to capital per effective person, $\\alpha_k$, as a function of capital per effective person, $k$, and model parameters.\n\nIn\u00a0[\u00a0]:\n\n\n\n### (5 points) Part n)\u00b6\n\nDifferentiate your result from part m) with respect to capital per effective person, $k$, and discuss under what conditions the derivative will be positive, negative, or zero.\n\nIn\u00a0[\u00a0]:\n\n\n\n### (5 points) Part o)\u00b6\n\nUse the fact that $\\frac{\\partial k}{\\partial s} > 0$ and the result from part n) to relate the sign of $\\frac{\\partial \\alpha_k(k)}{\\partial s}$ to the elasticity of substitution between capital and effective labor.\n\nIn\u00a0[\u00a0]:\n\n\n\n### (15 points) Part p)\u00b6\n\nThe code in the cell below regresses $\\alpha_k(k)$ on the investment's share of GDP for the U.S., $s$ during two different time periods: 1950-1970 and 1970-2011. Can you \"explain\" these pattern using your result from part o)?\n\nIn\u00a0[\u00a0]:\nfig = plt.figure(figsize=(8,6))\n\n# capital's share for US (pre-1970)\ny = 1 - model.data.labsh.loc[:1970]\n\n# savings rate for US (pre-1970)\nx = model.data.csh_i.loc[:1970]\n\n# regress capital's share on savings rate\nres1 = pd.ols(y=y, x=x)\n\nax1.scatter(x, y)\nax1.set_xlabel('s', family='serif', fontsize=15)\nax1.set_ylabel(r'$\\alpha_k(k)$', fontsize=15, family='serif', rotation='horizontal')\nax1.set_title('U.S. pre-1970', family='serif', fontsize=15)\n\n# plot regression line pre-1970\ngrid = np.linspace(0.15, 0.25, 100)\nax1.plot(grid, res1.beta[1] + res1.beta[0] * grid, 'r')\n\n# capital's share for US (post-1970)\ny = 1 - model.data.labsh.loc[1970:]\n\n# savings rate for US (post-1970)\nx = model.data.csh_i.loc[1970:]\n\n# regress capital's share on savings rate post-1970\nres2 = pd.ols(y=y, x=x)\n\nax2.scatter(x, y)\nax2.set_xlabel('s', family='serif', fontsize=15)\nax2.set_title('U.S. post-1970', family='serif', fontsize=15)\n\n# plot regression line post-1970\ngrid = np.linspace(0.15, 0.25, 100)\nax2.plot(grid, res2.beta[1] + res2.beta[0] * grid, 'r')\n\nfig.suptitle(\"Patterns in capital's share for the U.S?\", x=0.5, y=1.05,\nfontsize=20, family='serif')\nfig.tight_layout()\nplt.show()\n\nIn\u00a0[\u00a0]:\n# summary of the regression results for 1950-1970\nprint res1\n\nIn\u00a0[\u00a0]:\n# summary of the regression results for 1970-2011\nprint res2\n\nIn\u00a0[\u00a0]:","date":"2022-09-29 11:12:29","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 4, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5254571437835693, \"perplexity\": 5252.775904301632}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-40\/segments\/1664030335350.36\/warc\/CC-MAIN-20220929100506-20220929130506-00584.warc.gz\"}"}
| null | null |
\section{Introduction}
Metastable aluminum scandium nitride (denoted by Al$_{1-x}$Sc$_x$N or (Al,Sc)N in the following) with the wurtzite-type crystal structure belongs to the class of polar-piezoelectric materials. It can be synthesized up to approximately $x\simeq0.41$ by reactive DC or RF magnetron sputtering and is known to have outstanding electroacoustic properties, surpassing reported values for all other group-III
nitrides.\cite{Matloub2011,Umeda2013,Konno2014,Parsapour2018,Kurz2019,Ichihashi2014,Ichihashi2016,
Carlotti2017,Lu2018,Mertin2018}
The electroacoustic properties of (Al,Sc)N depend strongly on the Sc concentration, which offers an additional degree of freedom for adjusting, e.g., the phase velocity and electromechanical coupling in the design of resonator devices.\cite{Wingqvist2010,Feil2019}
Experimentally, elastic and piezoelectric tensor components have been acquired from acoustic resonance experiments\cite{Matloub2011,Umeda2013,Konno2014,Parsapour2018,Kurz2019} or Brillouin scattering\cite{Ichihashi2014,Ichihashi2016,Carlotti2017} on (Al,Sc)N thin films with usually low Sc concentrations. Recently, the full set of electroacoustic properties was determined experimentally from Al$_{1-x}$Sc$_x$N thin films in a large range of compositions, $0\le x\le 0.32$, from the same material source using Rayleigh-type waves in surface acoustic wave (SAW) resonators.\cite{Kurz2019}
The elastic and piezoelectric properties of (Al,Sc)N have also been obtained theoretically by means of density functional theory (DFT).\cite{Tasnadi2010, Hoglund2010, Zhang2013, Caro2015}
However, the quantitative computation of material properties of randomly disordered alloys remains a difficult and time consuming task and raises principal conceptual questions.
We present here a comprehensive study of the electro\-acoustic properties of aluminum scandium nitride. The full set of material property data relevant for electroacoustic device design, namely the full tensors of elastic and piezoelectric constants, are computed by means of atomistic simulations based on DFT. A combinatorial approach is chosen which includes a large number of structure models and allows for a statistical analysis of the microscopic structural parameters, namely bond lengths and bond angles. This analysis gives insight into the microscopic origin of the observed highly non-linear dependence of the most relevant elastic and piezoelectric constants as a function of Sc content.
The paper is divided into three major sections that present and discuss the results for the structural parameters (Sec.\ \ref{sec:model_structures}), the elastic tensor (Sec.\ \ref{sec:Elastic_tensor}), and the piezoelectric tensor (Sec.\ \ref{sec:Piezo_tensor}) of Al$_{1-x}$Sc$_x$N. A summary is given in Sec.\ \ref{sec:summary}.
\section{Methodology}
\subsection{Modelling of disorder}
Mixed crystals and random alloys are characterized by two (or more) atomic species sharing the same (sub)lattice without giving rise to long range order. The modeling using DFT simulations of bulk materials requires the use of supercells containing a limited number of atoms (typically from a few tens to a few hundreds) in combination with periodic boundary conditions. Therefore, every structure model of finite size will be biased by the choice of the specific disorder representation. One possibility to address this problem is to construct specific model structures with as many atoms as possible (limited by computational resources) for which site occupation correlations are minimized. Such representative structure models are referred to as special quasirandom structures (SQS).\cite{Zunger1990}
The advantage of the SQS approach is that it reduces the propensity of artifacts generated by a special (e.g. highly symmetric) local atomic environment. The drawback is the need of rather big supercells. Therefore, often only a single SQS supercell is examined as being representative for a specific atomic composition ratio. However, a single SQS structure is not a unique representation of a disordered alloy, even for large supercells. Moreover, the assumption of a purely random distribution of the different elements on the lattice is not a unique choice and in general there is the possibility of short range correlations.
A second possibility to model mixed crystals is to take a combinatorial approach and to study the large variety of different realizations belonging to the same chemical composition and to extract physical properties by an appropriate averaging procedure. Here, the variation in the physical property of interest may be traced back to specific local atomic environments. This opens up the possibility of gaining a deeper understanding of the interplay of structural elements and material properties. Both theoretical approaches, the SQS-method and the combinatorial approach, have advantages and disadvantages and complement each other. In this work we take the second approach.
In order to model the (Al,Sc)N alloy with random distribution of Al and Sc atoms on the metal sublattice we used various supercell representations with varying Sc content. It is necessary to find a good compromise for the choice of the supercell models regarding the following three aspects: (i) A reasonable number of representative structure models for each Sc content are required in order to account for the influence of different local atomic configurations and to obtain reasonable statistics with respect to the local atomic environments considered. (ii) The supercell size should be large enough to avoid serious finite size effects. (iii) The supercell size should be small enough to keep the computational resources for a precise evaluation of the material parameters at a tractable level. We have therefore chosen supercell models which contain 36 atoms in order to adequately address the above mentioned three points (see Sec. \ref{sec:model_structures}).
\subsection{Computational settings}
The calculation of elastic and piezoelectric constants was carried out using the PWscf code of the Quantum Espresso (QE) software package \cite{PWSCF, Giannozzi2009} using the GGA-PBE functional for exchange-correlation. The wave functions of the valence electrons are represented by a plane-waves basis set with a cutoff energy of 55 Ry (1 Rydberg $\approx 13.606$ eV), and the electron density and effective Kohn-Sham potential by discrete Fourier series with a cutoff energy of 440 Ry. The interactions of valence electrons with the atomic nuclei and core electrons are described by pseudopotentials taken from the open-source
Standard Solid State Pseudopotentials (SSSP) library.\cite{Prandini2018, Lejaeghere2016} Here, ultrasoft pseudopotentials were chosen for N and Sc, while the pseudopotential for Al is of PAW type. Brillouin-zone integrals for the 36-atom supercells were evaluated on a Monkhorst-Pack mesh of 3x3x6 k-points with a Gaussian smearing of 0.01 Ry. The convergence threshold was set to 10$^{-5}$ Ry for the total energy and to 10$^{-4}$ Ry/Bo (1 Bohr = 0.529\AA) for the forces on atoms. Elastic stresses and interatomic forces were relaxed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm.
\section{Structure of (Al,Sc)N}
\label{sec:model_structures}
This section introduces our representation of disordered model structures for (Al,Sc)N. The energy criterion guiding the choice of model structures is presented in Sec. \ref{subsec:low_E_SCmodels} and the evaluation of lattice parameters in Sec.\ \ref{subsec:lattice_param}. An explanation of the origin of the observed highly anisotropic change of lattice parameters in terms of bond lengths and bond angles is given in Sec.\ \ref{subsec:origin_anisotropy}.
\begin{figure}[]
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(85,38)(0,0)
\put(0,0){\includegraphics[width=3cm,draft=false]{Fig1a_AlN_wurtzite.eps}}
\put(40,0){\includegraphics[width=4.5cm,draft=false]{Fig1b_Sketch_supercell.eps}}
\end{picture}
\caption{
Left: The AlN unit cell of the wurtzite crystal structure which is characterized by the hexagonal lattice parameters $\alat$ and $\clat$ and one internal structure parameter $u$. The latter determines the relative shift of the N sublattice with respect to the Al sublattice. Right: Top view on the 36-atom supercell illustrating the two shifted hexagonal lattices of the wurtzite structure and the positions of the 18 metal atoms.
\label{fig:wurtzite}}
\end{center}
\end{figure}
\subsection{Low-energy supercell realizations of (Al,Sc)N}
\label{subsec:low_E_SCmodels}
In this work we consider supercell models which contain 36 atoms and are built from 3x3x1 AlN wurtzite unit cells with individual Al atoms being substituted by Sc atoms, c.f.\ Fig.\ \ref{fig:wurtzite}.
The choice of the representative set of disorder configurations is guided by comparing the DFT total energies of the various possible atomic configurations at fixed Al:Sc ratio for this supercell size. These total energies are the ground-state energies of the structurally optimized supercell models which are obtained by relaxation of the atom positions and the cell shape (i.e. lattice parameter $\alat$ and $\clat$) to zero elastic stress and zero atomic forces. In other words, the lattice constants and atomic coordinates are determined such that the total energy is minimal for the given distribution of Al and Sc atoms on the metal sublattice in the supercell.
\begin{figure}[]
\begin{center}
\includegraphics[width=0.91\columnwidth]{Fig2a_Emix_vs_x.eps}
\includegraphics[width=0.9\columnwidth]{Fig2b_relEform_vs_x.eps}
\caption{Formation enthalpies of metastable wurtzite (Al,Sc)N.
Upper panel: Formation enthalpies $H_f$ with respect to the binary nitride phases, evaluated for all the inequivalent 36-atom supercells that are combinatorially possible. Data taken from Refs. [\onlinecite{Zhang2013, Hoglund2010}] are shown for comparison. Lower panel: Relative formation energy $\Delta H_f$ zoomed in on the low-energy range. Here, $\Delta H_f$ is defined as the difference in formation energy with respect to the lowest-energy structure at each given $x$. Red circles mark the structures for the detailed analysis which subsequently enter the fitting of the functional dependence of the material properties on the Sc content.
\label{fig:Eform}}
\end{center}
\end{figure}
Note that we have kept the hexagonal symmetry for our supercell models in the structural optimization, i.e. we optimized the cell volume and c/a ratio while keeping the angles in the hexagonal system fixed.
Microscopically there will be local shear strains, because the hexagonal supercell symmetry is broken in most cases of disordered arrangements of Sc atoms on Al sites.
However, due to the periodic boundary conditions used in the DFT simulations, we always have a structure with identical atomic arrangements in the neighboring supercells. This is not the case in the macroscopic experimental realization of a (truly) disordered material. Here, strain effect average out and the wurtzite crystal structure is observed experimentally with zero off-diagonal elements in the lattice matrix. Therefore, by keeping the hexagonal shape fixed for our supercell models, we eliminate all microscopic broken-symmetry effects in the simulations like in the experiments.
We have screened the ground-state energy (total energy) for all the Al$_{18-n}$Sc$_n$N$_{18}$ supercells, which are combinatorically possible. Symmetry inequivalent structures were generated using the software package SOD.\cite{Grau2007} While this results in only a small number of structures for small numbers $n$ of Sc atoms in the 36 atom supercell, namely 1, 5 and 14 inequivalent structures for $n=1$, 2, and 3, respectively, this number grows considerably at higher Sc content. For $n=4$, 5, 6, 7 and 8 there are 46, 99, 219, 336 and 475 structures and for a Sc content of 50\% the wurtzite structure has 504 inequivalent possibilities for how to distribute the 9 Sc atoms on the 18 metal sublattice sites.
The upper panel of Fig.\ \ref{fig:Eform} displays the computed formation enthalpy $H_f$ for all 36-atom supercell realizations as a function of the Sc content $x=n/18$. Here, $H_f$ is defined
with respect to the two binary nitride phases, namely wurtzite AlN and cubic rocksalt-type ScN, and is computed as weighted difference in total energies.
Wurtzite (Al,Sc)N is known to be thermodynamically metastable (i.e. $H_f >0$) and can only be stabilized experimentally as thin films. Other numerical data taken from literature \cite{Zhang2013, Hoglund2010} are shown for comparison. Note that the respective authors have used 128-atoms SQS supercells with one specifically selected distribution of Sc atoms for each considered value of Sc content.
\begin{figure}[]
\begin{center}
\includegraphics[width=\columnwidth]{Fig3_lattice_param.eps}
\caption{
Lattice parameters $\alat$ and $\clat$ as a function of the Sc content $x$. The results of the quadratic fitting to the dataset are shown as solid lines. Results for $N=128$ SQS supercells taken from literature\cite{Zhang2013, Hoglund2010} are shown for comparison. The dashed blue line indicates Vegard's rule, i.e.\ the linear interpolation between the properties of the two binary compounds AlN and hexagonal ScN.
\label{fig:alat_clat}}
\end{center}
\end{figure}
The lower panel of Fig.\ \ref{fig:Eform} shows a close-up on the low-energy range and plots the relative formation energy $\Delta H_f$, which is the energy difference in formation energy with respect to the lowest energy structure at each given $x$.
For (i) the further analysis of the structural parameters, (ii) the evaluation of elastic and piezoelectric tensors, and (iii) the extraction of their functional dependence on $x$, we have selected a set of lowest-energy structures for each Al:Sc ratio considered. These structures are marked by red symbols in Fig.\ \ref{fig:Eform}. Naturally, for $n=0$ and $1$ there is only one model structure each and for $n=2$ we have taken all five available structures. For $n=3$, 4, 5, 6, and 7 we have chosen the six lowest-energy structures, each. As the energetical separation between the individual structures becomes very small at large Sc content we have selected 11 and 15 sample structures for $n=8$ and 9, respectively.
Note that in the thin-film-deposition synthesis of such disordered semiconductor alloys it is equally unlikely that the resulting film yields a super-structure corresponding to the lowest-energy structure model or that it has a completely randomly disordered structure. Therefore, we decided to analyze not only the particular lowest energy structure at each given Al/Sc ratio but a larger ensemble of structures in the given energy range (shown in the lower panel of Fig.\ \ref{fig:Eform}) with equal statistical weights.
\subsection{Results: Structural parameters of (Al,Sc)N}
\label{subsec:lattice_param}
Our results for the optimized lattice parameters $\alat$ and $\clat$ are shown in Fig.\ \ref{fig:alat_clat} (see Fig.\ \ref{fig:wurtzite} for the definition of these quantities). They are found to be in very good agreement with the data from Refs.\ [\onlinecite{Hoglund2010, Zhang2013}] and indicate that our combinatorial supercell approach yields equivalent results to theirs obtained with the much larger 128-atoms cells. Naturally, the $N=36$ supercells show a dependency on the specific distribution of Sc atoms in the cell, which becomes more pronounced at larger $x$. The authors of Refs.\ [\onlinecite{Hoglund2010, Zhang2013}] each have used one specifically selected 128-atoms supercell obtained via the SQS-approach for each Sc-concentration $x$, at the expense of using a relatively low plane-wave energy cut-off and k-points density. It is interesting to note that, although the SQS are designed to distribute the Sc atoms in an uncorrelated manner as well as possible, the results of Refs.\ [\onlinecite{Hoglund2010, Zhang2013}] obtained with two distinct disorder representations differ noticeably and in a similar range as our data.
In order to extract the functional dependence of the calculated structural parameters on the Sc content we have fitted a quadratic function to our selected set of data points. Therefore we have first averaged the datapoints separately for each $x$ value (c.f.\ black filled circles in Fig.\ \ref{fig:alat_clat}) and then applied a least-squares fitting procedure where the value of the quadratic fitting function at $x=0$ was kept fixed to the respective data point. The results for the variation in lattice parameters with Sc content $x$ are
\begin{eqnarray}
\alat(x) &=& 3.131 \left(1 + 0.126\,x + 0.077\,x^2 \right)\,{\rm \AA},\\
\clat(x) &=& 5.020 \left(1 + 0.073\,x - 0.223\,x^2 \right)\,{\rm \AA}.
\end{eqnarray}
The corresponding quadratic fit of the respective cell volume data yields the mass density
\begin{eqnarray}
\rho(x) &=& 3.194 \left(1 + 0.108\,x + 0.030\,x^2 \right)\,{\rm g/cm^3}.
\end{eqnarray}
\begin{table}[]
\begin{center}
\begin{tabular}{l c c c c c c c}
& $\alat$ [\AA] & $\clat$ [\AA] & $u$ & $\alpha$ [$^\circ$] & $\beta$ [$^\circ$] & $\ell_{ab}$ [\AA] & $\ell_{c}$ [\AA]\\
\hline
w-AlN & 3.131 & 5.019 & 0.381 & 108.2 & 110.7 & 1.903 & 1.915 \\
h-ScN & 3.723 & 4.498 & 0.5 & 90 & 120 & 2.149 & 2.249 \\
average & 3.437 & 4.759 & 0.441 & 99.2 & 115.4 & 2.026 & 2.082
\end{tabular}
\caption{
Equilibrium lattice parameters $\alat$ and $\clat$, internal parameter $u$, bond angles $\alpha$ and $\beta$,
and bond lengths $\ell_{ab}$ and $\ell_{c}$ for wurtzite AlN and hexagonal ScN from
DFT calculations. (See Figs.\ \ref{fig:wurtzite} and \ref{fig:geom_def} for the geometric definitions.) The third line gives the arithmetic mean of the values of \mbox{w-AlN} and \mbox{h-ScN}.
Note that the equilibrium lattice parameter of cubic ScN obtained
with comparable numerical settings is 4.509~\AA, yielding a ScN bond length of 2.254~\AA.
\label{tab:binary_phases}}
\end{center}
\end{table}
The evolution of the lattice parameters with increasing Sc content is found to be highly anisotropic in agreement with experimental results.\cite{Kurz2019} The lattice parameter $\alat$ grows essentially linearly following Vegard's rule
$\alat(x)\sim (1-x) a_{\rm{AlN}} + x\, a_{\rm{ScN}}$,
where $a_{\rm{AlN}}$ and $a_{\rm{ScN}}$ are the equilibrium lattice parameters of wurtzite AlN and hexagonal ScN. Note that the latter structure corresponds to wurtzite with the internal parameter set to $u=0.5$ and is a hypothetical crystal structure for ScN.\cite{Farrer2002,Tasnadi2010} The equilibrium crystal structure of ScN is cubic rocksalt. However, the Sc--N bond length in hexagonal ScN is very close to the one of cubic rocksalt ScN.
In contrast, the lattice parameter $\clat$ changes on a much smaller scale and remains almost constant for a wide range of Sc content. This behavior is very different from the other mixed wurtzite nitrides like (Al,Ga)N or (Al,In)N (see e.g.\ Ref.\ \onlinecite{Dridi2003} and Refs.\ therein) and has so far not yet been fully explained. Our set of model structures, however, allows us to clarify the origin of the anisotropic dependence on the Sc content, as discussed in the following section.
\begin{figure}[b]
\begin{center}
\includegraphics[width=0.48\columnwidth,draft=false]{Fig4a_MN4_angles.eps}
\includegraphics[width=0.48\columnwidth,draft=false]{Fig4b_MN4_length.eps}
\caption{
Definition of the bond angles (left) and bond lengths (right) for the tetrahedral MN$_4$ structural unit. Here M refers to a metal atom, M=Al or Sc.
While the three angles $\alpha_i$ ($i=1,2,3$) for all three nitrogen atoms in the basal plane are equal in perfect wurtzite AlN, they individually differ in the mixed, symmetry-broken case of (Al,Sc)N compounds. The same applies for the angles $\beta_i$ and $\delta_i$ and the bond lengths $\ell_{ab,i}$.
\label{fig:geom_def}}
\end{center}
\end{figure}
\subsection{Microscopic origin of anisotropic change of lattice parameters}
\label{subsec:origin_anisotropy}
The almost perfect tetrahedra AlN$_4$ of nearest-neighbor atoms in bulk wurtzite AlN are characterized by two bond lengths $\ell_c$ and $\ell_{ab}$ for the Al--N bond parallel to the lattice vector c ($z$ axis) and the three bonds forming the basal plane (xy plane) of the tetrahedra, respectively. Moreover, there is one characteristic angle $\alpha$ between these two types of bonds, or alternatively, the angle $\beta$ between each of the two basal plane bonds may be chosen. There is a direct correspondence\cite{Ambacher2002} of these parameters with the lattice parameters $\alat$ and $\clat$ and the internal parameter $u$ of the wurtzite structure. The respective values are summarized in Tab.\ \ref{tab:binary_phases}.
The situation is more complicated in (Al,Sc)N where the MN$_4$ tetrahedra (we use the notation M for a \emph{metal atom}) in general have a broken symmetry which results in many more parameters that are needed for their characterization, see Fig.\ \ref{fig:geom_def}. All four tetrahedral \mbox{M--N} bonds can have different lengths. With $\ell_c$ we refer to the bond length of the \mbox{M--N} bond which is oriented roughly in c direction but may have a small tilting angle $\gamma$ with respect to the $z$ axis. The \mbox{M--N} bonds involving the three N atoms in the basal plane in general have three different lengths $\ell_{ab,i}$ (i=1,2,3) and three different angles $\delta_i$ measuring the tilt with respect to the $xy$ plane. The three bond angles $\alpha_i$ differ as well, the same applies to the three $\beta_i$.
\begin{figure}[]
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(85,133)(0,0)
\put(0,52){\includegraphics[width=\columnwidth]{Fig5a_bond_angles.eps}}
\put(0,0) {\includegraphics[width=\columnwidth]{Fig5b_bond_lengths.eps}}
\end{picture}
\caption{
Bond lengths and bond angles averaged over the set of structurally relaxed low-energy supercell models as a function of the Sc content. Values from AlN$_4$ tetrahedra (blue circles) and ScN$_4$ tetrahedra (red diamonds) are shown separately and the black symbols mark their weighted average at given Sc content $x$. Error bars indicate $\pm$ one standard deviation from the average value.
\label{fig:average_geom}}
\end{center}
\end{figure}
We have conducted a statistical analysis in order to derive a correspondence between the lattice parameters and these bond lengths and bond angles that in general vary for all considered atomic bonds. Therefore we have averaged each of the parameters $\ell_{ab}$, $\ell_{c}$, $\alpha$, $\beta$, $\gamma$ and $\delta$ over all the Al--N and Sc--N bonds in all the structurally relaxed supercells of our dataset at each given Sc content. The respective results are summarized in Fig.\ \ref{fig:average_geom}. The histograms for Al--N and Sc--N bonds have been evaluated separately and the blue circles and red diamonds give the respective mean values. Error bars of $\pm$ one standard deviation indicate the spread of the distributions. Finally, the averaged values weighted by the respective Al:Sc ratios are shown as black squares.
The average Al--N bond lengths $\langle\ell_{ab}\rangle_{\rm{Al}}$ and $\langle\ell_c\rangle_{\rm{Al}}$ are found to be very close to the values of bulk wurtzite AlN, c.f.\ Table \ref{tab:binary_phases}. Moreover, both lengths vary only marginally with the Sc content. By contrast, the values for the Sc--N bond lengths are found to be substantially smaller than the values of cubic ScN and hexagonal ScN and they gradually grow with increasing number of Sc atoms in the supercell.
For the bond angles, the situation is different. While $\langle\alpha\rangle_{\rm{Sc}}$ is a few degrees smaller than $\langle\alpha\rangle_{\rm{Al}}$, both decrease monotonously and with a similar slope as a function of the Sc content. The disorder and symmetry breaking introduced by the Sc atoms leads to a tilting of the MN$_4$ tetrahedra as reflected in the increase of $\langle\gamma\rangle$ for both M = Al and Sc. Here, the latter is less affected than the former. The observed decrease in $\langle\delta\rangle$ is directly connected with the decrease in $\langle\alpha\rangle$. Since $\langle\gamma\rangle$ is small, the relation $\langle\delta\rangle \simeq \langle\alpha\rangle - 90^\circ$ holds to a large extent.
The lattice parameter $\alat$ can be obtained by averaging over the projection of the M--N bonds onto the $xy$ plane
\begin{eqnarray}
\label{eq:a_approx}
\langle a\rangle&=&\sqrt{3}\,\langle{\cal P}_{\!xy}\ell_{ab}\rangle
\simeq\sqrt{3}\;\langle\ell_{ab}\rangle\;\sin\langle\alpha\rangle.
\end{eqnarray}
The averaged projection $\langle{\cal P}_{\!xy}\ell_{ab}\rangle$ grows even faster than the average $\langle\ell_{ab}\rangle$ with increasing Sc content because $\langle\alpha\rangle$ is decreasing. Both effects add up and give the observed almost linear dependence of $\alat$ on $x$. By contrast, the averaged projection onto the z axis $\langle{\cal P}_{\!z}\ell_{ab}\rangle$ decreases for the same reason and largely compensates the increase of $\langle\ell_c\rangle$ with increasing Sc content. This in combination leads to the observed dependence of lattice parameter $\clat$ on $x$ since
\begin{eqnarray}
\label{eq:c_approx}
\langle c\rangle &=&2\langle{\cal P}_{\!z}\ell_{c}\rangle+2\langle{\cal P}_{\!z}\ell_{ab}\rangle
\nonumber\\
&\simeq&2\langle\ell_{c}\rangle\cos\langle\gamma\rangle+2\langle\ell_{ab}\rangle\sin\langle\delta\rangle.
\end{eqnarray}
For small values of $\langle\gamma\rangle$ equation (\ref{eq:c_approx}) can be well approximated by setting
$\sin\langle\delta\rangle\simeq-\cos\langle\alpha\rangle$ and $\cos\langle\gamma\rangle\simeq1$.
\section{Elastic tensor}
\label{sec:Elastic_tensor}
This section introduces our method of evaluating the elastic tensor as a function of Sc content $x$
in Sec.\ \ref{subsec:Evaluation_Cij}, and the respective results are presented in Sec.\ \ref{subsec:resultsCij}. The observed behavior can be well correlated with the change in the interatomic bonds due to an applied strain as shown and discussed in Sec.\ \ref{subsec:origin_softening}.
\subsection{Evaluation of tensor components $C_{\mu\nu}$}
\label{subsec:Evaluation_Cij}
\begin{figure*}[t]
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(175,90)(0,0)
\put(0,45){\includegraphics[width=0.65\columnwidth]{Fig6a_C11.eps}}
\put(60,45){\includegraphics[width=0.65\columnwidth]{Fig6b_C12.eps}}
\put(120,45){\includegraphics[width=0.65\columnwidth]{Fig6c_C13.eps}}
\put(0,0){\includegraphics[width=0.65\columnwidth]{Fig6d_C33.eps}}
\put(60,0){\includegraphics[width=0.65\columnwidth]{Fig6e_C44.eps}}
\put(128,15){\includegraphics[width=0.4\columnwidth]{Fig6f_Cij_legend.eps}}
\end{picture}
\caption{
Symmetrized elastic tensor components $C_{\mu\nu}$ calculated for 36-atom (Al,Sc)N supercells with varying Sc content x. The results of the quadratic fitting are marked as solid lines. Results taken from Refs. [\onlinecite{Zhang2013,Caro2015,Momida2016}] are included for comparison. The arithmetic mean of the elastic properties of binary AlN and ScN is displayed by blue diamond symbols at x=50\%.
\label{fig:Cij}}
\end{center}
\end{figure*}
The tensor of elastic constants is of rank 4, which implies tensor components $C_{ijkl}$ with four cartesian indices. Due to symmetry, it is convenient to use the Voigt notation in order to write the tensor components in matrix form with elements $C_{\mu\nu}$ (and with $C_{\mu\nu}=C_{\nu\mu}$). Here and in the following we use Greek letters for tensor indices in Voigt notation and Latin letters for the cartesian indices.
The matrix representing the elastic tensor has five independent non-zero components
for the hexagonal symmetry of the wurtzite crystal. These are
$C_{11}$, $C_{12}$, $C_{13}$, $C_{33}$, and $C_{44}$. By symmetry $C_{22}=C_{11}$, $C_{23}=C_{13}$, $C_{55}=C_{44}$, and $C_{66}=(C_{11}-C_{12})/2$.
The random distribution of Sc atoms on the metal sublattice a priori breaks the hexagonal symmetry for the considered (Al,Sc)N supercell, so that a calculation will yield the full set of 21 non-vanishing independent components $C_{\mu\nu}$. In order to restore the hexagonal symmetry of the elastic tensor as it is observed experimentally for (Al,Sc)N films on the macroscopic level, we make use of the appropriate point group symmetry C$_{\rm 6v}$ (6mm). This group comprises 12 symmetry elements, namely five rotation angles (60$^\circ$, 120$^\circ$, 180$^\circ$, 240$^\circ$, 300$^\circ$), six mirror planes and the identity. The transformation of the elastic tensor (tensor of rank 4) under a symmetry operation $R(\alpha)$ with corresponding transformation matrices $R_{ij}^{(\alpha)}$ is given by
\begin{equation}
C^{(\alpha)}_{ijkl}=\sum_{m=1}^3\sum_{n=1}^3\sum_{p=1}^3\sum_{q=1}^3
R_{im}^{(\alpha)} R_{jn}^{(\alpha)}R_{kp}^{(\alpha)}R_{lq}^{(\alpha)}C_{mnpq}\,.
\end{equation}
The symmetrized tensor is obtained as an average with respect to the 12 symmetry elements of the point group symmetry C$_{\rm 6v}$,
\begin{equation}
C^{(sym.)}_{ijkl}=\frac{1}{12}\sum_{\alpha=1}^{12}C^{(\alpha)}_{ijkl}\,.
\end{equation}
We have evaluated the elastic tensor from first-principles stress calculations for all of the selected 36-atom sample structures using the ElaStic package.\cite{Golesorkhtabar2013} Depending on the space group of the crystal, a set of deformation matrices is selected. Stress calculations are carried out for all deformed structures and the computed stresses are fitted as polynomial functions of the applied strains in order to extract the derivatives at zero strain. The knowledge of these derivatives allows for the determination of all independent components of the elastic tensor. In this context, the accuracy of the elastic constants critically depends on the polynomial fit,
namely the order of the polynomial used and the range of deformations considered. The ElaStic tool allows for a systematic study of the influence of these fitting parameters on the numerical derivatives in order to obtain the most reliable results. We have used third order polynomials and the strain interval [-0.004, 0.004] with 17 equally spaced data points for each deformation.
\subsection{Results: Elastic tensor of (Al,Sc)N}
\label{subsec:resultsCij}
\begin{table}[]
\begin{center}
\begin{tabular}{l c c c c c}
&$C_{11}\,$[GPa] & $C_{12}\,$[GPa] &$C_{13}\,$[GPa] &$C_{33}\,$[GPa] &$C_{44}\,$[GPa]\\
\hline
w-AlN & 374 & 129 & 101& 351 & 112 \\
h-ScN & 218 & 160 & 89 & 346 & 132 \\
average & 296 & 145 & 95 & 349 & 122 \\
\end{tabular}
\caption{Elastic tensor components computed for wurtzite AlN and hexagonal ScN. The third line gives the arithmetic mean of the values of w-AlN and h-ScN.
\label{tab:comp_Cij_AlN_ScN}}
\end{center}
\end{table}
The results for the symmetrized elastic tensor are compiled in Fig.\ \ref{fig:Cij}, where they are also compared with other DFT results from literature.\cite{Zhang2013,Caro2015,Momida2016}
The elastic tensor components vary for the individual structure models at a given Sc content $x$. However, their averaged values (black circles in Fig.\ \ref{fig:Cij}) change monotonously as a function of $x$. As for the lattice parameters we have fitted a quadratic function to these data with the constraint that the function at $x=0$ has the value of the AlN parameter. The results of the fit (solid red lines in Fig.\ \ref{fig:Cij}) are given by
\begin{eqnarray}
C_{11}(x)&=&374.1 \left(1 - 0.882\, x + 0.602\, x^2 \right) {\rm GPa} ,\\
C_{12}(x)&=&128.6 \left(1 + 0.400\, x - 0.082\, x^2 \right) {\rm GPa} ,\\
C_{13}(x)&=&100.3 \left(1 + 0.793\, x - 0.481\, x^2 \right) {\rm GPa} ,\\
C_{33}(x)&=&351.7 \left(1 - 1.160\, x - 0.256\, x^2 \right) {\rm GPa} ,\\
C_{44}(x)&=&111.6 \left(1 - 0.848\, x + 1.369\, x^2 \right) {\rm GPa} .
\end{eqnarray}
The quadratic fitting works very well for all five tensor components. Note however, that there is a small modulation in the $C_{12}$ data around the fitted, almost linear curve which cannot be captured by the quadratic fitting ansatz. Our results agree qualitatively with the values obtained by the other theory groups except from $C_{12}$ for which we predict a considerably stronger increase with increasing Sc content.
Blue diamond symbols in Fig.\ \ref{fig:Cij} mark the arithmetic mean of the tensor components of pure wurtzite AlN and hexagonal ScN (cf.\ Tab.\ \ref{tab:comp_Cij_AlN_ScN}) at x=50\%.
The comparison of these estimates with our data allows us to distinguish two cases. On the one hand, the change of the elastic tensor components $C_{11}$ and $C_{12}$ with increasing Sc content can be fairly well approximated by the interpolation between the two pure phases. On the other hand, this does not hold for $C_{13}$, $C_{33}$, and $C_{44}$.
Although $C_{33}$ has roughly the same value for the pure components (cf.\ Tab.\ \ref{tab:comp_Cij_AlN_ScN}) there is a considerable softening for the mixed crystal. The behavior of $C_{13}$ as well cannot be inferred from an interpolation between the pure phases which would predict a decrease with growing Sc content instead of the observed increase. Finally, $C_{44}$ is also found to soften; it starts to increase at a large Sc content of $\simeq50\%$ which is directly correlated with the significant nonlinear variation of the lattice parameter $\clat$ in this range.
\subsection{Microscopic origin of $C_{33}$ softening}
\label{subsec:origin_softening}
The elastic constants of other mixed wurtzite-type nitrides, namely (Al,Ga)N, (Al,In)N, or (In,Ga)N, are found to depend linearly on composition.\cite{Lepkowski2015} Deviations from this Vegard's rule behavior are small and typically of the order of a few percent only. By contrast, (Al,Sc)N apparently does not follow this trend.
\begin{figure}[b]
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(85,38)(0,0)
\put(1.5,3){\includegraphics[width=0.95\columnwidth]{Fig7_Sketch_Strain.eps}}
\put(4,0){(a) equilibrium}
\put(35,0){(b) strain $\perp z$}
\put(64,0){(c) strain $\parallel z$}
\end{picture}
\caption{Sketch of the average atomic configuration (a) in equilibrium, and under an applied uniaxial strain (b) within the $xy$ plane and (c) parallel to the $z$ axis. Dashed lines serve as a guide for the eye and mark the equilibrium positions. Little red arrows highlight the directions of the changes in bond lengths and angles under strain. All relative changes are largely magnified for better visibility.
\label{fig:sketch_strain}}
\end{center}
\end{figure}
The qualitative different dependencies on composition of the C$_{\mu\nu}$ of (Al,Sc)N can be seen as analogous to those of the lattice parameters $\alat$ and $\clat$ on the Al/Sc ratio. Therefore, we correlate the dependence of the elastic tensor components on the Al/Sc-ratio with the microscopic atomic structure. We have analyzed the distribution of bond lengths and angles for our supercell models when a strain is applied either in $z$ direction ($\varepsilon_\parallel$) or in a direction within the $xy$ plane ($\varepsilon_\perp$). The atoms react to the applied strain and the averaged atomic configuration is modified with respect to the equilibrium structure, as sketched in Fig.~\ref{fig:sketch_strain}.
For this comparison we have chosen an uniaxial strain of $\varepsilon=0.004$ which is the maximum applied strain in our calculation of elastic tensors. Hence we have strained the crystal in the respective direction accordingly while keeping the dimensions in the other two directions fixed at their equilibrium values. For the case of an applied strain perpendicular to the $z$ direction we have considered both the $x$ and $y$ directions. Their averages will be discussed in the following. This procedure corresponds once more to averaging over the symmetry equivalent supercell realizations.
\begin{figure}[]
\begin{center}
\includegraphics[width=\columnwidth]{Fig8_strain_epsXY.eps}
\caption{Averaged change in bond lengths and bond angles for a strain $\varepsilon_{\perp}=0.004$ applied perpendicular to the $z$ direction. The black square symbols display the weighted average of the results for Al--N (blue circles) and Sc--N (red diamonds) at the respective Sc content $x$.
\label{fig:strainXY}}
\end{center}
\end{figure}
The results for the change in the average bond lengths $\langle\ell_{ab}\rangle$ and $\langle\ell_c\rangle$ and bond angle $\langle\alpha\rangle$ due to an applied strain perpendicular to the $z$ direction are visualized in Fig.\ \ref{fig:strainXY}. All quantities are apparently proportional to the Sc content within a wide range of $x$. Moreover, the average elongation $\langle\ell_c\rangle$ of the bonds in $z$ direction and the decrease in bond angle $\langle\alpha\rangle$ are nearly independent of the Sc content for both, Al--N and Sc--N bonds.
As the Al--N bonds are stiffer than the Sc--N bonds, the admixture of Sc leads to the observed softening of $C_{11}$ and $C_{12}$ which roughly follows the linear interpolation between the two binary compounds. The nonlinearity in both tensor components can be traced back to the response of $\langle\ell_{ab}\rangle$ (Fig.\ \ref{fig:strainXY}, middle panel). The three bonds forming the basal plane of the MN$_4$ tetrahedra are forced to take up more of the applied strain the more the bond angle $\alpha$ decreases with increasing Sc content.
The situation is qualitatively different for an applied strain in $z$ direction as visualized in Fig.\ \ref{fig:strainZ}. Here, the interplay of changing Al--N and Sc--N bond lengths and bond angles leads to an overall decreasing strain on the bonds in $z$ direction, which is reflected in a decrease of $\langle\ell_{c}\rangle$ as a function of $x$. Opposed to that, the response of $\langle\ell_{ab}\rangle$ is almost independent of x when averaged over all metal atoms. The strong decrease of $\Delta\langle\ell_{c}\rangle_M$ with $x$ is directly related to the observed softening of $C_{33}$ and is accomplished by a considerable change in the average bonding angle $\langle\alpha\rangle_M$. In other words, most of the applied strain in $z$ direction is reflected in the increase of the projection of the basal plane bonds onto the $z$ axis,
\begin{eqnarray}
\langle{\cal P}_{z}\ell_{ab}\rangle\simeq\langle\ell_{ab}\rangle\sin\langle\alpha\rangle .
\end{eqnarray}
This length measures the average distance between the M- and N-planes.
\begin{figure}[]
\begin{center}
\includegraphics[width=\columnwidth]{Fig9_strain_epsZ.eps}
\caption{Averaged change in bond lengths and bond angles for a strain $\varepsilon_{\parallel}=0.004$ applied in $z$ direction. The black square symbols display the weighted average of the results for Al--N (blue circles) and Sc--N (red diamonds) at the respective Sc content x.
\label{fig:strainZ}}
\end{center}
\end{figure}
\section{Piezoelectric tensor}
\label{sec:Piezo_tensor}
In the following, we describe the method to compute the $x$-dependent piezoelectric tensor in
Sec.\ \ref{subsec:Evaluation_eij}. Results are presented in Sec.\ \ref{subsec:resultseij}. They are analyzed and traced back to their microscopic origin in Secs.\
\ref{subsec:Origin_piezo} and \ref{subsec:competition_bonding}.
\subsection{Evaluation of tensor components $e_{i\mu}$}
\label{subsec:Evaluation_eij}
The piezoelectric tensor is of rank 3 with tensor components $e_{ijk}$. Frequently, the second and third Cartesian indices are merged into one index in the Voigt notation, so that the tensor components can be written in matrix form with elements $e_{i\mu}$. Given the hexagonal symmetry of the wurtzite structure, this matrix has three independent non-zero coefficients. These are $e_{15}$, $e_{31}$, and $e_{33}$; by symmetry $e_{32}=e_{31}$ and $e_{25}=e_{15}$. The random distribution of Sc atoms on the metal sublattice breaks the symmetry for the considered (Al,Sc)N supercell, so that there will be the full set of 18 independent components.
Corresponding to our workflow for the calculation of elastic constants, we make use of the point group symmetry C$_{\rm 6v}$ (6mm) in order to restore the hexagonal symmetry of the piezoelectric tensor as it is observed experimentally on the macroscopic level. The symmetry averaged tensor components
are obtained from
\begin{equation}
e^{(sym.)}_{ijk}=\frac{1}{12}\sum_{\alpha=1}^{12}e^{(\alpha)}_{ijk}
\end{equation}
with
\begin{equation}
e^{(\alpha)}_{ijk}=\sum_{m=1}^3\sum_{n=1}^3\sum_{p=1}^3
R_{im}^{(\alpha)} R_{jn}^{(\alpha)}R_{kp}^{(\alpha)}e_{mnp},
\end{equation}
using the 12 symmetry elements $R^{(\alpha)}$ of point group C$_{\rm 6v}$ with corresponding transformation matrices $R_{ij}^{(\alpha)}$.
For the determination of the piezoelectric tensors we have adapted and extended the workflow as implemented in the ElaStic tool. Following the \emph{modern theory of polarization} \cite{Vanderbilt2000, Resta2007} the piezoelectric response is related to the dependence of the Berry phase $\phi$ on the elastic strain,
\begin{equation}
e_{ijk} = \frac{1}{2\pi}\frac{e}{\Omega}\sum_{\alpha=1}^3\frac{\phi_\alpha}{\varepsilon_{jk}\;}r_{\alpha, i}.
\end{equation}
Here, $\varepsilon_{jk}$ is a strain tensor component, $r_{\alpha, i}$ the $i$-th component of one of the three (primitive) lattice vectors $\vec{r}_{\alpha}$, $\Omega=\vec{r}_1\cdot(\vec{r}_{2}\times\vec{r}_3)$ is the unit-cell volume, and $e$ is the electron charge.
The Berry phase is computed for the three primitive reciprocal lattice vectors $\vec{g}_\alpha$ (corresponding to the real-space lattice vectors $\vec{r}_\alpha$),
\begin{equation}
\phi_\alpha = \frac{1}{\Omega_{\rm{BZ}}}{\rm{Im}}\sum_{n \rm (occ.)}\int_{\rm{BZ}}d^3k\left\langle u_{n\vec{k}} \left|
\vec{g}_\alpha\cdot\vec{\nabla}_{\vec{k}}\right|u_{n\vec{k}}\right\rangle.
\end{equation}
Here $\Omega_{\rm{BZ}}$ is the volume of the first Brillouin zone and the $u_{n\vec{k}}$ are the Bloch states. The sum includes all occupied bands.
We use the same set of deformation matrices and strained deformed structure models as in Sec.\ \ref{sec:Elastic_tensor} for the analysis of elasticity. Calculations of the Berry phase are carried out using the implementation in QE for each deformed structure.
We have used 5, 5, and 11 discrete k-points for the integration along the three reciprocal lattice directions. Subsequently, the data are fitted as third order polynomial functions of the applied strains in order to extract the derivatives at zero strain. The knowledge of these derivatives allows for the determination of all independent components of the piezoelectric tensor.
The piezoelectric tensor coefficients are commonly discussed by dividing them into two parts.\cite{Bernardini1997} (i) The first part captures the change in polarisation due to a straining of the lattice. This so-called \emph{clamped-ion term} represents the effect of external macroscopic strain on the electronic structure. It is computed without a relaxation of interatomic forces in the strained structure models. (ii) The second part to the piezoelectric tensor coefficients then reflects the presence of internal strain. It explicitly involves the piezoelectric response with respect to the change in internal structure parameters by displacements of atoms induced by the strain.
\subsection{Results: Piezoelectric tensor of (Al,Sc)N}
\label{subsec:resultseij}
\begin{figure}[]
\begin{center}
\includegraphics[width=\columnwidth]{Fig10_eij.eps}
\caption{
Symmetrized piezoelectric tensor components calculated for 36-atom (Al,Sc)N supercells with varying Sc content x. The results of the quadratic fitting are shown as solid lines. Data taken from Ref.\ [\onlinecite{Caro2015}] are shown as dashed lines for comparison.
\label{fig:eij}}
\end{center}
\end{figure}
We have evaluated the full set of tensor components for the subset of low-energy sample structures.
The results for the symmetrized piezoelectric tensor are presented in Fig.\ \ref{fig:eij}, and compared there with other DFT results from literature.\cite{Caro2015}
The individual structure models yield varying tensor components, like what was observed for the elastic tensor in Sec.\ \ref{subsec:resultsCij}. Nevertheless, the averaged values at each given Sc content (black circles in Fig.\ \ref{fig:eij}) change monotonously as a function of $x$. We have fitted a quadratic function to the data thereby constraining the function at $x=0$ to the AlN parameters. The results of the fit (solid red lines in Fig.\ \ref{fig:eij}) are given by
\begin{eqnarray}
e_{15}(x) &=& -0.313 \left(1 - 0.296\, x - 1.687\, x^2 \right) {\rm C/m}^2, \\
e_{31}(x) &=& -0.593 \left(1 + 0.311\, x + 0.971\, x^2 \right) {\rm C/m}^2 ,\\
e_{33}(x) &=& 1.471 \left(1 + 0.699\, x + 4.504\, x^2 \right) {\rm C/m}^2.
\end{eqnarray}
All three components vary significantly as a function of $x$. While $e_{15}$ decreases by $\sim57\%$ in magnitude when x is increased from 0 up to 50$\%$, $e_{31}$ increases by $\sim40\%$ in the same x range.
Most notably $e_{33}$ increases by $\sim150\%$ when comparing (Al,Sc)N with 50$\%$ Sc with pure AlN.
For further analysis we single out the clamped-ion terms $e_{15}^{(0)}$, $e_{31}^{(0)}$, and $e_{33}^{(0)}$ which are plotted in Fig.\ \ref{fig:eij_clamped_ion}. They do not contribute strongly to the large variations of the full piezoelectric coefficients as can be seen by direct comparison with Fig.\ \ref{fig:eij}.
\begin{figure}[]
\begin{center}
\includegraphics[width=\columnwidth,draft=false]{Fig11_eij_clamped_ions.eps}
\caption{
Clamped-ion contributions $e_{i\mu}^{(0)}$ to the respective piezoelectric coefficients. Symbols mark the symmetry averaged values for each specific Sc concentration. The result of the quadratic fitting is shown as solid lines. Note that $e_{33}^{(0)}$ is opposite in sign compared with $e_{15}^{(0)}$ and $e_{31}^{(0)}$.
\label{fig:eij_clamped_ion}}
\end{center}
\end{figure}
\subsection{Microscopic origin of significant non-linear increase in $e_{33}$}
\label{subsec:Origin_piezo}
As described in the previous sections, the set of supercell models of our study maps to a wurtzite crystal if the results are statistically averaged according to the hexagonal C$_{\rm 6v}$ point group symmetry. Therefore it is possible to define an averaged $u$ parameter as
\begin{equation}
\label{eq:def:u}
\langle u \rangle = \frac{1}{2}\frac{\langle{\cal P}_{z}\ell_{c}\rangle}{\langle{\cal P}_{z}\ell_{ab}\rangle + \langle{\cal P}_{z}\ell_{c}\rangle},
\end{equation}
where $\langle{\cal P}_{z}\ell_{ab}\rangle$ and $\langle{\cal P}_{z}\ell_{c}\rangle$ are the averaged projections onto the z axis of the $\ell_{ab}$ and $\ell_{c}$ bonds, respectively (cf.\ Figs.\ \ref{fig:wurtzite} and \ref{fig:geom_def}). The dependence of $\langle u \rangle$ on the Sc content is shown in the left panel of Fig.\ \ref{fig:u_of_x}. This reflects the $x$ dependence of the piezoelectric coefficient $e_{33}$ and an almost linear relation between $e_{33}$ and $\langle u \rangle$ is found.
However, we need to consider the response of $\langle u \rangle$ with respect to strain in order to establish a more satisfactory correlation with the microscopic parameters which captures both, the variations in $e_{33}$ and $e_{31}$.
The piezoelectric tensor coefficient $e_{33}$ of wurtzite crystals is commonly discussed by dividing it into the following two parts,\cite{Bernardini1997}
\begin{eqnarray}
\label{eq:decomposition_eij_general}
e_{33} &=&\clat\,\frac{\partial P_z}{\partial\clat}+\frac{4e{\cal Z}^*}{\sqrt{3}\alat^2}\frac{du}{d\varepsilon_\parallel}.
\end{eqnarray}
Here ${\cal Z}^*$ is the dynamical Born charge in units of the electronic charge $e$ and $\varepsilon_\parallel$ is the applied strain in $z$ direction.
The clamped-ion term $e_{33}^{(0)}=\clat\;\partial P_z/\partial\clat$ captures the change in polarisation $P_z$ in $z$ direction due to a macroscopic strain on the lattice. The second term in Eq.\ (\ref{eq:decomposition_eij_general}) reflects the presence of internal strain and explicitly involves the derivative of the internal wurtzite structure parameter $u$ with respect to strain. The Born dynamical charge itself is defined via the partial derivative of the piezoelectric polarisation with respect to $u$,\cite{Bernardini1997}
\begin{eqnarray}
\label{def:Zstar}
{\cal Z}^*&=&\frac{\sqrt{3}\alat^2}{4e}\frac{\partial P_z}{\partial u}.
\end{eqnarray}
Note than an equation analogous to Eq. (\ref{eq:decomposition_eij_general}) holds for $e_{31}$ which then involves the derivative of $u$ with respect to a strain $\varepsilon_\perp$ applied in the $xy$ plane.
We postulate that Eq.\ (\ref{eq:decomposition_eij_general}) also holds for the case of disordered (Al,Sc)N when the internal parameter $u$ of the wurtzite crystal is replaced by the average $\langle u \rangle$, Eq.\ (\ref{eq:def:u}). When the derivative in the second term is replaced by a finite difference and we make use of Eq.\ (\ref{def:Zstar}), we obtain
\begin{eqnarray}
\label{eq:e31:decom}
e_{31}(x) &=& e_{31}^{(0)}(x)+\frac{\partial P_z}{\partial \langle u\rangle}\frac{\Delta\langle u\rangle}{\varepsilon_\perp},
\\
\label{eq:e33:decom}
e_{33}(x) &=& e_{33}^{(0)}(x)+\frac{\partial P_z}{\partial \langle u\rangle}\frac{\Delta\langle u\rangle}{\varepsilon_\parallel}.
\end{eqnarray}
Here $\Delta\langle u\rangle$ is the change in the average $\langle u\rangle$ when a uniaxial strain
$\varepsilon_{\parallel}$ or $\varepsilon_{\perp}$ is applied. The quantity $\Delta\langle u \rangle$ at a strain of $\pm 0.004$ is plotted for the four different cases in the right panel of Fig.\ \ref{fig:u_of_x}.
A positive strain in $z$ direction ($+\varepsilon_\parallel$) leads to a decrease of $\langle u \rangle$ while a positive strain applied in the $xy$ plane ($+\varepsilon_\perp$) yields an increase of the latter. This behavior is reversed for negative strain. The counteracting response and the different magnitude of $\Delta\langle u \rangle$ for the two cases $\varepsilon_\parallel$ and $\varepsilon_\perp$ are reflected in the opposite signs of $e_{33}$ and $e_{31}$ and their magnitudes.
\begin{figure}[]
\begin{center}
\setlength{\unitlength}{1mm}
\includegraphics[width=\columnwidth]{Fig12_u_vs_x.eps}
\caption{Left: Average internal parameter $\langle u \rangle$ as a function of Sc content. Values from AlN$_4$ and ScN$_4$ tetrahedra are averaged separately and the black symbols show their weighted average. Right: Change in the average parameter $\langle u \rangle$ due to uniaxial strain of $\pm 0.004$ in z direction ($\parallel$) or within the xy plane ($\perp$).
\label{fig:u_of_x}}
\end{center}
\end{figure}
\begin{figure}[]
\begin{center}
\includegraphics[width=0.6\columnwidth]{Fig13_eij_vs_du.eps}
\caption{Correlation of the piezoelectric coefficients $e_{31}$ and $e_{33}$ with the change in the $u$ parameter due to an uniaxial strain $\varepsilon_\perp$ and $\varepsilon_\parallel$, respectively. A linear fit to the data is shown as blue line.
\label{fig:eij_correlation}}
\end{center}
\end{figure}
Figure \ref{fig:eij_correlation} plots the second terms of Eqs. (\ref{eq:e31:decom}) and (\ref{eq:e33:decom}), i.e. the differences $e_{31}-e_{31}^{(0)}$ and $e_{33}-e_{33}^{(0)}$, as a function of ${\Delta\langle u\rangle}/{\varepsilon}$. A linear correlation is demonstrated which holds for both datasets. As a consequence thereof, the derivative ${\partial P_z}/{\partial \langle u\rangle}$ does not vary significantly as a function of the Sc content and is constant
to leading order.
In summary, the non-linear increase of $e_{33}$ has its origin essentially in the internal structural distortions induced by straining the crystal in z-direction.
The local structural sensitivity to the applied strain increases when the Sc content is raised, which is reflected in the dependence of $\langle u \rangle$ on $x$. A microscopic reason for this behavior is given in the following section. Hereby we extend and consolidate the seminal analysis of Ref.\ [\onlinecite{Tasnadi2010}].
\begin{table*}[]
\begin{center}
\begin{tabular}{l l c c c c c}
\hline\hline
Reference&Method&$C_{11}$ [GPa]& $C_{12}$ [GPa]&$C_{13}$ [GPa]&$C_{33}$ [GPa]&$C_{44}$ [GPa]\\
\hline
Kazan \emph{et al.}\cite{Kazan2007} & Experiment, single crystal, BLS & 394 & 134 & 95 & 402 & 121\\
Sotnikov \emph{et al.}\cite{Sotnikov2010} & Experiment, single crystal, BAW & $402.5\pm0.5$ & $135.6\pm0.5$ & $101\pm2$ & $387.6\pm1$ & $122.9\pm0.5$\\
McNeil \emph{et al.}\cite{McNeil1993} & Experiment, single crystal, BLS & $411\pm10$ & $149\pm10$ & $99\pm4$ & $389\pm10$ & $125\pm5$\\
Deger \emph{et al.}\cite{Deger1998} & Experiment, thin film, SAW & 410 & 140 & 100 & 390 & 120\\
Tsubouchi \emph{et al.}\cite{Tsubouchi1981}& Experiment, thin film, SAW & 345 & 125 & 120 & 395 & 118\\
Kurz \emph{et al.}\cite{Kurz2019} & Experiment, thin film, SAW & $404\pm3$ & --- & $103\pm15$ & $375\pm13$ & $124\pm2$ \\
Carlotti \emph{et al.}\cite{Carlotti2017} & Experiment, thin film, BLS & $392\pm8$ & --- & $106\pm15$ & $385\pm10$ & $112\pm2$\\
\hline
this work & DFT, PWPP (QE), PBE, stress-strain & 376 & 129 & 102 & 353 & 111\\
de Jong \emph{et al.}\cite{deJong2015a} & DFT, PWPP (VASP), PBE, stress-strain & 375 & 130 & 98 & 353 & 113\\
Zhang \emph{et al.}\cite{Zhang2013} & DFT, PWPP (VASP), PBE, stress-strain & 397 & 137 & 106 & 367 & 118\\
Caro \emph{et al.}\cite{Caro2015} & DFT, PWPP (VASP), PBE, stress-strain & 410 & 142 & 110 & 385 & 123\\
Wrigth \emph{et al.}\cite{Wright1997} & DFT, PWPP, LDA, energy-strain& 396 & 137 & 108 & 373 & 116\\
Kim \emph{et al.}\cite{Kim1996} & DFT, FP-LMTO, LDA, energy-strain& 398 & 140 & 127 & 382 & 96\\
\hline\hline
\end{tabular}
\caption{Comparison of experimentally measured and theoretically predicted elasticity tensor components of AlN taken from literature.
The second column contains information on the employed experimental and numerical methods used (see text for explanation and discussion).
\label{tab:Lit_Cij_AlN}}
\end{center}
\end{table*}
\subsection{Microscopic reason for variation of internal displacement parameter $\langle u \rangle$}
\label{subsec:competition_bonding}
There is an important difference between the group-IIIA simple-metal element Al (or Ga and In) and the group IIIB transition-metal element Sc (or Y and La) in their metal-nitride compounds. On the one hand, for Al the chemical nearest-neighbor bonds to 2s and 2p valence-electron orbitals of N atoms are formed by Al 3s and 3p orbitals. This results in the sp$^3$ hybridization and the tetrahedral coordination [AlN$_4$] in the hexagonal wurtzite structure of AlN.
On the other hand, for Sc the bonds to N are formed by Sc 3d and 4s orbitals, which leads to the octahedral coordination [ScN$_6$] in the cubic rocksalt structure of ScN.
Alloying Al and Sc in their nitrides leads to an energetic competition between the sp--sp character of \mbox{Al--N} bonds of tetrahedrally coordinated Al atoms and the \mbox{sd--sp} character of Sc--N bonds of preferential octahedrally coordinated Sc atoms. For (Al,Sc)N alloys with a Sc content $<50\%$ the tetrahedral coordination of the wurtzite structure is energetically favored. As a consequence,
the Sc atoms occupy tetrahedral sites instead of their favored octahedral sites in these wurtzite-type alloys. To avoid this site dilemma, Sc atoms are displaced more than Al atoms from the regular tetrahedral positions.
In the wurtzite structure, there are connections from a given tetrahedral site to three neighboring octahedral sites and to another neighboring tetrahedral site through the four triangular faces of the tetrahedron. An isolated single Sc atom at a tetrahedral site of the hexagonal N sublattice would be accommodated by a displacement to one of the three neighboring octahedral sites. However, shifting a Sc atom in the (Al,Sc)N nitride with fully occupied nitrogen and metal sublattices to a neighboring octahedral site would lead to a strong repulsion by metal atoms on next neighbor tetrahedral sites. This leaves only one possible way of achieving a better accommodation for a Sc atom: it is displaced along the hexagonal $c$ axis towards the next empty tetrahedral site. However, the displaced Sc atom cannot reach this tetrahedral site, again because of a strong repulsion by next neighbor metal atoms. Therefore, there is a balance of bonds and forces for Sc atoms close to the triangular N face between two connected tetrahedral sites. This approximately triangular Sc coordination has an internal displacement parameter value of $u\approx1/2$ instead of $u\approx3/8$ for the tetrahedral Al coordination.
In response to such local displacements of the Sc atoms the Al atoms get displaced as well in the relaxed random-alloy structure, but to a lesser extent. Altogether, a compromise between chemical Sc[sd]--N[sp] and Al[sp]--N[sp] bonds is a reason for the gradual raise of $\langle u \rangle$ between the two limiting values of $u$ with increasing Sc content (see left panel of Fig.\ \ref{fig:u_of_x}). Note that in the case of hexagonal ScN, there is no competing energy term that arises from deformed Al[sp]--N[sp] bonds and the Sc atoms are allowed to relax to the trigonal bipyramidal site with $u=0.5$ and triangular coordination in the $xy$ plane.
\begin{table*}[]
\begin{center}
\begin{tabular}{l l c c c}
\hline\hline
Reference & Method & $e_{33}$ [C/m$^2$] & $e_{31}$ [C/m$^2$] & $e_{15}$ [C/m$^2$]\\
\hline
Bu \emph{et al.}\cite{Bu2004} & Experiment, single crystal, SAW & $1.39\pm0.22$ & $-0.58\pm0.23$ & $-0.29\pm0.06$ \\
Sotnikov \emph{et al.}\cite{Sotnikov2010} & Experiment, single crystal, BAW & $1.34\pm0.10$ & $-0.60\pm0.20$ & $-0.32\pm0.05$ \\
Tsubouchi \emph{et al.}\cite{Tsubouchi1985}& Experiment, thin film, SAW & 1.55 & $-0.58$ & $-0.48$ \\
Kurz \emph{et al.}\cite{Kurz2019} & Experiment, thin film, SAW & $1.52\pm0.43$ & $-0.54\pm0.05$ & $-0.30\pm0.22$ \\
\hline
this work & DFT, PWPP (QE), PBE & 1.48 & $-0.58$ & $-0.32$ \\
Bernardini \emph{et al.}\cite{Bernardini1997} & DFT, PWPP, LDA & 1.46 & $-0.60$ & --- \\
Caro \emph{et al.}\cite{Caro2015} & DFT, PWPP (VASP), PBE & 1.45 & $-0.51$ & $-0.32$ \\
Momida \emph{et al.}\cite{Momida2016} & DFT, PWPP (VASP), PBE & 1.39 & $-0.55$ & $-0.30$ \\
de Jong \emph{et al.}\cite{deJong2015b} & DFT, PWPP (VASP), PBE & 1.46 & $-0.58$ & $-0.29$ \\
\hline\hline
\end{tabular}
\caption{Comparison of experimentally measured and theoretically predicted piezoelectricity tensor components of AlN taken from literature.
The second column contains information on the employed experimental and theoretical methods used (see text for explanation and discussion).
\label{tab:Lit_eij_AlN}}
\end{center}
\end{table*}
\begin{table*}[]
\begin{center}
\begin{tabular}{l l c c c c c c c}
\hline\hline
Composition & Reference & $C_{11}$ [GPa]&$C_{13}$ [GPa]&$C_{33}$ [GPa]&$C_{44}$ [GPa] &$e_{33}$ [C/m$^2$] & $e_{31}$ [C/m$^2$] & $e_{15}$ [C/m$^2$] \\
\hline
Al$_{0.86}$Sc$_{0.14}$N & Experiment\cite{Kurz2019} & $354\pm4$ & $108\pm7$ & $305\pm15$ & $112\pm3$ & $1.88\pm0.07$ & $-0.54\pm0.09$ & $-0.26\pm0.07$ \\
Al$_{0.86}$Sc$_{0.14}$N & This work (rescaled) & 359 & 113 & 312 & 113 & 1.80 & $-0.57$ & $-0.28$ \\
Al$_{0.68}$Sc$_{0.32}$N & Experiment\cite{Kurz2019} & $307\pm3$ & $123\pm5$ & $230\pm5$ & $110\pm2$ & $2.80\pm0.12$ & $-0.69\pm0.14$ & $-0.23\pm0.13$ \\
Al$_{0.68}$Sc$_{0.32}$N & This work (rescaled) & 315 & 124 & 226 & 108 & 2.56 & $-0.65$ & $-0.22$\\
\hline\hline
\end{tabular}
\caption{Comparison of experimentally measured and theoretically predicted elastic and piezoelectric tensor components of AlScN with $14\%$ and $32\%$ Sc content. The theoretically obtained functional dependence of the $C_{\mu\nu}$ end $e_{i\mu}$ have been rescaled with reference to binary AlN as explained in the text.
\label{tab:Compare_AlScN}}
\end{center}
\end{table*}
\section{Summary}
\label{sec:summary}
We have investigated the electroacoustic properties of (Al,Sc)N crystals with the metastable wurtzite structure. A combinatorial approach was chosen and a large variety of structure models with varying Sc content was analyzed. Thereby we sampled the different local atomic configurations of metal-sublattice disorder. For the chosen set of model structures (63 in total) we have evaluated the equilibrium lattice parameters and atomic positions, as well as the full elastic and piezoelectric tensors. The functional dependence of these properties on the Al:Sc ratio was obtained by an averaging and fitting procedure. Thereby we obtained a consistent set of material parameters for (Al,Sc)N extracted from a large data basis over the full range of experimentally accessible Sc content $0\le x\le 50\%$ .
Moreover, a statistical analysis of the microscopic structural parameters -- bond lengths and bond angles -- was conducted. The response of these parameters to an applied uniaxial strain was compared with their equilibrium averages. All structure models were strained parallel and perpendicular to the z axis. This analysis relates the observed variation in elastic and piezoelectric tensor components as a function of Sc content to the change in the averaged values of specific geometrical quantities.
The anisotropic evolution of the lattice parameters $\alat$ and $\clat$ with increasing Sc content is a consequence of an interplay of increasing average bond lengths and decreasing average bond angle
$\langle \alpha \rangle$.
The elastic softening in $z$ direction (C$_{33}$) is related to the disorder in local atomic configurations induced by the presence of the Sc atoms. Therefore, an applied strain $\varepsilon_\parallel$ is distributed over several of the microscopic degrees of freedom which, on average, leads to a reduced stretching of the bond lengths $\ell_c$ .
The extraordinary non-linear increase in the piezoelectric tensor component (e$_{33}$) has its origin in the increased sensitivity of the averaged parameter $\langle u \rangle$ to strain, the more Sc is added to the (Al,Sc)N crystal. Although $\langle u \rangle$ itself increases towards the value $0.5$ of nonpolar hexagonal ScN, its response to strain largely increases as a function of $x$.
All the above mentioned effects follow from the (energetic) competition between Al atoms that favor the tetrahedral coordination by N atoms in the wurtzite structure, and the Sc atoms that would prefer octahedral coordination and need to accommodate themselves as well as possible. The incorporation of Sc on the metal sublattice leads to the observed statistical distribution of bond lengths and bond angles that break the rigid wurtzite crystal symmetry on the microscopic level. This in turn adds flexibility to the atomic structure of (Al,Sc)N on how to respond to strain which finally determines the outstanding elastic and piezoelectric properties.
\section{Acknowledgement}
We thank Agne Zukauskaite and Nicolas Kurz for many valuable discussions.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,684
|
class Puppet::FileSystem::File19 < Puppet::FileSystem::FileImpl
def binread(path)
path.binread
end
end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,446
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{"url":"https:\/\/math.stackexchange.com\/questions\/2719947\/degree-of-maximal-tamely-ramified-extension-over-maximal-unramified-extension","text":"Degree of maximal tamely ramified extension over maximal unramified extension [closed]\n\nI am studying Neukirch's book, Chapter II but there is an exercise in it that I feel might be incorrect. As I am new to this stuff, I hope someone can help me with this. The problem is the following:\n\nExercise 2. The maximal tamely ramified abelian extension V of $\\mathbb{Q_p}$ is finite over the maximal unramified abelian extension T of $\\mathbb{Q_p}$.\n\nIt appears to be infinite to me.\n\nclosed as off-topic by Shailesh, Jos\u00e9 Carlos Santos, A. Goodier, Brandon Carter, Matthew LeingangApr 3 '18 at 17:17\n\nThis question appears to be off-topic. The users who voted to close gave this specific reason:\n\n\u2022 \"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level.\" \u2013 Shailesh, Jos\u00e9 Carlos Santos, A. Goodier, Brandon Carter, Matthew Leingang\nIf this question can be reworded to fit the rules in the help center, please edit the question.\n\n\u2022 The key is that $V$ needs to be abelian as an extension of $\\mathbb Q_p$, not just as an extension of $T$. \u2013\u00a0Mathmo123 Apr 3 '18 at 14:13\n\u2022 I can't answer your question, but I think the people who could help would want to know why you believe it to be infinite. \u2013\u00a0Kevin Long Apr 3 '18 at 18:18\n\u2022 I can answer your question if it is reopened. \u2013\u00a0nguyen quang do Apr 4 '18 at 9:49\n\u2022 ... As pointed out by Mathmo123, there is an interesting difference between V\/T and V\/Q_p \u2013\u00a0nguyen quang do Apr 4 '18 at 10:02\n\u2022 @KevinLong I think many of the people who could answer the question already understand why the OP would believe that. This question has been prematurely closed - not a great welcome for a first time poster. \u2013\u00a0Mathmo123 Apr 4 '18 at 14:41","date":"2019-08-23 22:22:33","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5550724267959595, \"perplexity\": 555.1500064842487}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-35\/segments\/1566027319082.81\/warc\/CC-MAIN-20190823214536-20190824000536-00304.warc.gz\"}"}
| null | null |
{"url":"https:\/\/www.shaalaa.com\/question-bank-solutions\/a-room-has-window-fitted-single-10-m-20-m-glass-thickness-2-mm-a-calculate-rate-heat-flow-through-closed-window-when-temperature-inside-room-32-c-heat-transfer-conduction_68589","text":"Share\n\nA Room Has a Window Fitted with a Single 1.0 M \u00d7 2.0 M Glass of Thickness 2 Mm. (A) Calculate the Rate of Heat Flow Through the Closed Window When the Temperature Inside the Room is 32\u00b0C - Physics\n\nConceptHeat Transfer Conduction\n\nQuestion\n\nA room has a window fitted with a single 1.0 m \u00d7 2.0 m glass of thickness 2 mm. (a) Calculate the rate of heat flow through the closed window when the temperature inside the room is 32\u00b0C and the outside is 40\u00b0C. (b) The glass is now replaced by two glasspanes, each having a thickness of 1 mm and separated by a distance of 1 mm. Calculate the rate of heat flow under the same conditions of temperature. Thermal conductivity of window glass = 1.0 J s\u22121\u00a0m\u22121\u00b0C\u22121 and that of air = 0.025 m-1\u00b0C-1\u00a0.\n\nSolution\n\n(a)\n\nLength,\u00a0l = 2 mm = 0.0002 m\n\nRate of flow of heat =(Delta\"T\")\/(l\/(\"KA\"))\n\n={1xx2xx(4032)}\/{2xx10^-3}\n\n={KA.DeltaT}\/{l}\n\n=\u00a0 {1xx2xx(40-32)}\/{2xx10^-3}\n\n= 8000 J \/ sec\n\n(b)\n|\nResistance of glass, R_g = {l}\/{K_g.A}\n\nResistance of air, R_A = {l}\/{K_A.A}\n\nFrom the circuit diagram, we can find that all the resistors are connected\n\nR_s = R_g + R_A + R_g\n\n=10^-3\/2 (2\/K_g + 1\/K_A)\n\n=10^-3 ( 2\/1 + 1\/0.025)\n\n= 10^-3\/2 xx((2xx0.025 + 1))\/0.025\n\nRate of flow of heat ,= q ={DeltaT}\/{R_5}\n\n= ( T_1 - T_2)\/R_s\n\n= {(40-32) xx2xx0.025}\/{40^_3xx(2xx0.025 + 1 )}\n\n=381W\n\nIs there an error in this question or solution?\n\nAPPEARS IN\n\nSolution A Room Has a Window Fitted with a Single 1.0 M \u00d7 2.0 M Glass of Thickness 2 Mm. (A) Calculate the Rate of Heat Flow Through the Closed Window When the Temperature Inside the Room is 32\u00b0C Concept: Heat Transfer - Conduction.\nS","date":"2020-04-03 00:10:40","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.35130441188812256, \"perplexity\": 1164.3557680483198}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-16\/segments\/1585370509103.51\/warc\/CC-MAIN-20200402235814-20200403025814-00171.warc.gz\"}"}
| null | null |
// ***********************************************************************
// Assembly : EveLib.EveOnline
// Author : Lars Kristian
// Created : 03-06-2014
//
// Last Modified By : Lars Kristian
// Last Modified On : 06-19-2014
// ***********************************************************************
// <copyright file="NotificationList.cs" company="">
// Copyright (c) . All rights reserved.
// </copyright>
// <summary></summary>
// ***********************************************************************
using System;
using System.Xml.Serialization;
using eZet.EveLib.EveXmlModule.Util;
namespace eZet.EveLib.EveXmlModule.Models.Character {
/// <summary>
/// Class NotificationList.
/// </summary>
[Serializable]
[XmlRoot("result", IsNullable = false)]
public class NotificationList {
/// <summary>
/// Gets or sets the notifications.
/// </summary>
/// <value>The notifications.</value>
[XmlElement("rowset")]
public EveXmlRowCollection<Notification> Notifications { get; set; }
/// <summary>
/// Class Notification.
/// </summary>
[Serializable]
[XmlRoot("row")]
public class Notification {
/// <summary>
/// Gets or sets the notification identifier.
/// </summary>
/// <value>The notification identifier.</value>
[XmlAttribute("notificationID")]
public long NotificationId { get; set; }
/// <summary>
/// Gets or sets the type identifier.
/// </summary>
/// <value>The type identifier.</value>
[XmlAttribute("typeID")]
public int TypeId { get; set; }
/// <summary>
/// Gets or sets the sender identifier.
/// </summary>
/// <value>The sender identifier.</value>
[XmlAttribute("senderID")]
public long SenderId { get; set; }
/// <summary>
/// Gets or sets the name of the sender.
/// </summary>
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get { return SentDate.ToString(XmlHelper.DateFormat); }
set { SentDate = DateTime.ParseExact(value, XmlHelper.DateFormat, null); }
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"redpajama_set_name": "RedPajamaGithub"
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Follow the life of Anna Pavlova, the world's most famous prima ballerina, as she discovers the world of dance in this beautifully narrated and exquisitely illustrated book. Inspirational and moving, Swan, is sure to be a favorite for children and adults alike. Written by Laurel Snyder and illustrated by Julie Morstand. See More
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Follow the life of Anna Pavlova, the world's most famous prima ballerina, as she discovers the world of dance in this beautifully narrated and exquisitely illustrated book. Inspirational and moving, Swan, is sure to be a favorite for children and adults alike. Written by Laurel Snyder and illustrated by Julie Morstand.
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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Blake James McDermott
Blake James McDermott, 15, died peacefully at home with family by his side on Jan. 6, 2023, after a courageous battle with Sanfillipo Syndrome.
Blake was all "boy." He loved anything he could throw; football, baseball, basketball, you name it. Blake also enjoyed four-wheeler rides, being outside, ice cream, wearing his baseball cap, singing songs with his mom, throwing the ball with his dad, spending time with his sister, Morgan, and all of his amazing caretakers that quickly became family. He had an infectious laugh and showed strength, resiliency and utmost joy for life. His inspiration will live on within his family, friends and the Sanfillipo Community.
Blake was born Feb. 13, 2007, at Mercy Hospital in Dubuque, Iowa.
He is survived by his parents, Mike and Jill McDermott; his grandparents, Leo and Janet Cook, and Linus and Shirley McDermott; and many aunts, uncles and cousins.
He was preceded in death by his sister, Morgan, who recently passed after a courageous battle with Sanfillipo Syndrome, and his cousin, Ryder.
A Mass of Christian Burial will be held at 11 a.m. Wednesday, Jan. 11, at the Sacred Heart Catholic Church. Visitation will be held prior from 9 to 10:45 a.m. In lieu of flowers, memorials may be made to the MSP Society, Make a Wish Foundation or Camp Courageous.
Viola Evelyn Frey (86) of Newton
Earl David William Baldwin, former pastor of TrinityLife church in Timonium, dies
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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{"url":"https:\/\/www.nature.com\/articles\/s41598-021-85425-w","text":"Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.\n\n# UV-C irradiation is highly effective in inactivating SARS-CoV-2 replication\n\n## Abstract\n\nThe potential virucidal effects of UV-C irradiation on SARS-CoV-2 were experimentally evaluated for different illumination doses and virus concentrations (1000, 5, 0.05 MOI). At a virus density comparable to that observed in SARS-CoV-2 infection, an UV-C dose of just 3.7\u00a0mJ\/cm2 was sufficient to achieve a more than 3-log inactivation without any sign of viral replication. Moreover, a complete inactivation at all viral concentrations was observed with 16.9\u00a0mJ\/cm2. These results could explain the epidemiological trends of COVID-19 and are important for the development of novel sterilizing methods to contain SARS-CoV-2 infection.\n\n## Introduction\n\nThe COVID-19 pandemic caused by SARS-CoV-2 virus1 has had an enormous, as yet barely understood, impact on health and economic outlook at the global level2. The identification of effective microbicide approaches is of paramount importance in order to limit further viral spread, as the virus can be transmitted via aerosol3,4 and can survive for hours outside the body5,6,7. Non-contact disinfection technologies are highly desirable, and UV radiation, in particular UV-C (200\u2013280\u00a0nm) has been suggested to be able to inactivate different viruses, including SARS-CoV8,9,10,11,12. The interaction of UV-C radiations with viruses has been extensively studied13,14,15, and direct absorption of the UV-C photon by the nucleic acid basis and\/or capsid proteins leading to the generation of photoproducts that inactivate the virus was suggested to be one of the main UV-C-associated virucidal mechanisms16,17. Some models have been proposed to correlate the nucleic acid structure with the required dose to inactivate the virus, but a reliable model is still unavailable18. This is also due to the fact that UV-C measurements were conducted using different viruses and diverse experimental conditions19,20,21,22. This led to an extremely wide range of values for the same virus and, e.g., in the case of SARS-CoV-1 values reported in the literature range from a few mJ\/cm2 to hundreds mJ\/cm219,22,23. Likewise, recent papers reported values for UVC inactivation ranging from 3 to 1000\u00a0mJ\/cm224,25,26,27. A better understanding of the effects of UV-C on SARS-CoV-2, which take into account all the key factors involved in the experimental setting (including culture medium, SARS-CoV-2 concentration, UV-C irradiance, time of exposure, and UV-C absorbance) will allow to replicate the results in other laboratory with different devices. Moreover, as recent evidences suggest that UV light from sunlight are efficient in inactivating the virus28, these measurements will be relevant for the setting up of further experiment considering the role of UV-A and UV-B on SARS-CoV-2 replication.\n\n## Results and discussion\n\nHerein, we report the effect of monochromatic UV-C (254\u00a0nm) on SARS-CoV-2, showing that virus inactivation can be easily achieved. Experiments were conducted using a custom-designed low-pressure mercury lamp system, which has been spectral-calibrated providing an average intensity of 1.082 mW\/cm2 over the illumination area (see the details reported in the Method section). Three different illumination exposure times, corresponding to 3.7, 16.9 and 84.4\u00a0mJ\/cm2, were administered to SARS-CoV-2 either at a multiplicity of infection (MOI) of 0.05, 5, 1000. The first concentration is equivalent to the low-level contamination observed in closed environments (e.g. hospital rooms), the second one corresponds to the average concentration found in the sputum of COVID-19 infected patients, and the third one is a very large concentration, corresponding to that observed in terminally diseased COVID-19 patients29. After UV-C exposure, viral replication was assessed by culture\u2010polymerase chain reaction (C-RT\u2010PCR) targeting two regions (N1 and N2) of the SARS-CoV-2 nucleocapsid gene, as well as by analyzing SARS-CoV-2-induced cytopathic effect. Analyses were performed in the culture supernatant of infected cells at three different time points (24, 48 and 72\u00a0h for SARS-CoV-2 at MOI 1000 and 5; 24, 48\u00a0h and 6\u00a0days for SARS-CoV-2 at MOI 0.05), as well as on cell lysates at the end of cellular culture (72\u00a0h: MOI 1000 and 5; 6\u00a0days: MOI 0.05). This approach allows to follow the kinetic of viral growth and to verify whether the used dose is sufficient to completely inactivate the virus over time. This is useful from a practical point of view, when UV-C devices are used to disinfect surfaces and the environment.\n\nThe effect of the UV-C exposure on SARS-CoV-2 replication was extremely evident and independent from the MOI employed; dose\u2013response and time-dependent curves were observed. Figures\u00a01, 2 and 3 report for different MOI the number of SARS-CoV-2 copies for the three concentrations as a function of the UV-C dose and time, quantified on a standard curve from a plasmid control. The corresponding normalised curves of the virus copies are reported in the same figures.\n\nViral replication was not observed at the lowest viral concentration (0.05 MOI) in either untreated or in UV-C-irradiated samples in the initial 48\u00a0h (Fig.\u00a01). However, 6\u00a0days after infection, viral replication was distinctly evident in the UV-C unexposed condition, but was completely absent following UV-C irradiation even at 3.7\u00a0mJ\/cm2 both in cell culture supernatants (Fig.\u00a01A,B) and in cell lysate (Fig.\u00a01C). A two-way ANOVA analysing the effect of UV-C dose and time of incubation failed to identify a significant effect of the UV exposure on viral replication. This is due to the fact that at very low MOI relevant increases in N1 and N2 copy numbers were detectable only in a single condition\u2014at six days in the absence of UV-C exposure\u2014thus hampering the statistical power of the analysis.\n\nAt the intermediate viral concentration (5 MOI), a significant reduction of copy number starting from the 3.7\u00a0mJ\/cm2 dose with a decrease of a factor of 2000 (>\u20093-log decrease) after 24\u00a0h was observed (Fig.\u00a02D). A two-way ANOVA confirmed that this UV-C dose significantly dampened viral replication (p\u2009=\u20090.000796, and p\u2009=\u20090.000713 for N1 and N2 copies respectively). Even more important, the copy number did not increase over time, suggesting an effective inactivation of the virus, which was further confirmed by cytopathic effect assessment (Fig.\u00a03A\u2013C).\n\nUsing a high viral input (MOI\u2009=\u20091000), the two-way ANOVA confirmed that all the tree UV doses analysed resulted in a significant suppression of viral replication for both N1 (3.7\u00a0mJ\/cm2: p\u2009=\u20090.008455; 16.9\u00a0mJ\/cm2: p\u2009=\u20090.004216; and 84.4\u00a0mJ\/cm2: p\u2009=\u20090.000202) and N2 copies (3.7\u00a0mJ\/cm2: p\u2009=\u20096.43E\u221205; 16.9\u00a0mJ\/cm2: p\u2009=\u20091.68E\u221205; and 84.4\u00a0mJ\/cm2: p\u2009=\u20091.68E\u221205) (Fig.\u00a04). Notably, a different course of infection was observed, in which the inhibitory effect was not accompanied by viral suppression for the UV-C dose of 3.7\u00a0mJ\/cm2 (Fig.\u00a04A,B,D). Indeed, a relevant reduction in N1 e N2 copy numbers was observed in a UV-C dose-dependent manner as early as 24\u00a0h (by a factor of 103 at 3.7\u00a0mJ\/cm2 and 104 at 16.9\u00a0mJ\/cm2, Fig.\u00a04A,B,D), but longer culture times resulted in an increase in N1 and N2 copy numbers for the UV-C dose of 3.7\u00a0mJ\/cm2. This indicates that the residual viral input left by the 3.7\u00a0mJ\/cm2 was able to replicate and sufficient to generate an effective infection. This is not the case in cultures exposed to higher UV-C doses, as no replication could be detected in these conditions. All the results were further confirmed by 2-ANOVA statistical analyses performed on viral replication at intracellular level (3.7\u00a0mJ\/cm2 vs. untreated: N1, p\u2009=\u20090.008455; N2: p\u2009=\u20096.43E\u221205; 16.9\u00a0mJ\/cm2 vs. untreated: N1, p\u2009=\u20090.004216; N2: p\u2009=\u20091.68E\u221205; 84.4\u00a0mJ\/cm2 vs. untreated: N1, p\u2009=\u20090.004216; N2: p\u2009=\u20091.68E\u221205) (Figs.\u00a01C, 2C, 4C).\n\nWe compared our results with data available in the literature and observed that our inactivating dose is much smaller than that reported in Heilingloh et al.26 (1000\u00a0mJ\/cm2 for the complete inactivation). This discrepancy is likely to be the consequence of the UV-C absorption by the medium used in Heilingloh et al., which has a fourfold higher thickness compared to the one used in our experiments. This possibility is supported by the observation that 200\u00a0mJ\/cm2 of UV-A, which is not absorbed by the medium, was sufficient to reduce viral replication of 1-log. As UV-A light is significantly less efficient (order of magnitudes) than UV-C, the reported UV-C inactivating dose (100\u00a0mJ\/cm2) seems to be questionable.\n\nTwo other papers measured the effect of UV-C light on SARS-CoV-2. In Ruetalo et al.25, the illumination of 254\u00a0nm light was employed on a dried sample of SARS-CoV-2. Complete inactivation was obtained with 20\u00a0mJ\/cm2, a value greater than ours, but in the same range. It has to be underlined that in the dried film a shielding effect by the organic component present in the liquid can occur, reducing the efficiency of the UV-C light. This was shown by Ratnesar-Shumate et al.28, who demonstrated that the dose required to obtain a similar degree of viral inactivation was twice in dried samples from gMEM compared to the ones resuspended in simulated saliva. Notably, the two mediums differ for their composition, mainly in terms of protein and solid percentage, with higher values for the gMEM.\n\nInagaki et al. used a 285\u00a0nm UV LED and showed that a dose of about 38\u00a0mJ\/cm2 was sufficient to completely inactivate SARS-CoV-2. This dose is greater compared to the one we established; this discrepancy can be explained by the observation that the 285\u00a0nm is less efficient than the 254\u00a0nm wavelength24. Finally, in an elegant study Storm et al.27 compared the virucidal effect of UV-C in wet and dry systems. Results were based on the use of a very small volume of viral stock in DMEM (5\u00a0\u03bcl) and showed that a dose of 3.4\u00a0mJ\/cm2 inactivated wet samples, whereas a dose that twice as high was needed in dried samples. These results are comparable to the ones herein, and the shielding effect in dried samples is almost evident. Such comparisons show how the experimental conditions adopted significantly impact on the definition of the dose of UV-C resulting in virus inactivation. It is therefore crucial to accurately describe all the details of the experiments to perform a reliable comparison.\n\nIn conclusion, we report the results of a highly controlled experimental model that allowed us to identify the UV-C radiation dose sufficient to inactivate SARS-CoV-2. The response depends on both the UV-C dose and the virus concentration. Indeed, for virus concentrations typical of low-level contaminated closed environment and sputum of COVID-19 infected patients, a very small dose of less than 4\u00a0mJ\/cm2 was enough to achieve full inactivation of the virus. Even at the highest viral input concentration (1000 MOI), viral replication was totally inactivated with a dose\u2009\u2265\u200916.9\u00a0mJ\/cm2. These results show how the SARS-CoV-2 is extremely sensitive to UV-C light and they are important to allow the proper design and development of efficient UV based disinfection methods to contain SARS-CoV-2 infection.\n\n## Methods\n\n### In vitro SARS-CoV-2 infection assay\n\n3\u2009\u00d7\u2009105 VeroE6 cells were cultured in DMEM (ECB7501L, Euroclone, Milan, Italy) with 2% FBS medium, with 100 U\/ml penicillin and 100\u00a0\u03bcg\/ml streptomycin, in a 24-well plate one day before viral infection assay. SARS-CoV-2 (Virus Human 2019-nCoV strain 2019-nCoV\/Italy-INMI1, Rome, Italy) at a multiplicity of infection (MOI) of 1000, 5 and 0.05 were treated with different doses of UV-C radiation (see the dedicated section) before inoculum into VeroE6 cells. UV-C-untreated virus served as positive controls. Cell cultures were incubated with the virus inoculum in duplicate for three hours at 37\u00a0\u00b0C and 5% CO2. Then, cells were rinsed three times with warm PBS, replenished with the appropriate growth medium and observed daily for cytopathic effect. Viral replication in culture supernatants was assessed by an Integrated Culture\u2010polymerase chain reaction (C-RT\u2010PCR) method30 at 24, 48, and 72\u00a0h post-infection (hpi) while infected cells were harvested for RNA collection at 72 hpi. Cell cultures from SARS-CoV-2 at 0.05 MOI were harvested 6\u00a0days post infection. RNA was extracted from VeroE6 cell culture supernatant and cell lysate by the Maxwell RSC Instrument with Maxwell RSC Viral Total Nucleic Acid Purification Kit (Promega, Fitchburg, WI, USA), quantified by the Nanodrop 2000 Instrument (Thermo Scientific) and purified from genomic DNA with RNase-free DNase (RQ1 DNase; Promega). One microgram of RNA was reverse transcribed into first-strand cDNA in a 20-\u03bcl final volume as previously described31,32.\n\nReal-time PCR was performed on a CFX96 (Bio-Rad, CA, USA) using the 2019-nCoV CDC qPCR Probe Assay emergency kit (IDT, Iowa, USA), which targets two regions (N1 and N2) of the nucleocapsid gene of SARS-CoV-2. Reactions were performed according to the following thermal profile: initial denaturation (95\u00a0\u00b0C, 10\u00a0min) followed by 45 cycles of 15\u00a0s at 95\u00a0\u00b0C (denaturation) and 1\u00a0min at 60\u00a0\u00b0C (annealing-extension).\n\nViral copy quantification was assessed by creating a standard curve from the quantified 2019-nCoV_N positive Plasmid Control (IDT, Iowa, USA).\n\n### UV illumination test\n\nThe illumination of the virus solution was conducted using a low-pressure mercury lamp mounted in a custom designed holder, which consist in a box with a circular aperture 50\u00a0mm in diameter placed at approximately 220\u00a0mm from the source. The aperture works as a spatial filter to make the illumination of the area behind more uniform. A mechanical shutter is also present to start the illumination process. The plate is placed 30\u00a0mm below the circular aperture and a single dwell (34.7\u00a0mm in diameter), centered in respect to the 50\u00a0mm aperture, has been irradiated from the top. The dwell was filled with 0.976\u00a0ml of the virus suspended in Dulbecco\u2019s Modified Eagle\u2019s Medium (DMEM) in order to have a 1\u00a0mm thick liquid layer. After the irradiation, the sample was treated as described in the previous section.\n\nThe intensity of the lamp and its spectral properties have been measured using an Ocean Optics HR2000\u2009+\u2009spectrometer (Ocean Optics Inc., Dunedin, USA). The HR2000\u2009+\u2009spectrometer was calibrated against a reference deuterium\u2013halogen source (Ocean Optics Inc. Winter Park, Winter Park, Florida) and in compliance with National Institute of Standards and Technology (NIST) practices recommended in NIST Handbook 150-2E, Technical guide for Optical Radiation Measurements. The last calibration was performed in March 2019. The detector of our spectrometer is a high-sensitivity 2048-element Charge-Coupled Device (CCD) array from Sony. The spectral range is 200\u20131100\u00a0nm with a 25\u00a0\u03bcm wide entrance slit and an optical resolution of 1.4\u00a0nm (FWHM). The cosine-corrected irradiance probe, model CC-3-UV-T, is attached to the tip of a 1\u00a0m long optical fibre and couples to the spectrometer. The intensity of the lamp has been measured by positioning the spectrometer in five positions: in the center and at the ends of a 20\u00a0mm cross arm after a warming up time of 30\u00a0s. The spectra in the five positions are reported in Fig.\u00a05A together with a scheme of the dwell and illuminated area.\n\nAs expected, the emission is dominated by the UV-C line (Fig.\u00a05A) and its intensity was uniform in the area with an average value of 1.082 mW\/cm2. The stability of the lamp was evaluated in\u2009\u00b1 11E\u22123\u00a0mW\/cm2 during a 130\u00a0s measurement. According to this value, three exposure times were set: 5, 23 and 114\u00a0s (with an accuracy of 0.2\u00a0s), which correspond to following doses: 5.4, 25.0, 123.4\u00a0mJ\/cm2. This is the nominal UV doses provided to the dwell, but we were interested in the effective doses (De) reaching the virus. It was necessary to calculate the effective irradiance (Ie). This step was performed considering both the reflection losses at the air\/water interface (Rw) and the Transmittance (Ts) of the DMEM solution at 254\u00a0nm (from the spectrum in Fig.\u00a05B, considering the cuvette losses, Ts\u2009=\u20090 0.70). It is important to notice that the spectrum was measured in a quartz cuvette (1\u00a0mm thick) by means of a Jasco V770 spectrophotometer and this thickness was the same of the solution in the dwell during the UV irradiation step.\n\nThe reflection loss was computed as follow:\n\n$${\\text{R}}_{w} = { }\\frac{{\\left( {{\\text{n}}_{w} - 1} \\right)^{2} }}{{\\left( {{\\text{n}}_{w} + 1} \\right)^{2} }},$$\n(1)\n\nwhere nw\u2009=\u20091.375 is the refractive index of water at 254\u00a0nm. Then, Ie was calculated:\n\n$$I_{e} = I_{n} \\left( {1 - R_{w} } \\right) \\times T_{s} .$$\n(2)\n\nThe final transmission of the DMEM solution was equal to 0.68 and the corresponding effective doses were derived simply multiplying Ie by the exposure time.\n\nAccording to this value, the effective doses provided to the viruses were: 3.7\u2009\u00b1\u20090.15, 16.9\u2009\u00b1\u20090.2 and 84.4\u2009\u00b1\u20090.9\u00a0mJ\/cm2. We have to notice that we are neglecting here the absorption of the virus at this wavelength and the possible scattering. Such approximations are valid considering the relative low concentration of the virus and small thickness of the layer (the solution appeared fully transparent).\n\n### Statistical analyses\n\nTo assess the effect of the different UV-C doses on N1 and N2 copy numbers, two-way ANOVAs were performed. For the analysis of intracellular N1 and N2 doses in the supernatant, UV-C dose and MOI represented the dependent variables, while for the analysis of N1 and N2 in the supernatant, different analyses were performed for individual MOI, using UV-C dose and time as dependent variables.\n\n## References\n\n1. Zhu, N. et al. A novel coronavirus from patients with pneumonia in China, 2019. N. Engl. J. Med. 382, 727\u2013733 (2020).\n\n2. Cobey, S. Modeling infectious disease dynamics. Science 368, 713\u2013714 (2020).\n\n3. Jarvis, M. C. Aerosol transmission of SARS-CoV-2: Physical principles and implications. Front. Public Health. 8, 590041 (2020).\n\n4. Tang, S. et al. Aerosol transmission of SARS-CoV-2? Evidence, prevention and control. Environ. Int. 144, 106039 (2020).\n\n5. van Doremalen, N. et al. Aerosol and surface stability of SARS-CoV-2 as compared with SARS-CoV-1. N. Engl. J. Med. 382, 1564\u20131567 (2020).\n\n6. Chin, A. W. H. et al. Stability of SARS-CoV-2 in different environmental conditions. Lancet Microbe 1, e10 (2020).\n\n7. Aboubakr, H. A., Sharafeldin, T. A. & Goyal, S. M. Stability of SARS-CoV-2 and other coronaviruses in the environment and on common touch surfaces and the influence of climatic conditions: A review. Transbound. Emerg. Dis. https:\/\/doi.org\/10.1111\/tbed.13707 (2020).\n\n8. Pirnie, M., Linden, K. G. & Malley, J. P. J. Ultraviolet disinfection guidance manual for the final long term 2 enhanced surface water treatment rule. Environ. Prot. 2, 1\u2013436 (2006).\n\n9. Reed, N. G. The history of ultraviolet germicidal irradiation for air disinfection. Public Health Rep. 125, 15\u201327 (2010).\n\n10. Kovalski, W. Ultraviolet Germicidal Irradiation Handbook: UVGI for Air and Surface Disinfection (Springer Science & Business Media, 2010).\n\n11. Darnell, M. E. R., Subbarao, K., Feinstone, S. M. & Taylor, D. R. Inactivation of the coronavirus that induces severe acute respiratory syndrome, SARS-CoV. J. Virol. Methods 121, 85\u201391 (2004).\n\n12. Raeiszadeh, M. & Adeli, B. A critical review on ultraviolet disinfection systems against COVID-19 outbreak: Applicability, validation, and safety considerations. ACS Photon. 7, 2941\u20132951 (2020).\n\n13. Bosshard, F., Armand, F., Hamelin, R. & Kohn, T. Mechanisms of human adenovirus inactivation by sunlight and UVC light as examined by quantitative PCR and quantitative proteomics. Appl. Environ. Microbiol. 79, 1325\u20131332 (2013).\n\n14. Nishisaka-Nonaka, R. et al. Irradiation by ultraviolet light-emitting diodes inactivates influenza a viruses by inhibiting replication and transcription of viral RNA in host cells. J. Photochem. Photobiol. B Biol. 189, 193\u2013200 (2018).\n\n15. Araud, E., Fuzawa, M., Shisler, J. L., Li, J. & Nguyen, T. H. UV inactivation of rotavirus and tulane virus targets different components of the virions. Appl. Environ. Microbiol. 86, e02436-e2519 (2020).\n\n16. Qiao, Z. & Wigginton, K. R. Direct and indirect photochemical reactions in viral RNA measured with RT-qPCR and Mass Spectrometry. Environ. Sci. Technol. 50, 13371\u201313379 (2016).\n\n17. Wigginton, K. R. & Kohn, T. Virus disinfection mechanisms: The role of virus composition, structure, and function. Curr. Opin. Virol. 2, 84\u201389 (2012).\n\n18. Lytle, C. D. & Sagripanti, J.-L. Predicted inactivation of viruses of relevance to biodefense by solar radiation. J. Virol. 79, 14244\u201314252 (2005).\n\n19. Walker, C. M. & Ko, G. Effect of ultraviolet germicidal irradiation on viral aerosols. Environ. Sci. Technol. 41, 5460\u20135465 (2007).\n\n20. McDevitt, J. J., Rudnick, S. N. & Radonovich, L. J. Aerosol susceptibility of influenza virus to UV-C light. Appl. Environ. Microbiol. 78, 1666\u20131669 (2012).\n\n21. Calgua, B. et al. UVC inactivation of dsDNA and ssRNA viruses in water: UV Fluences and a qPCR-based approach to evaluate decay on viral infectivity. Food Environ. Virol. 6, 260\u2013268 (2014).\n\n22. Eickmann, M. et al. Inactivation of three emerging viruses\u2014severe acute respiratory syndrome coronavirus, Crimean-Congo haemorrhagic fever virus and Nipah virus\u2014in platelet concentrates by ultraviolet C light and in plasma by methylene blue plus visible light. Vox Sang. 115, 146\u2013151 (2020).\n\n23. Duan, S.-M. et al. Stability of SARS coronavirus in human specimens and environment and its sensitivity to heating and UV irradiation. Biomed. Environ. Sci. 16, 246\u2013255 (2003).\n\n24. Inagaki, H., Saito, A., Sugiyama, H., Okabayashi, T. & Fujimoto, S. Rapid inactivation of SARS-CoV-2 with deep-UV LED irradiation. Emerg. Microbes Infect. 9, 1744\u20131747 (2020).\n\n25. Ruetalo, N., Businger, R. & Schindler, M. Rapid and efficient inactivation of surface dried SARS-CoV-2 by UV-C irradiation. bioRxiv 2020.09.22.308098 (2020).\n\n26. Heilingloh, C. S. et al. Susceptibility of SARS-CoV-2 to UV irradiation. Am. J. Infect. Control 48, 1273\u20131275 (2020).\n\n27. Storm, N. et al. Rapid and complete inactivation of SARS-CoV-2 by ultraviolet-C irradiation. Sci. Rep. 10, 22421 (2020).\n\n28. Ratnesar-Shumate, S. et al. Simulated sunlight rapidly inactivates SARS-CoV-2 on surfaces. J. Infect. Dis. 222, 214\u2013222 (2020).\n\n29. W\u00f6lfel, R. et al. Virological assessment of hospitalized patients with COVID-2019. Nature 581, 465\u2013469 (2020).\n\n30. Reynolds, K. A. Integrated cell culture\/PCR for detection of enteric viruses in environmental samples BT\u2014public health microbiology: Methods and protocols. in (eds. Spencer, J. F. T. & Ragout de Spencer, A. L.) 69\u201378 (Humana Press, 2004). https:\/\/doi.org\/10.1385\/1-59259-766-1:069.\n\n31. Saulle, I. et al. Endoplasmic reticulum associated aminopeptidase 2 (ERAP2) is released in the secretome of activated MDMs and reduces in vitro HIV-1 infection. Front. Immunol. 10, 1648 (2019).\n\n32. Ibba, S. V. et al. Analysing the role of stat3 in HIV-1 infection. J. Biol. Regul. Homeost. Agents 33, 1635\u20131640 (2019).\n\n## Acknowledgements\n\nThis research was partially supported by a grant from Falk Renewables and it has been carried out in the context of the activities promoted by the Italian Government and in particular, by the Ministries of Health and of University and Research, against the COVID-19 pandemic. Authors are grateful to INAF\u2019s President, Prof. N. D\u2019Amico, for the support and for a critical reading of the manuscript.\n\n## Author information\n\nAuthors\n\n### Contributions\n\nP.G., L.L. E.R. and A.Z. designed and produced the illumination system; A.C., C.C. and M.L. performed the lamp calibration; A.B. performed the lamp setup and lamp dosimetry, wrote the main manuscript; M.B. performed biological experiments, analyzed the data, wrote the main manuscript; C.F., I.S. designed and performed some biological tests; E.T, A.A. performed the statistical analysis; D.T. discussed the results; G.P. and M.C. supervised the study and review the manuscript.\n\n### Corresponding author\n\nCorrespondence to Mario Clerici.\n\n## Ethics declarations\n\n### Competing interests\n\nThe authors declare no competing interests.\n\n### Publisher's note\n\nSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\n## Rights and permissions\n\nOpen Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:\/\/creativecommons.org\/licenses\/by\/4.0\/.\n\nReprints and Permissions\n\nBiasin, M., Bianco, A., Pareschi, G. et al. UV-C irradiation is highly effective in inactivating SARS-CoV-2 replication. Sci Rep 11, 6260 (2021). https:\/\/doi.org\/10.1038\/s41598-021-85425-w\n\n\u2022 Accepted:\n\n\u2022 Published:\n\n\u2022 DOI: https:\/\/doi.org\/10.1038\/s41598-021-85425-w\n\n\u2022 ### The moderating effect of solar radiation on the association between human mobility and COVID-19 infection in Europe\n\n\u2022 Wenyu Zhao\n\u2022 Yongjian Zhu\n\u2022 Oon Cheong Ooi\n\nEnvironmental Science and Pollution Research (2022)\n\n\u2022 ### Ultraviolet C lamps for disinfection of surfaces potentially contaminated with SARS-CoV-2 in critical hospital settings: examples of their use and some practical advice\n\n\u2022 Manuela Lualdi\n\u2022 Emanuele Pignoli\n\nBMC Infectious Diseases (2021)\n\n\u2022 ### Acaricidal efficacy of ultraviolet-C irradiation of Tetranychus urticae adults and eggs using a pulsed krypton fluoride excimer laser\n\n\u2022 Jean-Luc Gala\n\u2022 Ott Rebane\n\u2022 Thierry Hance\n\nParasites & Vectors (2021)\n\n\u2022 ### Public toilets with insufficient ventilation present high cross infection risk\n\n\u2022 M. C. Jeffrey Lee\n\u2022 K. W. Tham\n\nScientific Reports (2021)\n\n\u2022 ### The effectiveness of commercial household ultraviolet C germicidal devices in Thailand\n\n\u2022 Pasita Palakornkitti\n\u2022 Prinpat Pinyowiwat\n\u2022 Ploysyne Rattanakaemakorn\n\nScientific Reports (2021)","date":"2022-05-26 19:16:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5378368496894836, \"perplexity\": 5948.613336590674}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652662619221.81\/warc\/CC-MAIN-20220526162749-20220526192749-00545.warc.gz\"}"}
| null | null |
from django.db import models, migrations
import django.utils.timezone
import model_utils.fields
class Migration(migrations.Migration):
dependencies = [
('main', '0004_location'),
]
operations = [
migrations.CreateModel(
name='ValueSet',
fields=[
(u'id', models.AutoField(verbose_name=u'ID', serialize=False, auto_created=True, primary_key=True)),
('created', model_utils.fields.AutoCreatedField(default=django.utils.timezone.now, verbose_name=u'created', editable=False)),
('modified', model_utils.fields.AutoLastModifiedField(default=django.utils.timezone.now, verbose_name=u'modified', editable=False)),
('name', models.CharField(max_length=25)),
('system_name', models.SlugField(unique=True, max_length=25)),
],
options={
u'db_table': 'value_set',
},
bases=(models.Model,),
),
]
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 637
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Compare the Senate and House Transpo Bills, Side-By-Side
Now that the Senate has passed a transportation bill and everyone's waiting to see what the House will do next, Transportation for America has done us all a great service and compared the Senate's bill to the House's — well, to the last thing the House showed us before things fell apart for John Boehner's extreme attack on transit, biking, and walking.
The T4A analysis breaks down each bill, policy by policy, and lays out any pending amendments to the House bill that could potentially change it for the better.
Here's an excerpt from their detailed comparison:
Public transportation & transit-oriented development
Senate: Continues dedicated funding for public transportation at traditional 20 percent share. Creates some new flexibility to spend federal funds on operations, i.e., keeping buses and trains running, not just buying new equipment. A new transit-oriented development planning program was incorporated into the bill via the Banking title.
House: Original bill ends 30 years of dedicated funding for public transit (read the letter we organized by more than 600 groups and individuals opposing this). Allows loans for transit-oriented development as an eligible expense under the TIFIA loan program. It doesn't provide large transit operators with any flexibility to spend federal money on operating their transit systems.
Possible House amendment fix: LaTourette/Carnahan 16 would allow all transit agencies to use a portion of their federal transit funding for operating expenses during times of economic crisis. (This amendment is similar to this bill the two representatives offered back in 2011.)
Walking and bicycling, local control of funds
Senate: Due in part to this amendment offered by Senators Cardin and Cochran and incorporated into the bill, MAP-21 consolidates programs for making biking and walking safer (as well as for other small local projects) and gives 50 percent of this consolidated program directly to metro areas. States and metro areas must create a competitive grant process to distribute that funding to local communities that apply. The Commerce Committee title also includes a new Complete Streets provision.
House: Eliminates most dedicated funding for bicycling & walking. Those uses remain "eligible" but without any dedicated funding for them. The bill also deletes numerous references throughout the bill that encourage multimodal projects. The bill retains the Recreational Trails program.
Possible House amendment fix: Petri-Blumenauer 103 creates consolidated program for bike/ped and other local projects and provides local governments access to new consolidated pot of funding.
Filed Under: House of Representatives, Reauthorization, Transportation for America, U.S. Senate
LaHood to House: "Get on the Bus" With a Bipartisan Transportation Bill
This morning, at the American Public Transportation Association's annual legislative conference, Secretary of Transportation Ray LaHood said he was recently asked by the House Appropriations Committee if he prefers a two-year transportation bill or a five-year transportation bill. Neither, he said: "I prefer a bipartisan bill." "Bipartisanship is the reason the Senate bill is a […]
Senate Transit Bill Would Let Federal Funds Support Transit Service
By Ben Goldman | Jan 31, 2012
All eyes are on the House side of Capitol Hill today in anticipation of the Republicans' grand unveiling of their American Energy & Infrastructure Jobs Act at 3:00 p.m. But last night, some enduring questions about the Senate's transportation bill finally got some answers. Senators Tim Johnson and Richard Shelby, respectively the chairman and ranking member of […]
How Will the House Answer the Senate's Transportation Funding Bill?
The full Senate passed a major appropriations bill yesterday, including funding levels for transportation and housing. The Senate put the kibosh on Sen. Rand Paul's attempt to strip bike/ped funding from the federal transportation program, as we reported yesterday. Here's the lowdown on the bill as a whole. The upper chamber maintained funding for several key livability […]
House GOP Won't Let Transit-Oriented Development Get Federal TIFIA Loans
House Republicans introduced a six-year transportation bill this week, and while it's not the utter disaster that past GOP proposals have been, advocates for smarter federal transportation policy are playing defense. Today, the House Transportation & Infrastructure Committee marked up the new bill. About 150 amendments were introduced, according to Transportation for America. All but a few […]
Livable Communities Act Clears Senate Committee
By Ben Fried | Aug 4, 2010
The Senate Banking Committee voted 12-10 yesterday in favor of the Livable Communities Act, legislation that would bolster the Obama administration's initiatives to link together transportation, housing, economic development, and environmental policy. Shaun Donovan, Ray LaHood, Lisa Jackson: Together forever? The Livable Communities Act would codify the partnership between HUD, US DOT, and the EPA. […]
Senate Climate Bill Triples the House's Investments in Clean Transport
By Elana Schor | Oct 26, 2009
The Senate environment committee released new details of its climate change legislation over the weekend, including the share of "emissions allowances" — the revenue generated by regulating carbon in a cap-and-trade system — that the bill would reserve for various sectors of the American economy. Sens. John Kerry (D-MA) and Barbara Boxer (D-CA), the climate […]
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 381
|
OH HEY THERE WHAT IS UP. Finally back, and with a new episode of Frank Ecto. It has been so long that you have all surely died and become ghosts, so I won't keep you here in the upper text for long. I hope the wait between this episode and the next is not as long!! BYE.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 6,384
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Perceived Stress and Coping Profile of Undergraduate Medical Students: A Cross Sectional Study
You are here: The International Journal of Indian Psychȯlogy > Articles > Volume 04, Issue 1, October-December, 2016 > Perceived Stress and Coping Profile of Undergraduate Medical Students: A Cross Sectional Study
Cross Sectional
| Published: December 25, 2016
Rohan Kalra
Junior Resident, Department of Psychiatry, S.N.Medical College, Bagalkot, India Google Scholar More about the auther
, Narayan R Mutalik
M.D., Assistant Professor, Department of Psychiatry, S.N.Medical College, Bagalkot, India Google Scholar More about the auther
, Vinod A
M.D, DPM. Senior Resident, Department of Psychiatry, S.N.Medical College, Bagalkot, India Google Scholar More about the auther
, Shankar Moni
Clinical Psychologist, Department of Psychiatry, S.N.Medical College, Bagalkot, India Google Scholar More about the auther
, S B Choudhari
M.D., Professor, Department of Psychiatry, S.N.Medical College, Bagalkot, India Google Scholar More about the auther
, Govind S Bhogale
Background: In the current competitive world, every student's life is very stressful due to various factors like studies, exams, batch mates, lecturers or pressure by parents. Stress is sometimes called as the wear and tear experienced by everyone's body because we need to adjust to the ever changing environment. Objective: Aim was to assess the perceived stress and coping profile among undergraduate medical students in Bagalkot. A total of 100 undergraduate students from S. N. Medical College, Bagalkot were included based on systematic random sampling test methods. Each enrolled student was given two self-rating questionnaires-Perceived Stress Scale and Brief Cope Inventory. Chi-square test and Fisher's exact were used for analysis. Result: Majority of study participants had belonged to very high health concern level followed by high health concern level. Most of the participants used self-distraction and active coping strategy. Perceived stress was not associated with sex, religion, place of domicile or type of the family. Conclusion: The effect of stress depends on the way it is perceived. The coping strategies are usually influenced by socioeconomic and cultural characteristics. So they vary from individuals to individuals. Students who are stressed must receive counseling on how to manage and cope up with the stress. We need to enforce early interventions strategies to improve the quality of life of each student by reducing the stress.
Perceived Stress, Coping Profile, Medical Undergraduates.
The author appreciates all those who participated in the study and helped to facilitate the research process.
The author declared no conflict of interests.
© 2016, R Kalra, N Mutalik, A Vinod, S Moni, S Choudhari, G Bhogale
How to cite this article: R Kalra, N Mutalik, A Vinod, S Moni, S Choudhari, G Bhogale (2016), Perceived Stress and Coping Profile of Undergraduate Medical Students: A Cross Sectional Study, International Journal of Indian Psychology, Volume 4, Issue 1, No. 69, ISSN:2348-5396 (e), ISSN:2349-3429 (p), DIP:18.01.008/20160401, ISBN:978-1-365-45447-9
Received: October 25, 2016; Revision Received: November 16, 2016; Accepted: December 25, 2016
Narayan R Mutalik @ narayanmutalik@gmail.com
Download: 19
Published in Volume 04, Issue 1, October-December, 2016
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,764
|
Q: Advice on basic Search Function I have a basic search function where I want to find a product according to the title(name) of the product.
rep.GetDomainObjectsByType("Visuals Product");
var visualsProducts = rep.DomainObjects;
prodSearched = (from p in visualsProducts
from pf in p.DomainObjectFields
where pf.FieldName == "Product Title" && pf.FieldValue.Contains(txtSearchValue)
select p).Distinct().ToList();
It works fine when entire title is entered such as 'The pros and cons of hitchiking'
How can I alter the query so as to return the title on partial matches only such as 'Pros and Cons'
regards
A: Your code is already using the String.Contains() method that looks for a substring. The issue with your sample test case is more likely to be associated with the casing of the search string.
Usually this would be handled at the data source, for example, by setting Case Insensitive collation to the database column.
Alternatively you can rewrite the query to use
&& pf.FieldValue.ToUpper().Contains(txtSearchValue.ToUpper())
It is possible to use
&& pf.FieldValue.IndexOf(txtSearchValue, StringComparison.OrdinalIgnoreCase) > -1
but this is less likely to be supported by the LINQ provider (for example, Entity Framework does not support it).
A: In your example, are you overlooking that "pros and cons" and "Pros and Cons" have mixed case?
There are a few different ways to ignore case. Here is one:
var foo = "The Pros and Cons";
bool matched = foo.IndexOf("pros and cons", StringComparison.OrdinalIgnoreCase) >= 0;
Some other options include 1) lowercase or uppercase both strings before comparing them, or 2) use CultureInfo and CompareInfo, or 3) use case-insensitive regular expression matching.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 6,887
|
Crescent street just got a little younger with the addition of Dragon & Dame. This urban style pub offers a variety of fun things to do inside and on their beautiful terrace. One of the most exciting things about this pub is the quality of their cocktail menu. It's evident that they take pride in demonstrating to Montreal that cocktails should be enjoyed by everyone as their prices are reasonable and the drinks are delicious.
As we entered, we were welcomed by a very friendly staff and a beautiful bar located at the center of the pub. The decor has a classic pub feel with an urban menu. Their menu is set up so you can enjoy a variety of things with a group of friends, or splurge by yourself if you enjoy eating more than one menu item. They have starters, snacks, plates to share, and mains that range from nachos, fried baby shrimp, fried chicken tacos, and of course, burgers!
We had the opportunity to try their nachos, which is everything you'd expect! You can add chicken or stick to the classic pub style. The fried baby shrimp were delicious, served with its own sweet and mild dipping sauce.
Another menu item we totally recommend for everyone is their Asian style cauliflower. We're calling it Asian style because when it comes out it looks like general Thai chicken! The cauliflower is seasoned with a spicy sauce that manipulates its flavours, making it actually taste like chicken! It may be incorporated in the menu for vegans but it truly is something everyone can enjoy.
Now, we've put emphasis on their cocktail menu, so let's introduce you to something we've never tried before. "The Mario Cart": Limoncello, Grappa, pineapple juice. The flavours work in harmony as you taste the power of the grappa at first, but then that punch slowly drifts away into your palate as the sweetness from the limoncello and the pineapple juice take over. The drink is layered with flavours that are easily a favourite for everyone.
Another cocktail that was another smashing hit is their "Smash Bash." Gin, lime juice, simple syrup, basil, cucumber: incredibly smooth and refreshing! Enjoy this on the terrace during our hot summer months and you can't go wrong.
While Dragon & Dame offers food and drink, you can also spice up your evening playing one of the several board games they have. They also have pool tables and a giant Jenga set that should be put to use. Maybe you and your friends can even lock the loser of your choice of game in the giant life size bird cage. Yup, they have that too.
Go for a drink, a bite, or a game or two. Spend your night on the terrace or in the lively atmosphere of the bar. Whatever you do, check out Dragon and Dame this summer.
Photos by Alex Spina (@kitchen___121) and Dragon and Dame.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,527
|
{"url":"https:\/\/www.physicsforums.com\/threads\/lhospitals-rule.3520\/","text":"# L'hospital's rule\n\nHow to prove it? I've watched a tv program before and I vaguely remember the proof consists of 4 parts, which includes the mean value theorem, Cauchy's mean value theorem and the other 2 theorems. I haven't learnt mean value theorem at that time and I didn't understand it, perhaps I can now.\n\nCheck out http:\/\/mathforum.org\/library\/drmath\/view\/53340.html. It's a bit too large to type in the forum. The proof that uses Cauchy's mean value theorem begins\n\nCode:\nDate: 12\/23\/98 at 11:43:47\nFrom: Doctor Rob\nSubject: Re: Proof of L'hopital's rule\nThe first proof uses Taylor expansions. The second uses Cauchy's MVT.\n\nDx\nOriginally posted by KL Kam\nHow to prove it? I've watched a tv program before and I vaguely remember the proof consists of 4 parts, which includes the mean value theorem, Cauchy's mean value theorem and the other 2 theorems. I haven't learnt mean value theorem at that time and I didn't understand it, perhaps I can now.\nVisual Calculus","date":"2020-09-25 13:27:32","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8133357763290405, \"perplexity\": 536.928974506183}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-40\/segments\/1600400226381.66\/warc\/CC-MAIN-20200925115553-20200925145553-00205.warc.gz\"}"}
| null | null |
← George Rodriguez – We will not be suckered by elitist Republicans!
Video-TFIRE – Who Killed The Texas Solution with Peter Batura 6/23/2014 →
Dale Huls – A Grassroots Analysis of 2014 RPT Immigration Plank Options
Posted by Dale Huls on June 12, 2014
Fellow Grassroots,
Since the convention there has been a serious effort coming out of SD 7 to mischaracterize the immigration platform plank that was adopted as the less conservative option. We were challenged to compare the Mark Ramsey option vs the Peter Batura option and decide which was the more conservative.
I have accepted this challenge and developed a white paper analyzing the two options. While we may still disagree, I believe this provides the tea party and conservative basis as to why approximately 60% of the delegates chose the Batura amendment.
Please read, share and comment regarding this analysis. I believe the wisdom of the body selected the right course of action.
I apologize in advance for any errors and mistakes that may be in the document. I only had time to do a first pass without a vetting review. I can only sit behind a computer so long and am now on my way to the border to stand watch against the tsunami of illegals crossing into Texas.
Dale Huls
Texas Border Volunteer and Executive Board Member, Clear Lake Tea Party
PDF available for printing: Whitepaper_-_Analysis_of_2014_RPT_Immigration_Plank_Proposals.pdf
A Grassroots Analysis of 2014 PRT Platform Immigration Plank Proposals
Dale Thomas Huls
2951 Marina Bay Dr. #130-394
League City, Texas 77573
dhuls912@gmail.com
A challenge from SD 7 Republican leaders Valoree Swanson and Mark Ramsey to compare the two main immigration plank options and decide whether the platform committee's amended (trigger) draft immigration plank was more conservative than the immigration plank eventually adopted by the convention delegates. This challenge has been accepted and this document is the result of that analysis.
The analysis and conclusions presented in this paper, document the assumptions and bias of the majority conservative grassroots Republicans that removed the Texas Solution from the 2014 RPT Platform Report.
Based on the side-by-side pro and con comparisons in section 2.3 it can be reasonably concluded that the Batura immigration plank (#53) was the more conservative option presented to the delegates at the 2014 RPT Convention in Ft. Worth, Texas. While both planks offered conservative provisions the Ramsey amended plank (#56) based on the PPARC draft immigration plank was found to be fundamentally flawed in many areas. Consequently, it can be concluded the RPT immigration plank was truly "perfected" during the convention process.
1.1. Purpose
The purpose of this whitepaper is to address the relative conservative merits regarding the immigration plank issue that arose during the 2014 RPT Convention in Ft. Worth, Texas.
1.2. Background
During the 2012 Republican of Texas convention the legal and illegal immigration planks of the previous RPT Platform was replaced by the Texas Solution, described as a market-based approach to solving illegal immigration issues. The main feature of the Texas Solution was a guest worker program. Many grassroots Republicans felt that this approach was a ruse for "cheap labor" and amnesty under guise of a so-called solution. Furthermore, many believed that the Texas Solution had been adopted through parliamentarian maneuvering under the guidance of senior Party officials.
After two years of waiting, activists across the State gathered at the 2014 RPT Convention in Ft. Worth determined to repeal the Texas Solution and replace it with a common sense immigration plank. After a contentious debate in the platform committee, a draft immigration plank was offered that replaced the Texas Solution but kept a guest worker program under the new name of a Provisional Visa Program. During the platform committee's work, a substitution amendment was offered which removed the guest worker language and lost due to a 15 to 15 tie in committee. However, a minority report was generated and presented on the convention floor. After a spirited floor fight on the convention floor, the platform committee's draft immigration plank was initially amended to include a secure border "trigger" and the minority report was defeated. Later that day, a substitute amendment which removed the contentious guest worker language that had been the main focus of the previous Texas Solution plank was proposed and adopted.
1.3. Issue
Although the debate was passionate throughout the convention and the amending process was conducted with fairness by the Chair, the oft-described "perfecting" process of the platform has left many Texans in confusion as to which platform plank was the more conservative plank. For example, Senate District 7 voted overwhelmingly against the substituted amendment that was eventually adopted. Mark Ramsey from SD 7 had offered the original "trigger" amendment to the original draft platform committee report which kept a provisional visa program in place with implementation occurring after the border is secured. Once the amendment offered by Peter Batura was adopted and the convention closed, many activists celebrated the removal of the Texas Solution and the guest worker program.
However, the debate continued across social media and emails as to the true ramifications of the immigration plank debate, Republican leaders in SD 7 began to claim that the defeated immigration plank with a trigger amendment was, in fact, the more conservative of the two options debated on the convention floor. They contended that they were stronger on border security and immigration reform and offered a one page table to back up their claims. They offered up a challenge to the grassroots supporters of the adopted plank to compare the two planks and decide for themselves.
This whitepaper is the result of responding to this challenge by analyzing each plank on its own merits and then comparing the results to each other.
For the purposes of this analysis, the original immigration plank as proposed by the RPT PPARC and the accompanying Minority Report #2 is not analyzed. Analysis is limited to the PPARC's immigration plank as amended (Mark Ramsey offered amendment, Ref. 1) and the final RPT adopted immigration plank (Peter Batura offered amendment, Ref. 2). The original PPARC plank and Minority Report #2 became irrelevant after being amended in the case of the former and being defeated by the delegates in the case of the latter.
Additionally, the language of the first three paragraphs of each plank version will not be addressed in this analysis since both planks contain the exact same language.
Each plank version will be analyzed separately and then comparatively with respect to the following topics:
Securing the Border
Modernizing Immigration Laws
Guest Worker/Provisional Visa Programs
2.1. Analysis of the Amended Draft Platform Committee Immigration Plank Proposed by Mark Ramsey
2.1.1. Securing the Border
The PPARC immigration plank as amended (M. Ramsey) begins its border security language under a discrete set of three bulleted items:
"Secure Our Borders First –
We demand the federal government immediately secure the borders and bring safety and security for all Americans.
We demand Congress develop and fund a National Border Security Plan based upon the recommendations of lawmakers in Texas and other border states.
Because the federal government has failed to act, we call on the Texas legislature to develop and fund a border and port of entry security plan utilizing state and local law enforcement."
Additional language related to border security is as follows:
"In order to deal with the current undocumented population, only after the borders are secured and verified by the States, we urge Congress…"
ANALYSIS – The border security bullet language is adequate in vision and general terminology. The title of the border security section is a declarative statement heading the emphasizing securing the border first. The first bullet is a call for the federal government to secure the border. This bullet links the safety and security of Americans to border enforcement and properly defines border security as a federal issue. This bullet language is a restatement of the 2012 Texas Solution plank bullet on border security.
The second bullet calls for a National Border Security Plan to be developed by Congress. While the intent of resolution is commendable, planning and implementation of a border security plan remains in the purview of the Executive Branch per the US Constitution. Congress does not have the authority to develop an executable plan. Congress may only pass legislation and fund activities related to border security. Consequently, this bullet as written requests an unconstitutional action by Congress which would further expand the role of the legislative branch and duplicate the authority of the Executive branch. However, it will be assumed to be poorly written and the intent was to merely pass legislation regarding the development of a plan. Finally, while Texas and the other 15 Border States can offer excellent suggestions regarding border security, it is believed that all States are greatly impacted by lax border security and have equal standing in developing a National Border Security Plan.
The final bullet addressing border security recognizes the failure of the federal government to control the border and calls on Texas to develop and fund its own border and port of entry security plan. While Texas may have sovereign State rights at the border, clearly the US Ports of Entry are entirely within the federal domain and not enforceable by State legislative actions. Otherwise, this bullet is entirely consistent with the Governor and Lt. Governor, as well as, the Republican candidates for both offices. The Department of Public Safety has already drawn up plans to control the border once sufficient funding is available.
Additional language inserted into the Provisional Visa Program text again emphasizes a State verified secure border before the legalization of the approximately 11 million illegal aliens currently residing in the United States.
Overall, the border security language in this plank is better than the previous 2012 Texas Solution plank. It offered a National Border Security Plan by Congress (although not constitutional as written) and called for a Texas law enforcement solution to control the border. And finally, it does appear to emphasis securing the border first before the implementation of a mass legalization program for illegal aliens residing in the country.
2.1.2. Modernizing Immigration Laws
The PPARC immigration plank as amended (M. Ramsey) begins its immigration reform language under the heading "Modernize the Immigration Laws" and supported the following five bulleted items:
"Modernize the Immigration Laws –
We support the improvement of our 1936 Social Security card to use anti-counterfeit technology.
We support replacement of current employment visa system with an efficient, cost effective system that responds to actual and persistent labor shortages and family re-unification.
We support the reallocation of immigration slots balanced to meet labor shortages.
We support ending country of origin quotas.
We support ending the annual green card lottery."
ANALYSIS – The first bullet addressing immigration reform advocates a technological update for the Social Security card system which would produce a counterfeit resistant card. Historically, the US Social Security card has never been used or accepted as a form of identification. It is the number itself that has value and once provided to an employer or applicable government agency can be checked against a government database. The call for an updated SS card in an immigration plank can reasonably be construed as the premise for a national identification card. This item was also in the 2012 Texas Solution plank but unlike the 2012 version, the statement declaring that this will not be used as a national ID for US citizens was dropped in the 2014 version. While updating Social Security cards is not a problem for conservatives, a national ID card is.
The second bullet does not truly address immigration reform but focuses on the current guest worker program in terms of efficiencies, cost effectiveness and responding to actual and persistent labor shortages. It is assumed that this item is related to the high skilled labor visa program used to fill critical labor shortages. This is the first discrete item referencing a guest worker program. This item is not supported in the first three paragraphs of this plank with an applicable rationale.
The third bullet also addresses guest workers by promoting a market-based approach to reallocating immigration slots to meet labor shortages. This bullet also supports "chain migration" by mentioning "family re-unification as a Republican goal.
The fourth and fifth bullets are true immigration reform items that call for ending country of origin quotas and ending the annual green card lottery. Conservatives believe that you should be accepted into this country based on merit and individual circumstance rather than being limited to a home country's quota. America should not welcome its legal immigrants based on a game of chance.
Ultimately, this section of the plank does address true immigration reform in the fourth and fifth bullets but lays a pretext under the guise of immigration reform for a national ID card (1st bullet), a guest worker program (2nd & 3rd bullet) and chain migration (3rd bullet). Overall, these provisions are not conservative positions.
2.1.3. Guest Worker/Provisional Visa Programs
The PPARC immigration plank as amended (M. Ramsey) its guest worker section under a new heading called the "Provisional Visa Program" and supported by the following five bulleted items:
"Provisional Visa Program – In order to deal with the current undocumented population, only after the borders are secured and verified by the States, we urge Congress to establish a new provisional visa with a term of five (5) years that does not provide amnesty, does not cause mass deportation, and does not provide a pathway to citizenship but does not preclude existing pathways.
An eligibility criterion should consider criminal history, completion of penalties and fines for immigration violations and payment of current and back taxes.
Participants must be responsible for their own and families private health insurance.
Participants must waive any and all rights to apply for financial assistance from public entitlement programs.
Participants must show a proficiency in the English Language.
We urge Congress and the state legislature to strengthen enforcement and penalties on employers that do not comply with labor and employment laws to ensure an equitable labor market. There will be no penalties to those employers that comply with effective employment verification systems."
ANALYSIS – Prior to the bulleted items, the introductory paragraph definitively calls for the establishment of a provisional visa program (aka guest worker program). In this plank, Republicans have adopted the language of the Democrats in using terminology such as "undocumented population" rather than the correct term of "illegal aliens." This is a normalization step needed to peddle legalization of non-citizens. A so-called "trigger" was added to satisfy the secure the border first crowd and still keep a guest worker program. This amendment was an improvement to the original PPARC language. It calls for verification of a secure border by the States (assume Border States) as a trigger for Congress to establish a provisional visa program. This provision also mandates a 5-year guest worker program without any specifics such as is a one-time only visa or is it a renewable provisional visa? Will a guest worker have to return to his or her country of origin to renew their visa? Will they be allowed to bring their families and if they have children will they be American citizens? Who will police such a program when it has been demonstrated that the federal government cannot even track foreigners in the United States here on student visas? What would be the penalties if a guest worker loses his/her visa due to loss of job, expiration of visa, or criminal activity? None of these questions are answered or even addressed. The guest worker provision language goes even further in declaring that the provisional visa program would not provide amnesty. How is that possible? With no provision requiring the illegal alien to leave the United States in order to sign up for the new visa program, it is concluded that legalization of status while remaining in situ is indeed amnesty. A nominal fee or penalty as a way to buy a spot to the front of the line does not negate the basic fact that if you sneak into this country, you can stay provided you purchase a visa. That is an open borders process. The provision does state that this legalization process should not lead to a path for citizenship but other citizenship pathways would be open. Will the provisional visa be the equivalent of a "green card" that legal immigrants use awaiting citizenship? It is believed that a new Republican sponsored Provisional Visa Program has too many questions and could be used for a variety abuses to the foreign workers by unscrupulous intermediaries and corrupt businesses. The federal government will demonstrably seek to expand a provisional visa program that will collapse under its own incompetence or create a new normal by which anyone (terrorist, criminal, coyote, multinational gang member, human trafficker, or victim) can gain entry to the United States under a provisional guest worker visa program.
The first bulleted item under the new Provisional Visa Program calls for eligibility criterion that includes criminal history, payment of penalties and fines, and payment of current and back taxes. How is this supposed to happen? Doing criminal background checks in this country may be barely possible. Background checks in foreign countries will be impossible. If illegal aliens have been living under the radar due to their illegal status, how will the authorities determine what taxes are owed? It is concluded that this item has been put in to give the appearance of legitimizing the illegal alien population that would come under a guest worker program.
The 2nd and 3rd bullets are intended to show that a guest worker would not be a burden to the American taxpayer. A voluntary disavowal of benefits will never stand up in today's courts. Once a person is in the United States, they become eligible for all kinds of benefits and entitlements. The Supreme Court has already ruled that States cannot deny illegal aliens a public education or medical care. They get in-state tuition rates in our universities. They are allowed tax credits and welfare. It is not believed that these items could be enforced or stand-up to a court challenge given the contemporary rulings from the federal courts on these issues. Again, it is concluded that these bulleted items were included in the plank to assuage conservative critics of a guest worker program regarding the taxpayer burden of the sudden legalization of 11 million illegal aliens.
2.1.4. Miscellaneous Items
The PPARC immigration plank as amended (M. Ramsey) retains an additional two provisions:
"Oppose Amnesty – We oppose any form of amnesty to include any granting of legal status to persons in the country illegally."
"Oppose Mass Deportation – We oppose any form] of mass deportation."
ANALYSIS – It was assumed that these two items were set apart in the same manner as "Secure Our Borders First," "Modernize the Immigration Laws," and "Provisional Visa Program" to emphasize the importance of these issues. However, these two items are diametrically opposed to each other. Either one or the other can be true but not both of them. You cannot oppose the granting of legal status to illegal aliens and then be opposed to the mass deportation of such aliens. If the logic trail is followed from the other side, you also cannot allow millions of illegal aliens to remain in the United States and not grant legal status to that population. Since both statements cannot be true, it is determined that these statements were placed in the plank simply to mollify those on the right who demand "no amnesty" and those on the left who decry conservatives for promoting "mass deportation" and destroying families. In conclusion, given the context of the overall plank it can be deduced that the purpose of the plank is to provide legal status to persons illegally in the country (Provisional Visa Program) and therefore a form of amnesty while opposing mass deportations of the same. The "Oppose Amnesty" provision is a false statement.
2.2. Analysis of the Adopted Immigration Plank Offered by Peter Batura
The adopted immigration plank as substituted (P. Batura) provides for border security language as follows:
"Secure the borders through
Increasing the number of border security officers
Increasing joint operations and training with local law enforcement, DPS and the Texas State Guard
Contiguous physical barrier coupled with electronic, infrared and visual monitoring"
ANALYSIS – The statements regarding border security are simple and discrete. Border security is discussed in real terms by increasing resources (more border security officers), more integrated operations and training, and a physical barrier (assume a fence) to deter illegal aliens from crossing the border and detect attempts when they occur.
However, this provision does not set a time frame address the immediacy of the problem or offer a prioritization with respect to other actions (e.g., secure the border first). Furthermore, it does not address private property issues in constructing such a barrier.
With the level of specificity and the immediacy of the problem apparent on the news every day, it can be determined that the plank adequately addresses the border security issue.
The adopted immigration plank contains language addressing the modernization of immigration laws as follows:
"Modernizing Current immigration Laws to address the following:
Any form of Amnesty should not be granted, including the granting of legal status to persons in the country illegally
We support replacement of the current employment visa system with an efficient cost effective system
We support ending country of origin quotas
We support ending the annual green card lottery"
ANALYSIS – The 1st bullet addressing immigration laws is a declarative statement forbidding the granting of amnesty to illegal aliens. There are no other statements in the plank that contradict opposing granting legal status to illegal aliens in the United States.
The third and fourth bullets are true immigration reform items that call for ending country of origin quotas and ending the annual green card lottery. Conservatives believe that you should be accepted into this country based on merit and individual circumstance rather than being limited to a home country's quota. America should not welcome its legal immigrants based on a game of chance.
Ultimately, this section of the plank does address true immigration reform in the third and fourth bullets and sets a marker for "no amnesty" with any subsequent immigration reform.
The adopted immigration plank does contain language referencing a guest worker program as follows:
"In addition, with 92 million Americans not working, the labor force at 36-year low and a lethargic economy, the United States of America can ill-afford a guest worker program designed to depress wages."
"Once the borders are verifiably secure, and E-verify system use is fully enforced, creation of a visa classification for non-specialty industries which have demonstrated actual and persistent labor shortages"
ANALYSIS – The fourth paragraph in the adopted plank definitively states that America cannot afford a guest worker program to provide corporate interests a legal source of cheap labor.
However, the bulleted item does speak to a new visa classification and recognizes the fact that there are issues within the unskilled labor workforce. It is unclear whether this is to be part of the existing current employment visa program or if a new program needs to be developed.
Certainly, this immigration plank greatly deemphasizes the guest worker provisions in the 2012 Texas Solution. It is clear that a "market-based solution" to immigration is not an approach the Republican Party of Texas endorses. Additionally, this language does indicate that the new unskilled worker classification should not be developed until the border is verifiably secure. Yet, it leaves open the question regarding who is responsible for verification – States of the federal government.
Ultimately, it is determined that the adopted plank does not support a new "market-based" guest worker approach to the illegal alien problem in America.
The adopted immigration plank also included the following provisions:
"Ending In-State Tuition for illegal immigrants
Enhancing State smuggling laws
Prohibiting Sanctuary cities
Prohibiting the knowing employment of illegal immigrants
Providing civil liability protections for landowners against illegal immigrants
Protecting the ability of law enforcement to inquire of the status of someone in custody"
ANALYSIS – The above bullets are a laundry list of items aimed at ending the magnets for illegal aliens (in-State tuition, sanctuary cities, and employment), enhanced enforcement (smuggling laws, status inquiries) and protecting ranchers and property owners from illegal alien activities. These items represent a conservative viewpoint regarding the immigration issues they represent. There are no contradictory statements.
2.3. Comparative Analysis of the Amended and Substituted Immigration Planks
The following table represents the pros and cons regarding each amendment's relative merits on securing the border.
Ramsey Amendment (#56) Batura Amendment (#53)
Emphasizes border security first
Increase border security officers
State verification of border security
Joint ops and training integration with BP, DPS, and State Guard
National Border Security Plan
Contiguous physical barrier
Calls for Texas law enforcement border solution
Calls for Texas control of US Ports of Entry
No timeline (secure the border first)
No stated priority except with reference to a guest worker classification visa
In the pro/con side-by-side analysis of the border security issue, it is evident that two different approaches were taken with respect to securing the border. The Ramsey amendment focused on the immediacy of the problem, provided a prioritization, and called for formal plans to control the border. The Batura amendment provided specific strategies to control the border. Under the issue of securing the order, it can be reasonably concluded that either amendment would be adequate and neither amendment can be considered the more conservative.
The following table represents the pros and cons regarding each amendment's relative merits on modernizing immigration laws.
End country of origin quotas
End green card lotteries
No amnesty/legal status for illegal aliens in country
Basis for a National ID card (updated SS Card)
Calls for chain migration
In the pro/con side-by-side analysis of the modernizing immigration laws issue, there were some pros that each plank promoted (origin quotas and green card lotteries). However, the Ramsey amendment had some serious flaws which could reasonably construe as a basis for a National ID Card and a call for chain migration. Neither of these positions are conservative positions. On the other hand, the Batura amendment explicitly rejected granting amnesty/legal status to illegal aliens as a "modernization" of immigration laws. While the Ramsey amendment does have a line item that rejects amnesty (see further discussion in section 2.3.4) it cannot be listed as a pro in this section. Furthermore, the listed cons in the Ramsey amendment are so egregious that the the Batura amendment can only be considered the more conservative alternative.
The following table represents the pros and cons regarding each amendment's relative merits on a guest worker/provisional visa program.
Recognizes there maybe issues with America's unskilled labor work force
States America cannot afford a cheap labor guest worker program
Requires a verifiable secure border by the States
Requires a verifiable secure border
Deemphasizes guest worker program as a solution to illegal immigration
Emphasizes provisional visa program as a solution to illegal immigration
Uses terminology of the left (undocumented population)
Lack of clarity regarding the parameters of the 5-yr guest worker plan
Allows illegal aliens to "buy" a place at the front of the line for residency in the US
Unworkable restrictions on healthcare, benefits and entitlements
In regards to the comparative analysis between the two planks, the evaluator recognizes the fact that those who think a guest worker program is necessary will not agree with those who don't. The offered analysis in this document is from the perspective that a guest worker program is not necessary or desirable at this time. With that said, the Batura amendment is clearly the more conservative.
The following table represents the pros and cons regarding each amendment's relative merits on planks miscellaneous items.
Oppose Amnesty
Ending In-State tuition
Oppose Mass Deportations
Enhancing smuggling laws
Prohibit sanctuary cities
Prohibit known illegal alien employment
Civil liability protections
Law enforcement status inquiries
Oppose Amnesty and Oppose Mass Deportations cannot both be true
In the pro/con side-by-side analysis of miscellaneous plank issues, clearly show that the Batura amendment contains many accepted conservative provisions. The two miscellaneous provisions in the Ramsey amendment were found to be mutually exclusive. Consequently, the Batura plank was determined to be the more strongly conservative plank with respect to miscellaneous provisions.
Filed Amendment #56 to amend the Immigration Plank on page 39 of the 2014 Republican Party of Texas Report of Permanent Platform Committee, dated June 7 2014.
Filed Amendment #53 to substitute the Immigration Plank on page 39 of the 2014 Republican Party of Texas Report of Permanent Platform Committee, dated June 7 2014.
http://www.clearlaketeaparty.com/a_grassroots_analysis_of_2014_rpt_immigration_plank_options
This entry was posted in Dale Huls. Bookmark the permalink.
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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\section{Introduction}
\label{s_intro}
The so-called Knudsen regime in gas dynamics describes a very
dilute gas confined between solid walls. The gas is dilute in the
sense that the mean free path of gas molecules, that is, the typical
distance travelled between collisions of gas molecules, is much
larger than the typical distance between consecutive collisions of
the gas molecules with the walls. Hence molecules interact
predominantly with the walls, and the interaction among themselves
can be neglected.
A typical setting where this is relevant is in the motion of absorbed
guest molecules in the pores of a microporous solid
where both the pore
diameter and the typical number of guest molecules
inside the pores are small.
On molecular scale the wall-molecule interaction is usually
rather complicated and very difficult to handle explicitly.
Hence one
resorts to a stochastic description in which gas molecules, from now
on referred to as particles, move ballistically between collisions
with the walls where they interact in a random fashion. In the
Knudsen model one assumes that particles are pointlike and that the
kinetic energy of a particle is conserved in a collision with the
wall, but its direction of motion changes randomly.
The law of this random reflection is taken to be the cosine law
where the outgoing direction is cosine-distributed relative to the
surface normal at the point where the particle hits the wall.
For a motivation of this choice, sometimes also called Lambert
reflection law, see \cite{FY}. Notice that this dynamic implies
that the incoming direction is not relevant
and is ``forgotten'' once a collision has happened.
Thus this process defines a Markov chain which we call
``Knudsen stochastic billiard'' (KSB).
The random sequence of hitting points is referred to as
``Knudsen random walk'' (KRW) \cite{CPSV1}.
Pores in microporous solids may have a very complicated surface.
Among the many possibilities, an elongated tube-shaped pore surface
has recently
attracted very considerable attention \cite{ZRBCK}.
A three-dimensional connected
network of ``tubes'' may be regarded as constituting the entire
(nonsimply connected) interior empty space of microporous grain
in which particles can move. In this setting parts of the surface of
the individual tubes are open and connect to a neighboring pore so
that particles can move from one to another pore. It
is of great interest to study the large scale motion of a molecule
along the direction in which the tube
has its greatest elongation. We
think of the direction of longest elongation of a single tube as the
first coordinate in $d$-dimensional Euclidean space. Together with
the locally, usually very complicated surface of pores, this
leads us to introduce the notion of a random tube with a random
surface to be defined precisely below.
Knudsen motion in a tube has been studied heuristically for simple
regular geometries such as a circular pipe and also numerically for
self-similar random surfaces (see, e.g., \cite{CD,CM,RZBK}). For the
straight infinite pipe, it is not difficult to see that
in dimensions larger than two, the mean-square displacement grows
asymptotically linearly in time, that is, diffusively, while in two
dimensions the motion is superdiffusive due to sufficiently large
probability for very long flights between collisions.
Interestingly though, rigorous work on this conceptually simple
problem is rare. In fact, it is not even
established under which conditions on the pore surface the motion
of a Knudsen particle has diffusive mean square displacement and
converges to Brownian motion. Indeed, it is probable that
one may construct counterexamples to Brownian motion in three or
more dimensions without having to
invent physically pathological pore
surfaces, but considering a nonstationary (expanding or shrinking)
tube instead. We refer here to the work \cite{MVW} (there, only the
two-dimensional case is considered, but it seems reasonable that one
may expect similar phenomena in the general case as well). Even for
the stationary tube, it seems reasonable that the presence of
bottlenecks with random (not bounded away from $0$) width may cause
the process to be subdiffusive.
In this work we shall define a class of single
infinite random tubes
for which we prove convergence of KSB and KRW to Brownian motion.
Together with related earlier and on-going work, this lays the
foundation for addressing more subtle issues that arise in the study
of motion in open domains which are finite and which allow for
injection and extraction
of particles.
This latter problem is of
great importance for studying the relation between the
so-called self-diffusion coefficient, given by the asymptotic
mean square displacement of a particle in an infinite tube
under equilibrium conditions, on the one hand, and the
transport diffusion coefficient on the other hand. The
transport diffusion coefficient is given by the
nonequilibrium flux in a finite open tube with a density
gradient between two open ends of the tube. Often only
one of these quantities can be measured experimentally,
but both may be required for the correct interpretation of
other experimental data. Hence one would like to
investigate whether both diffusion coefficients are equal
and specify conditions under which this the case. This
is the subject of a forthcoming paper \cite{CPSV3}. Here we focus
on the question of diffusion in the infinite tube in
the absence of fluxes.
For a description of our strategy we first come to the modeling of
the infinite tube. The tube stretches to infinity
in the first direction. The collection of its sections in the
transverse direction can be thought as a ``well-behaved'' function
$\omega\dvtx \alpha\mapsto\omega_\alpha$ of the first
coordinate $\alpha$ which values are subsets of ${\mathbb R}^{d-1}$.
We assume
that the boundary of the tube is Lipschitz and almost everywhere
differentiable, in order to define the process.
We also assume the transverse sections are bounded and that there
exist
no long dead ends or too thin bottlenecks.
For our long-time asymptotics of the walk, we need some large-scale
homogeneity assumptions on the tube; it is quite natural to
assume that the process $\omega=( \omega_\alpha;
\alpha\in{\mathbb R})$ is random, stationary and ergodic.
Now, the process essentially looks like a one-dimensional
random walk in a random environment, defined by
random conductances since Knudsen random walk is reversible.
The tube serves as a random environment for our walk. The tube, as
seen from the walker, is a Markov process which has a (reversible)
invariant law.
From this picture, we understand that the random medium is
homogenized on large scales,
and that, for almost every environment, the walk is asymptotically
Gaussian in the longitudinal direction. More precisely, we will
prove that after the usual rescaling the trajectory of the KRW
converges weakly to Brownian motion with some diffusion constant
(and from this we deduce also the analogous result for the KSB).
This will be done by showing ergodicity for the environment
seen from the particle and using the classical ``corrector
approach'' adapted from \cite{Koz}.
The point of view of the particle has become useful
\cite{KV,DFGW,BS} in the study of reversible random walks
in a random environment and in obtaining the central limit theorem for
the annealed law (i.e., in the mean with respect to the
environment). The authors from \cite{FSS} obtain an (annealed)
invariance principle for a random walk on a random point process in
the Euclidean space, yielding an upper bound on the effective
diffusivity which agrees with the predictions of Mott's law.
The corrector approach, by correcting the walk into a martingale in
a fixed environment, has been widely used to obtain the quenched
invariance principle for the simple random walk on the infinite
cluster in a supercritical percolation \cite{SS} in dimension
$d \geq4$, \cite{BB} for $d \geq2$.
These last two references apply to walks defined by random
conductances which are
bounded and bounded away from 0. The authors in \cite{BP}
and \cite{M} gave a proof under the only
condition of bounded conductances.
In this paper we will leave untouched the questions
of deriving heat kernel estimates or spectral estimates (see \cite{Bar}
and \cite{FM}, respectively) for the corresponding results
for the simple random walk on the infinite cluster.
We will not need such estimates to show that the corrector
can be neglected in the limit. Instead we will benefit from the
essentially one-dimensional structure
of our problem and use the ergodic theorem;
this last ingredient will require
introducing reference points in Section \ref{s_refpoints}
below to recover stationarity.
The paper is organized as follows. In Section \ref{s_notations}
we formally define the random tube and construct the stochastic
billiard and the random walk and then formulate our results.
In Section \ref{s_environment} the process of the environment seen
from the particle is defined and its properties are discussed.
Namely, in Section \ref{s_env_discrete} we define
the process of the environment seen from the discrete-time random
walk and then prove that this process is reversible with an
explicit reversible measure. For the sake of completeness,
we do the same for the continuous-time stochastic billiard in
Section~\ref{s_env_continuous}, even though the results of this
section are not needed for the subsequent discussion.
In Section \ref{s_constr_corrector} we construct the corrector
function, and in Section \ref{s_refpoints} we show that the corrector
behaves sublinearly along a certain stationary sequence of reference
points and that one may control the fluctuations of the corrector
outside this sequence.
Based on the machinery developed in Section \ref{s_environment},
we give the proofs of our results in Section \ref{s_proofs}. In
Section \ref{s_proof_inv_pr} we prove the quenched
invariance principle for the discrete-time random walk, and in
Section \ref{s_b_finite} we discuss the question of
finiteness of the averaged second moment of the projected jump
length. In Section~\ref{s_proof_inv_pr_cont} we prove the quenched
invariance principle for the continuous-time stochastic billiard,
also obtaining an explicit relation between the corresponding
diffusion constants.
Finally, in the \hyperref[app]{Appendix} we discuss the general case of random tubes
where vertical walls are allowed.
\section{Notation and results}
\label{s_notations}
Let us formally define the random tube in ${\mathbb R}^d$, \mbox{$d\geq2$}.
In this paper, ${\mathbb R}^{d-1}$ will always stand for the linear
subspace of ${\mathbb R}^d$ which is perpendicular to the first coordinate
vector $e$; we use the notation \mbox{$\|\cdot\|$} for the Euclidean norm
in ${\mathbb R}^d$ or ${\mathbb R}^{d-1}$. For $k\in\{d-1,d\}$
let ${\mathcal B}(x,\varepsilon)=\{y\in{\mathbb R}^k\dvtx\|x-y\|
<\varepsilon\}$ be the open
$\varepsilon$-neighborhood of $x\in{\mathbb R}^k$. Define
${\mathbb S}^{d-1}=\{y\in{\mathbb R}^d\dvtx\|y\|=1\}$ to be the unit
sphere in ${\mathbb R}^d$,
and let ${\mathbb S}^{d-2}={\mathbb S}^{d-1}\cap{\mathbb R}^{d-1}$ be
the unit sphere
in ${\mathbb R}^{d-1}$. We write $|A|$ for the $k$-dimensional Lebesgue
measure in case $A\subset{\mathbb R}^k$ and $k$-dimensional Hausdorff
measure in case $A\subset{\mathbb S}^k$. Let
\[
{\mathbb S}_h = \{w\in{\mathbb S}^{d-1}\dvtx h\cdot w > 0\}
\]
be the half-sphere looking in the direction $h$.
For $x\in{\mathbb R}^d$, sometimes it will be convenient to write
$x=(\alpha,u)$; $\alpha$ being the first coordinate of $x$ and
$u\in{\mathbb R}^{d-1}$; then $\alpha=x\cdot e$,
and we write $u={\mathcal U}x$; ${\mathcal U}$ being the projector on
${\mathbb R}^{d-1}$.
Fix some positive constant ${\widehat M}$, and define
\begin{equation}
\label{def_Lambda}
\Lambda= \{u\in{\mathbb R}^{d-1} \dvtx \|u\| \leq{\widehat M}\}.
\end{equation}
Let $A$ be an open
domain in ${\mathbb R}^{d-1}$ or ${\mathbb R}^d$.
We denote by $\partial A$ the boundary of $A$ and
by $\bar A = A\cup\partial A$ the closure of $A$.
\begin{df}
\label{def_Lipschitz}
Let $k\in\{d-1,d\}$, and suppose that $A$ is an open
domain in ${\mathbb R}^k$. We say that $\partial A$ is
$({\hat\varepsilon},{\hat L})$-Lipschitz, if for any $x\in\partial A$
there exist an affine isometry ${\mathfrak I}_x \dvtx {\mathbb R}^k\to
{\mathbb R}^k$ and a
function $f_x\dvtx{\mathbb R}^{k-1}\to{\mathbb R}$ such that:
\begin{itemize}
\item$f_x$ satisfies Lipschitz condition with constant ${\hat L}$,
i.e., $|f_x(z)-f_x(z')| < {\hat L}\|z-z'\|$ for all $z,z'$;
\item${\mathfrak I}_x x = 0$, $f_x(0)=0$ and
\[
{\mathfrak I}_x\bigl(A\cap{\mathcal B}(x,{\hat\varepsilon})\bigr) = \bigl\{z\in
{\mathcal B}(0,{\hat\varepsilon})\dvtx
z^{(k)} > f_x\bigl(z^{(1)},\ldots,z^{(k-1)}\bigr)\bigr\}.
\]
\end{itemize}
In the degenerate case $k=1$ we adopt the convention
that $\partial A$ is $({\hat\varepsilon},{\hat L})$-Lipschitz
for any positive ${\hat L}$ if points in $\partial A$ have a mutual
distance larger than ${\hat\varepsilon}$.
\end{df}
Fix ${\widehat M}>0$, and define ${\mathfrak E}_n$ for $n \geq1$
to be the set of all open domains $A$ such that $A\subset\Lambda$
and $\partial A$ is $(1/n,n)$-Lipschitz.
We turn ${\mathfrak E}= \bigcup_{n \geq1}{\mathfrak E}_n$ into a
metric space by defining
the distance between $A$ and $B$ to be equal to
$|(A\setminus B)\cup(B\setminus A)|$, making ${\mathfrak E}$ a Polish space.
Let $\Omega={\mathcal C}_{\mathfrak E}({\mathbb R})$ be the space of
all continuous
functions ${\mathbb R}\mapsto{\mathfrak E}$; let ${\mathcal A}$ be the
sigma-algebra
generated by the cylinder sets with respect to the Borel
sigma-algebra on ${\mathfrak E}$, and let ${\mathbb P}$ be a
probability measure on
$(\Omega,{\mathcal A})$. This defines a ${\mathfrak E}$-valued process
$\omega=(\omega_\alpha, \alpha\in{\mathbb R})$ with continuous
trajectories.
Write $\theta_\alpha$ for the spatial shift: $\theta_\alpha
\omega_{\cdot} = \omega_{\cdot+\alpha}$. We suppose that the
process $\omega$ is stationary and ergodic with respect to the
family of shifts $(\theta_\alpha,\alpha\in{\mathbb R})$.
With a slight abuse of notation, we denote also by
\[
\omega= \{(\alpha,u)\in{\mathbb R}^d \dvtx u\in\omega_\alpha\}
\]
the random domain (``tube'') where the billiard lives.
Intuitively, $\omega_\alpha$ is the ``slice'' obtained
by crossing $\omega$ with the hyperplane
$\{\alpha\}\times{\mathbb R}^{d-1}$. One can check that, under
Condition \ref{ConditionL}
below, the domain $\omega$ is an open subset of
${\mathbb R}^d$, and we will assume that it is connected.
We assume the following:
\renewcommand{\theCondition}{L}
\begin{Condition}\label{ConditionL}
There exist ${\tilde\varepsilon},{\tilde L}$ such that $\partial
\omega$
is $({\tilde\varepsilon},{\tilde L})$-Lipschitz (in the sense of
Definition \ref{def_Lipschitz}) ${\mathbb P}$-a.s.
\end{Condition}
Let $\mu^{\omega}_\alpha$ be the $(d-2)$-dimensional Hausdorff
measure on
$\partial\omega_\alpha$
(in the case $d=2$, $\mu^{\omega}_\alpha$ is simply the counting measure),
and denote $\mu^{\omega}_{\alpha,\beta} = \mu^{\omega}_\alpha
\otimes\mu^{\omega}_\beta$.
Since it always holds that $\partial\omega_\alpha\subset\Lambda$, we
can regard $\mu^{\omega}_\alpha$ as a measure on $\Lambda$ (with
$\operatorname{supp}
\mu^{\omega}_\alpha= \partial\omega_\alpha$), and $\mu^{\omega
}_{\alpha,\beta}$
as a measure on $\Lambda^2$ (with $\operatorname{supp}\mu^{\omega
}_{\alpha,\beta} =
\partial\omega_\alpha\times\partial\omega_\beta$). Also, we denote
by $\nu^{\omega}$ the $(d-1)$-dimensional Hausdorff measure
on $\partial\omega$; from Condition \ref{ConditionL} one obtains that $\nu^{\omega}$
is locally finite.
We keep the usual notation $dx, dv, dh, \ldots$ for the
$(d-1)$-dimensional Lebesgue measure
on $\Lambda$ (usually restricted to $\omega_\alpha$ for
some $\alpha$) or the
surface measure on ${\mathbb S}^{d-1}$.
\begin{figure}
\includegraphics{504f01.eps}
\caption{Notation for the random tube.
Note that the sections may be disconnected.}
\label{f_tube}
\end{figure}
For all $x=(\alpha,u)\in\partial\omega$ where they exist,
define the normal
vector ${\mathbf n}_{\omega}(x)={\mathbf n}_{\omega}(\alpha,u)\in
{\mathbb S}^{d-1}$ pointing inside the
domain $\omega$
and the vector ${\mathbf r}_{\omega}(x)={\mathbf r}_{\omega}(\alpha
,u)\in{\mathbb S}^{d-2}$ which is the
normal vector at $u\in\partial\omega_\alpha$ pointing inside the
domain $\omega_\alpha$
(in fact, ${\mathbf r}_{\omega}$ is the normalized projection of
${\mathbf n}_{\omega}$
onto ${\mathbb R}^{d-1}$) (see Figure \ref{f_tube}).
Denote also
\[
\kappa_x=\kappa_{\alpha,u}={\mathbf n}_{\omega}(x)\cdot{\mathbf
r}_{\omega}(x).
\]
Observe that $\kappa$ also depends on $\omega$, but we prefer not
to write it explicitly in order not to overload the notation.
Define the set of regular points
\[
{\mathcal R}_{\omega}= \{x\in\partial\omega\dvtx \partial\omega\mbox
{ is
continuously differentiable in }x, |{\mathbf n}_{\omega}(x)\cdot
e|\neq1\}.
\]
Note that $\kappa_x\in(0,1]$ for all $x\in{\mathcal R}_{\omega}$.
Clearly, it holds that
\begin{equation}
\label{differentials}
d\nu^{\omega}(\alpha,u) = \kappa_{\alpha,u}^{-1} \,d\mu^{\omega
}_\alpha(u)\,
d\alpha
\end{equation}
(see Figure \ref{f_differentials}).
\begin{figure}
\includegraphics{504f02.eps}
\caption{On formula (\protect\ref{differentials});
note that $\kappa_{\alpha,u}=\cos\phi$.}
\label{f_differentials}
\end{figure}
We suppose that the following condition holds:
\renewcommand{\theCondition}{R}
\begin{Condition}\label{ConditionR}
We have $\nu^{\omega}(\partial\omega\setminus{\mathcal R}_{\omega
})=0$, ${\mathbb P}$-a.s.
\end{Condition}
We say that $y\in\bar\omega$ is \textit{seen from} $x\in\bar\omega$
if there exists $h\in{\mathbb S}^{d-1}$ and $t_0>0$ such that
$x+th\in\omega$ for all $t\in(0,t_0)$ and $x+t_0 h = y$.
Clearly, if $y$ is seen from $x$, then $x$ is seen from $y$,
and we write ``$x \stackrel{\omega}{\leftrightarrow}y$'' when this occurs.
One of the main objects of study in this paper is the
Knudsen random walk (KRW) $\xi=(\xi_n)_{n \in{\mathbb N}}$ which is a
discrete time Markov process on $\partial\omega$
(cf. \cite{CPSV1}). It is defined through its transition density $K$:
for $x,y\in\partial\omega$,
\begin{equation}
\label{def_K}
K(x,y) = \gamma_d \frac{ ((y-x)\cdot{\mathbf n}_{\omega}(x) )
((x-y)\cdot{\mathbf n}_{\omega}(y) )}{\|x-y\|^{d+1}}
{\mathbb I}{\{x,y\in{\mathcal R}_{\omega}, x \stackrel{\omega
}{\leftrightarrow}y\}},
\end{equation}
where $\gamma_d = (\int_{{\mathbb S}_{e}} h\cdot e \,dh )^{-1}$
is the normalizing constant.
This means that, being ${\mathtt P}_{\omega},{\mathtt E}_{\omega}$
the quenched (i.e.,
with fixed $\omega$) probability and expectation, for any $x\in
{\mathcal R}_{\omega}$
and any measurable $B\subset\partial\omega$
we have
\[
{\mathtt P}_{\omega}[\xi_{n+1}\in B \mid\xi_n=x] = \int_B K(x,y)\,
d\nu^{\omega}(y).
\]
Following \cite{CPSV1}, we shortly explain why this Markov chain
is of natural interest. From $\xi_{n}=x$, the next step
$\xi_{n+1}=y$ is performed by picking randomly the direction
$h=(y-x)/\|y-x\|$ of the step
according to Knudsen's cosine density
$\gamma_d h \cdot{\mathbf n}_{\omega}(x) \,dh$ on the half
unit-sphere looking toward the interior of the domain. By
elementary\vspace*{1pt} geometric considerations, one can check that
$d\nu^{\omega}(y)= (h \cdot{\mathbf n}_{\omega}(y))^{-1} \|y-x\|
^{d-1}\,dh$ and recover the
previous formulas.
Let us define also
\begin{equation}
\label{K->Phi}
\Phi(\alpha,u,\beta,v)= (\kappa_{\alpha,u}\kappa_{\beta,v})^{-1}
K ((\alpha,u),(\beta,v) ).
\end{equation}
From (\ref{def_K}) we see that
$K(\cdot,\cdot)$ is symmetric, that is, $K(x,y)=K(y,x)$ for all
$x,y\in{\mathcal R}_{\omega}$;
consequently, $\Phi$ has this property as well:
\begin{equation}
\label{symmetry_Phi}
\Phi(\alpha,u,\beta,v) = \Phi(\beta,v,\alpha,u)
\qquad\mbox{for all }\alpha,\beta\in{\mathbb R},
u\in\partial\omega_\alpha, v\in\partial\omega_\beta.
\end{equation}
Clearly, both $K$ and $\Phi$ depend on $\omega$ as well,
but we usually do not
indicate this in the notation in order to keep them simple.
When we have to do it,
we write $K^\omega, \Phi^\omega$ instead of $K,\Phi$.
For any $\gamma$ we have
\begin{equation}
\label{shift_Phi}
\Phi^{\theta_\gamma\omega}(\alpha,u,\beta,v) =
\Phi^\omega(\alpha+\gamma,u, \beta+\gamma,v).
\end{equation}
Moreover, the symmetry implies that
\begin{eqnarray}
\label{symm_K}
K^\omega((0,u),y ) &=& K^{\theta_{y\cdot e}\omega}
\bigl((0,{\mathcal U}y),(-y\cdot e,u) \bigr),
\\
\label{symm_Phi}
\Phi^\omega(0,u,\alpha,v) &=& \Phi^{\theta_\alpha\omega}
(0,v,-\alpha,u).
\end{eqnarray}
We need also to assume the following technical condition:
\renewcommand{\theCondition}{P}
\begin{Condition}\label{ConditionP}
There exist constants $N,\varepsilon,\delta$ such that for ${\mathbb
P}$-almost
every $\omega$, for any $x,y\in{\mathcal R}_{\omega}$ with
$|(x-y)\cdot e|\leq2$
there exist $B_1,\ldots,B_n\subset\partial\omega$,
$n\leq N-1$ with $\nu^{\omega}(B_i)\geq\delta$ for all $i=1,\ldots
,n$ and
such that:
\begin{itemize}
\item$K(x,z)\geq\varepsilon$ for all $z\in B_1$,
\item$K(y,z)\geq\varepsilon$ for all $z\in B_n$,
\item$K(z,z')\geq\varepsilon$ for all $z\in B_i$, $z'\in B_{i+1}$,
$i=1,\ldots,n-1$
\end{itemize}
[if $N=1$ we only require that $K(x,y)\geq\varepsilon$].
In other words, there exists a ``thick'' path of length at
most $N$ joining $x$ and $y$.
\end{Condition}
Now, following \cite{CPSV1}, we define also the
Knudsen stochastic billiard (KSB)
$(X,V)$. First, we do that for the process starting on the
boundary $\partial\omega$
from the point $x_0\in{\mathcal R}_{\omega}\subset\partial\omega$.
Let $x_0=\xi_0,\xi_1,\xi_2,\xi_3,\ldots$
be the trajectory of the random walk, and define
\[
\tau_n = \sum_{k=1}^n \|\xi_k-\xi_{k-1}\|.
\]
Then, for $t\in[\tau_n,\tau_{n+1})$, define
\[
X_t=\xi_n+(\xi_{n+1}-\xi_n)\frac{t-\tau_n}{\|\xi_{n+1}-\xi_n\|}.
\]
The quantity $X_t$ stands for the position of the particle
at time $t$.
Since $(X_t)_{t \geq0}$ is not a Markov process by itself,
we define also the c\`{a}dl\`{a}g version
of the motion direction at time $t$,
\[
V_t = \lim_{\varepsilon\downarrow0}\frac{X_{t+\varepsilon
}-X_t}{\varepsilon}.
\]
Then, $V_t\in{\mathbb S}^{d-1}$ and the couple $(X_t,V_t)_{t \geq0}$
is a Markov process. Of course, we can define also the stochastic
billiard starting from the interior of $\omega$ by specifying its
initial position $X_0$ and initial direction $V_0$.
Define
\[
{\mathfrak S}= \{(\omega,u) \dvtx \omega\in\Omega, u\in\partial\omega
_0\}.
\]
One of the most important objects in this paper is the
probability measure ${\mathbb Q}$ on ${\mathfrak S}$ defined by
\begin{equation}
\label{def_Q}
d{\mathbb Q}(\omega,u) = \frac{1}{{\mathcal Z}} \kappa_{0,u}^{-1}
\,d\mu^{\omega}_{0}(u)
\,d{\mathbb P}(\omega),
\end{equation}
where ${\mathcal Z}=\int_\Omega d{\mathbb P}
\int_\Lambda\kappa_{0,u}^{-1}\,d\mu^{\omega}_0(u)$
is the normalizing constant. (We will show that ${\mathbb Q}$ is the
invariant law of the environment seen from the walker.)
To see that ${\mathcal Z}$ is finite, note that
${\mathcal Z}= \int_\Omega d{\mathbb P}
\int_{0}^1 d\alpha\int_\Lambda
\kappa_{\alpha,u}^{-1}\,d\mu^{\omega}_\alpha(u)$
by translation invariance, that is,
the expected surface area of the tube
restricted to the slab $[0,1] \times{\mathbb R}^{d-1}$
which is finite by Condition \ref{ConditionL}.
Let $L^2({\mathfrak S})$ be the space of ${\mathbb Q}$-square
integrable functions
$f\dvtx {\mathfrak S}\mapsto{\mathbb R}$.
We use the notation $\langle f \rangle_{{\mathbb Q}}$ for the
${\mathbb Q}
$-expectation of $f$:
\[
\langle f \rangle_{{\mathbb Q}} = \frac{1}{{\mathcal Z}}\int_{\Omega
}d{\mathbb P}\int
_{\Lambda}
d\mu^{\omega}_0(u)\, \kappa_{0,u}^{-1}
f(\omega,u)
\]
and we
define the scalar product $\langle\cdot, \cdot\rangle_{{\mathbb
Q}}$ in
$L^2({\mathfrak S})$ by
\begin{equation}
\label{def_scalar}
\langle f, g \rangle_{{\mathbb Q}} = \frac{1}{{\mathcal Z}}\int
_{\Omega}d{\mathbb P}
\int_{\Lambda}
d\mu^{\omega}_0(u)\, \kappa_{0,u}^{-1}
f(\omega,u) g(\omega,u).
\end{equation}
Note that $\langle f \rangle_{{\mathbb Q}} = \langle{\mathbf1}, f
\rangle
_{{\mathbb Q}}$ where ${\mathbf
1}(\omega,u)=1$ for all $\omega,u$.
Now, for $(\beta,u)\in{\mathcal R}_{\omega}$ we define the local
drift and the second
moment of the jump projected on the horizontal direction:
\begin{eqnarray}\label{def_drift}
\Delta_\beta(\omega,u) &=& {\mathtt E}_{\omega}\bigl((\xi_1-\xi_0)\cdot
e \mid
\xi_0=(\beta,u) \bigr)\nonumber\\
&=& \int_{\partial\omega}(x\cdot e - \beta) K((\beta,u), x)
\,d\nu^{\omega}(x)
\\
&=& \int_{-\infty}^{+\infty} (\alpha-\beta)\, d\alpha
\int_\Lambda d\mu^{\omega}_\alpha(v)\,
\kappa_{\beta,u} \Phi(\beta,u,\alpha,v),
\nonumber\\
b_\beta(\omega,u) &=& {\mathtt E}_{\omega}\bigl(\bigl((\xi_1-\xi_0)\cdot e\bigr)^2
\mid
\xi_0=(\beta,u) \bigr)\nonumber\\
&=& \int_{\partial\omega}(x\cdot e - \beta)^2 K((\beta,u), x)
\,d\nu^{\omega}(x)
\nonumbe
\\
&=& \int_{-\infty}^{+\infty} (\alpha-\beta)^2 \,d\alpha
\int_\Lambda d\mu^{\omega}_\alpha(v)\,
\kappa_{\beta,u} \Phi(\beta,u,\alpha,v).
\nonumbe
\end{eqnarray}
When $\beta=0$, we write simply $\Delta(\omega,u)$ and
$b(\omega,u)$
instead of $\Delta_0(\omega,u)$ and $b_0(\omega,u)$.
In Section \ref{s_environment} we show that $\langle\Delta\rangle
_{{\mathbb Q}}=0$
[see (\ref{g_Delta})].
Let $Z^{(m)}_\cdot$ be the polygonal interpolation of
$n/m \mapsto m^{-1/2}\xi_n\cdot e$.
Our main result is the quenched invariance principle
for the horizontal projection of the random walk.
\begin{theo}
\label{t_q_invar_princ}
Assume Conditions \ref{ConditionL}, \ref{ConditionP}, \ref{ConditionR}, and suppose that
\begin{equation}
\label{finite_2nd_moment}
\langle b \rangle_{{\mathbb Q}} < \infty.
\end{equation}
Then, there exists a constant $\sigma>0$ such that for ${\mathbb P}$-almost
all $\omega$, for any starting point from ${\mathcal R}_{\omega}$,
$\sigma^{-1}Z^{(m)}_\cdot$
converges in law, under ${\mathtt P}_{\omega}$,
to Brownian motion as \mbox{$m\to\infty$}.
\end{theo}
The constant $\sigma$ is defined by (\ref{def:sigma}) below.
Next, we obtain the corresponding result for the continuous time
Knudsen stochastic billiard.
Define ${\hat Z}_t^{(s)} = s^{-1/2}X_{st}\cdot e$.
Recall also a notation from \cite{CPSV1}:
for $x\in\omega$, $v\in{\mathbb S}^{d-1}$,
define (with the convention $\inf\varnothing=\infty$)
\[
{\mathsf h}_x(v) = x+v\inf\{t>0 \dvtx x+tv \in\partial\omega\}
\in\{\partial\omega,\infty\}
\]
so that ${\mathsf h}_x(v)$ is the next point where the particle
hits the boundary when starting at the location $x$
with the direction $v$.
\begin{theo}
\label{t_q_invar_princ_cont}
Assume Conditions \ref{ConditionL}, \ref{ConditionP}, \ref{ConditionR}, and suppose
that (\ref{finite_2nd_moment}) holds.
Denote
\[
{\hat\sigma} = \frac{\sigma\Gamma({d}/{2}+1){\mathcal Z}}
{\pi^{1/2}\Gamma(({d+1})/{2})d}
\biggl(\int_\Omega|\omega_0| \,d{\mathbb P}\biggr)^{-1},
\]
where $\sigma$ is from Theorem \ref{t_q_invar_princ}.
Then, for ${\mathbb P}$-almost all $\omega$,
for any initial conditions $(x_0,v_0)$ such that
${\mathsf h}_{x_0}(v_0)\in{\mathcal R}_{\omega}$,
${\hat\sigma}^{-1}{\hat Z}^{(s)}_\cdot$
converges in law to Brownian motion as $s\to\infty$.
\end{theo}
Next, we discuss the question of validity
of (\ref{finite_2nd_moment}).
\begin{prop}
\label{pr_suff_2nd_moment}
If $d\geq3$ then (\ref{finite_2nd_moment}) holds.
\end{prop}
If $d=2$, then one cannot expect (\ref{finite_2nd_moment})
to be valid in the situation when $\omega$ contains an infinite
straight cylinder. Indeed, we have the following:
\begin{prop}
\label{pr_infinite_d=2}
In the two-dimensional case, suppose that there exists an interval
$S\subset\Lambda$ such that ${\mathbb R}\times S \subset\omega$ for
${\mathbb P}$-a.a. $\omega$. Then $\langle b \rangle_{{\mathbb
Q}}=\infty$.
\end{prop}
On the other hand, with $R_\alpha(\omega,u) =
\sup\{|\alpha- \beta|;(\beta,v)\stackrel{\omega}{\leftrightarrow
}(\alpha,u)\}$,
it is clear that (\ref{finite_2nd_moment}) holds when
$R_0(\omega,u)\leq\mbox{\textit{const}}$ for all
$u\in\omega_0$, ${\mathbb P}$-a.s. Such an example is given by the tube
$\{(\alpha,u)\in{\mathbb R}^2 \dvtx \cos\alpha\leq u \leq\cos\alpha
+1\}$,
a random shift to make
it stationary and ergodic (but not mixing).
\begin{rem}
(i) The continuity assumption of the map
$\alpha\mapsto\omega_\alpha$ has a
geometric meaning: it prevents the tube from having ``vertical
walls'' of nonzero surface measure. The reader may wonder what
happens without it. First, the disintegration formula
(\ref{differentials}) of the surface measure $\nu^\omega$ on
$\partial\omega$ becomes a product
$d {\bar\mu}^\omega_\alpha(u)\, d\phi^\omega(\alpha)$
where ${\bar\mu}^\omega_\alpha$ is a measure on the section of
$\partial\omega$
by the vertical hyperplane at $\alpha$ and where
$d \phi^\omega(\alpha)=\kappa_{\alpha,u}^{-1} \, d\alpha+
d \phi^\omega_{\mathrm{s}}
(\alpha)$ with a singular part $\phi^\omega_{\mathrm{s}}$.
If the singular part has atoms, one can see that the invariant
law ${\mathbb Q}$ [see (\ref{def_Q}) above] of the environment
seen from the particle has a marginal in $\omega$ which is singular
with respect to ${\mathbb P}$. This happens because, if the vertical walls
constitute a positive proportion of the tube's surface, in the
equilibrium the particle finds itself on a vertical wall with
positive probability;
on the other hand, if $\omega$ has the law ${\mathbb P}$,
a.s. there is no vertical wall at the origin.
The general situation is interesting but
complicated; in any case, our results continue to be valid in this
situation as well
[an important observation is that (\ref{IP<IQ})
below would still hold, possibly with another
constant]. To keep things simple, we will consider only,
all through the paper, random tubes satisfying the continuity
assumption. In the \hyperref[app]{Appendix}, we discuss the general case in more
detail. Another possible approach to this general case is to work
with the continuous-time stochastic billiard directly (cf.
Section \ref{s_env_continuous}).
(ii) A particular example of tubes is given by rotation invariant
tubes. They are obtained by rotating around the first axis the graph
of a positive bounded function. The main simplification is that,
with the proper formalism, one can forget the transverse
component $u$. Then the problem becomes purely one-dimensional.
\end{rem}
\section{Environment viewed from the particle and the construction
of the corrector}
\label{s_environment}
\subsection{Environment viewed from the particle: Discrete case}
\label{s_env_discrete}
One of the main methods we use in this paper is considering
the environment $\omega$ seen from the current location
of the random walk.
The ``environment viewed from the particle''
is the Markov chain
\[
\bigl((\theta_{\xi_n\cdot e}\omega,{\mathcal U}\xi_n), n=0,1,2,\ldots\bigr)
\]
with state space ${\mathfrak S}$.
The transition operator $G$ for this process
acts on functions $f\dvtx {\mathfrak S}\mapsto{\mathbb R}$ as follows
[cf. (\ref{differentials}) and (\ref{K->Phi})]:
\begin{eqnarray}\label{def_trans_operator}
Gf (\omega,u) &=& {\mathtt E}_{\omega}\bigl(f(\theta_{\xi_1\cdot e}\omega
,{\mathcal U}\xi_1)
\mid\xi_0 = (0,u)\bigr)\nonumber\\
&=& \int_{\partial\omega} K ((0,u),x )
f(\theta_{x\cdot e}\omega,{\mathcal U}x) \, d\nu^{\omega}(x)
\\
&=& \int_{-\infty}^{+\infty} d\alpha\int_{\Lambda}
d\mu^{\omega}_\alpha(v)\, \kappa_{0,u}
f(\theta_\alpha\omega,v) \Phi(0,u,\alpha,v).\nonumber
\end{eqnarray}
\begin{rem}
Note that our environment consists not only of the tube with an
appropriate horizontal shift, but also of the transverse component
of the walk.
Another possible choice for the environment
would be obtained by rotating the shifted tube
to make it pass through the origin with inner normal at this point
given by the last coordinate vector. However, we made the present
choice to keep notation simple.
\end{rem}
Next, we show that this new Markov chain
is reversible with reversible
measure ${\mathbb Q}$ given by (\ref{def_Q}),
which means that $G$ is a self-adjoint operator in
$L^2({\mathfrak S})=L^2({\mathfrak S},{\mathbb Q})$:
\begin{lmm}
\label{l_revers_discr}
For all $f,g\in L^2({\mathfrak S})$ we have $\langle g, Gf \rangle
_{{\mathbb Q}} =
\langle f, Gg \rangle_{{\mathbb Q}}$.
Hence, the law ${\mathbb Q}$ is invariant for the Markov chain of the
environment viewed from the particle which means that for any
$f\in L^2({\mathfrak S})$ and all $n$,
\begin{equation}
\label{IQ_is_invariant}
\langle{\mathtt E}_{\omega}[f(\theta_{\xi_n\cdot e}\omega
,{\mathcal U}\xi_n)\mid\xi
_0=(0,u)] \rangle_{{\mathbb Q}}
=\langle f \rangle_{{\mathbb Q}}.
\end{equation}
\end{lmm}
\begin{pf}
Indeed, from (\ref{def_Q}) and (\ref{def_trans_operator}),
\begin{eqnarray}\quad
\langle g, Gf \rangle_{{\mathbb Q}} &=& \frac{1}{{\mathcal Z}}\int
_{\Omega}d{\mathbb P}
\int_{\Lambda}
d\mu^{\omega}_0(u)\, g(\omega,u)\kappa_{0,u}^{-1}
\int_{-\infty}^{+\infty} d\alpha\nonumber\\
&&{} \times\int_{\Lambda} d\mu^{\omega}_\alpha(v)\, \kappa_{0,u}
\Phi(0,u,\alpha,v) f(\theta_\alpha\omega,v)\nonumber\\
\label{revers1}
&=& \frac{1}{{\mathcal Z}}\int_{-\infty}^{+\infty} d\alpha
\int_{\Omega}d{\mathbb P}
\int_{\Lambda^2} d\mu^{\omega}_{0,\alpha}(u,v)\, g(\omega,u)
f(\theta_\alpha\omega,v)\Phi(0,u,\alpha,v)
\\
\label{revers1'}
&=& \frac{1}{{\mathcal Z}}\int_{-\infty}^{+\infty} d\alpha
\int_{\Omega}d{\mathbb P}
\int_{\Lambda^2}
d\mu^{\theta_\alpha\omega}_{-\alpha,0}(u,v)\, g(\omega,u)
f(\theta_\alpha
\omega,v)\nonumber\\[-8pt]\\[-8pt]
&&\hspace*{96.7pt}{}\times\Phi^{\theta_\alpha\omega}(-\alpha,u,0,v)\nonumber\\
\label{revers2}
&=& \frac{1}{{\mathcal Z}}\int_{-\infty}^{+\infty} d\alpha
\int_{\Omega}d{\mathbb P}
\int_{\Lambda^2} d\mu^{\omega}_{-\alpha,0}(u,v)\,
g(\theta_{-\alpha} \omega,u)f(\omega,v)\nonumber\\[-8pt]\\[-8pt]
&&\hspace*{96.7pt}{}\times\Phi(-\alpha,u,0,v)\nonumber\\
&=& \frac{1}{{\mathcal Z}}\int_{\Omega}d{\mathbb P}
\int_{\Lambda} d\mu^{\omega}_0(v)\, f(\omega,v)\kappa_{0,v}^{-1}
\int_{-\infty}^{+\infty} d\alpha\nonumber\\
\label{revers3}
&&{} \times\int_{\Lambda} d\mu^{\omega}_{-\alpha}(u)\, \kappa_{0,v}
\Phi(0,v,-\alpha,u) g(\theta_{-\alpha} \omega,u)\\
&=& \langle f, Gg \rangle_{{\mathbb Q}},\nonumber
\end{eqnarray}
where we used (\ref{shift_Phi}) to pass from (\ref{revers1})
to (\ref{revers1'}),
the translation invariance of ${\mathbb P}$ to pass from (\ref{revers1'})
to (\ref{revers2}), the symmetry property (\ref{symmetry_Phi})
to pass from (\ref{revers2}) to (\ref{revers3}) and the
change of variable
$\alpha\mapsto- \alpha$ to obtain the last line.
\end{pf}
Let us define a semi-definite scalar product
$\langle g, f \rangle_{1}:=\langle g, (I-G)f \rangle_{{\mathbb Q}}$.
Again using (\ref{revers1}),
the translation invariance of ${\mathbb P}$ and the symmetry of $\Phi$,
we obtain
\begin{eqnarray*}
\langle g, f \rangle_{1}
&=& \frac{1}{{\mathcal Z}}\int_{-\infty}^{+\infty} d\alpha\int
_{\Omega}
d{\mathbb P}\int_{\Lambda^2} d\mu^{\omega}_{0,\alpha}(u,v)\,\Phi(0,u,\alpha,v)\\
&&\hspace*{97.74pt}{}\times
g(\omega,u) \bigl(f(\omega,u)-f(\theta_\alpha\omega,v)\bigr)\\
&=& \frac{1}{{\mathcal Z}}\int_{-\infty}^{+\infty} d\alpha\int
_{\Omega}
d{\mathbb P}
\int_{\Lambda^2} d\mu^{\omega}_{-\alpha,0}(u,v)\,
\Phi(-\alpha,u,0,v)\\
&&\hspace*{97.74pt}{}\times
g(\theta_{-\alpha}\omega,u)
\bigl(f(\theta_{-\alpha}\omega,u)-f(\omega,v)\bigr)\\
&=& \frac{1}{{\mathcal Z}}\int_{-\infty}^{+\infty} d\alpha
\int_{\Omega}d{\mathbb P}
\int_{\Lambda^2} d\mu^{\omega}_{0,\alpha}(u,v)\,
\Phi(0,u,\alpha,v)\\
&&\hspace*{97.74pt}{}\times
g(\theta_\alpha\omega,v)
\bigl(f(\theta_\alpha\omega,v)-f(\omega,u)\bigr).
\end{eqnarray*}
Consequently,
\begin{eqnarray*}
\langle g, f \rangle_{1} &=& \frac{1}{2{\mathcal Z}}\int_{-\infty
}^{+\infty}\hspace*{-1pt}
d\alpha\int_{\Omega}d{\mathbb P}
\int_{\Lambda^2} d\mu^{\omega}_{0,\alpha}(u,v)\,
\Phi(0,u,\alpha,v)
\bigl(f(\omega,u)-f(\theta_\alpha\omega,v)\bigr)\hspace*{1.5pt}\\
&&\hspace*{101.5pt}{} \times
\bigl(g(\omega,u)-g(\theta_\alpha\omega,v)\bigr),\hspace*{1.5pt}
\end{eqnarray*}
so the Dirichlet form $\langle f, f \rangle_{1}$ can be explicitly
written as
\begin{eqnarray}
\label{eq_Dirichlet}
\langle f, f \rangle_{1} &=& \frac{1}{2{\mathcal Z}}\int_{-\infty
}^{+\infty}
d\alpha\int_{\Omega}d{\mathbb P}
\int_{\Lambda^2} d\mu^{\omega}_{0,\alpha}(u,v)\,
\Phi(0,u,\alpha,v)\nonumber\\[-8pt]\\[-8pt]
&&\hspace*{102.5pt}{}\times\bigl(f(\omega,u)-f(\theta_\alpha\omega,v)\bigr)^2,\nonumber
\end{eqnarray}
or, by (\ref{differentials}) and (\ref{K->Phi}),
\begin{eqnarray}\label{eq_Dirichlet_K}
\langle f, f \rangle_{1} &=& \frac{1}{2{\mathcal Z}}\int_{\Omega
}d{\mathbb P}
\int_\Lambda\kappa_{0,u}^{-1} \,d\mu^{\omega}_0(u)\nonumber\\[-8pt]\\[-8pt]
&&{}\times\int_{\partial\omega} d\nu^{\omega}(x)\, K ((0,u),x )
\bigl(f(\omega,u)-f(\theta_{x\cdot e}\omega,{\mathcal
U}x)\bigr)^2.\nonumber
\end{eqnarray}
At this point it is convenient to establish the following result:
\begin{lmm}
\label{l_Q_ergodic}
The Markov process with initial law ${\mathbb Q}$ and transition
operator $G$ is ergodic.
\end{lmm}
\begin{pf}
Suppose that $f\in L^2({\mathfrak S})$
is such that $f=Gf$. Then $\langle f, f \rangle_{1}=0$
and so, by the translation invariance and (\ref{eq_Dirichlet_K}),
\[
\int_{\Omega}d{\mathbb P}\int_\Lambda\kappa_{s,u}^{-1} \,d\mu
^{\omega}_s(u)
\int_{\partial\omega} d\nu^{\omega}(x)\, K((s,u),x)
\bigl(f(\theta_s
\omega,u)-f(\theta_{x\cdot e}\omega,{\mathcal U}x)\bigr)^2 = 0
\]
for any $s$. Integrating the above equation in $s$ and
using (\ref{differentials}), we obtain
\begin{equation}
\label{int_f2=0}
\int_{\Omega}d{\mathbb P}
\int_{(\partial\omega)^2} d\nu^{\omega}(x)\, d\nu^{\omega}(y)\, K(x,y)
\bigl(f(\theta_{x\cdot e}\omega,{\mathcal U}x)
-f(\theta_{y\cdot e}\omega,{\mathcal U}y) \bigr)^2 = 0.\hspace*{-30pt}
\end{equation}
Let us recall Lemma 3.3(iii) from \cite{CPSV1}:
if for some $x,y\in{\mathcal R}_{\omega}$ we have $K(x,y)>0$,
then there exist $\delta>0$ and two neighborhoods $B_x$ of $x$
and $B_y$ of $y$ such that
$K(x',y')>\delta$ for all $x'\in B_x, y'\in B_y$.
Now, for such $x,y$, (\ref{int_f2=0})
implies that there exists a constant ${\hat c}(\omega,x,y)$
such that $f(\theta_{z\cdot e}\omega,{\mathcal U}z)={\hat c}(\omega,x,y)$
for $\nu^{\omega}$-almost all $z\in B_x\cup B_y$. By the irreducibility
Condition \ref{ConditionP} (in fact, a much weaker
irreducibility condition would be sufficient), this implies that
$f(\theta_{z\cdot e}\omega,{\mathcal U}z)={\hat c}(\omega)$ for
$\nu^{\omega}$-almost all $z\in{\mathcal R}_{\omega}$.
Since ${\mathbb P}$ is ergodic, this means that $f(\omega,u)={\hat c}$
for $\mu^{\omega}_0$-almost all $u$ and ${\mathbb P}$-almost all
$\omega$.
\end{pf}
\subsection{Environment viewed from the particle: Continuous case}
\label{s_env_continuous}
For the sake of completeness, we present also an analogous result
for the Knudsen stochastic billiard $(X_t,V_t)$. The notation and
the results of this section will not be used in the rest of this
paper.
Let $\widehat{\mathfrak S}= \{ (\omega,u)\dvtx \omega\in\Omega, u \in
\omega_0\}$,
and let ${\widehat{\mathbb Q}}$ be the probability measure
on $\widehat{\mathfrak S}\times{\mathbb S}^{d-1}$
defined by
\[
d{\widehat{\mathbb Q}}(\omega,u,h) = \frac{1}{{\widehat{\mathcal Z}}}
{\mathbb I}{\{u\in\omega_0\}} \,du \,dh \,d{\mathbb P}(\omega),
\]
where ${\widehat{\mathcal Z}}=|{\mathbb S}^{d-1}|\int_\Omega|\omega
_0|d{\mathbb P}$
is the normalizing constant.
The scalar product $\langle\cdot, \cdot\rangle_{{\widehat{\mathbb
Q}}}$ in
$L^2({\widehat{\mathbb Q}})$ is given,
for two ${\widehat{\mathbb Q}}$-square integrable functions
${\hat f}, {\hat g}\dvtx \widehat{\mathfrak S}\times{\mathbb S}^{d-1}
\mapsto{\mathbb R}$,
by
\[
\langle{\hat f}, {\hat g} \rangle_{{\widehat{\mathbb Q}}} = \frac
{1}{{\widehat{\mathcal Z}}}
\int_\Omega d{\mathbb P}\int_{\omega_0}du
\int_{{\mathbb S}^{d-1}}dh\,
{\hat f}(\omega,u,h){\hat g}(\omega,u,h).
\]
For the continuous\vspace*{1pt} time KSB, the ``environment viewed
from the particle'' is the Markov process
$ ((\theta_{X_t\cdot e}\omega,{\mathcal U}X_t,V_t),t\geq0 )$
with the state space
$\widehat{\mathfrak S}\times{\mathbb S}^{d-1}$.
The transition semi-group ${\widehat{\mathcal P}}_t$ for
this process acts on functions
${\hat f}\dvtx \widehat{\mathfrak S}\times{\mathbb S}^{d-1} \mapsto
{\mathbb R}$ in the following
way:
\[
{\widehat{\mathcal P}}_t{\hat f}(\omega,u,h)
= {\mathtt E}_{\omega}\bigl({\hat f}(\theta_{X_t\cdot e}\omega,{\mathcal
U}X_t,V_t)
\mid X_0=(0,u), V_0=h \bigr).
\]
We show that ${\widehat{\mathcal P}}$ is
quasi-reversible with respect to the law ${\widehat{\mathbb Q}}$.
\begin{lmm}
\label{l_revers_cont}
For all ${\hat f}, {\hat g}\in L^2({\widehat{\mathbb Q}})$ and $t>0$
we have
\begin{equation}
\label{eq:quasirev}
\langle{\hat g}, {\widehat{\mathcal P}}_t{\hat f} \rangle_{{\widehat
{\mathbb Q}}} =
\langle{\breve f}, {\widehat{\mathcal P}}_t{\breve g} \rangle
_{{\widehat{\mathbb Q}}}
\end{equation}
with $\breve f (\omega,u,h)=\hat f (\omega,u,-h)$.
In particular, the law ${\widehat{\mathbb Q}}$ is invariant for the process
$ ((\theta_{X_t\cdot e}\omega,{\mathcal U}X_t,V_t),t\geq0 )$.
\end{lmm}
\begin{pf}
We first prove that (\ref{eq:quasirev}) implies that the
law ${\widehat{\mathbb Q}}$ is invariant. Indeed, taking ${\hat
g}={\mathbf1}$,
we get for all test functions ${\hat f}$
\begin{eqnarray*}
\langle{\mathbf1}, {\widehat{\mathcal P}}_t{\hat f} \rangle
_{{\widehat{\mathbb Q}}} &=&
\langle{\breve f}, {\mathbf1} \rangle_{{\widehat{\mathbb Q}}}\\
&=& \langle{ f}, {\mathbf1} \rangle_{{\widehat{\mathbb Q}}}
\end{eqnarray*}
by the change of variable $h$ into $-h$ in the integral.
Hence ${\widehat{\mathbb Q}}$ is invariant.
We now turn to the proof of (\ref{eq:quasirev}).
Introducing the notation ${\mathtt P}_t^{\omega}$
for the transition kernel of KSB,
\[
{\mathtt P}_{\omega}( X_t \in dx', V_t \in dh' \mid X_0=x, V_0=h) =
{\mathtt P}_t^{\omega}( x,h; x',h') \,dx' \,dh',
\]
we observe that
\[
{\widehat{\mathcal P}}_t{\hat f}(\omega,u,h) =
\int_{\omega}dx'
\int_{{\mathbb S}^{d-1}}dh'\,
{\mathtt P}_t^{\omega}( (0,u),h;x',h' )
{\hat f}(\theta_{x' \cdot e}, \omega, {\mathcal U}x',h').
\]
In Theorem 2.5 in \cite{CPSV1}, it was shown that ${\mathtt
P}_t^{\omega}$
is itself quasi-reversible, that is,
\[
{\mathtt P}_t^{\omega}(x,h;x',h')={\mathtt P}_t^{\omega}(x',-h';x,-h).
\]
Therefore,
\begin{eqnarray*}
\langle{\hat g}, {\widehat{\mathcal P}}_t{\hat f} \rangle_{{\widehat
{\mathbb Q}}}
&=&
\frac{1}{{\widehat{\mathcal Z}}} \int_\Omega d{\mathbb P}\int
_{\omega_0}du
\int_{{\mathbb S}^{d-1}}dh\, {\hat g}(\omega,u,h)
{\widehat{\mathcal P}}_t {\hat f}(\omega,u,h)
\\
&=&
\frac{1}{{\widehat{\mathcal Z}}} \int_\Omega d{\mathbb P}\int
_{\omega_0}du
\int_{{\mathbb S}^{d-1}}dh\, {\hat g}(\omega,u,h)
\int_{\mathbb R}d \alpha
\int_{\omega_\alpha}du' \\
&&{} \times\int_{{\mathbb S}^{d-1}}dh'\,
{\mathtt P}_t^{\omega}( (0,u),h;(\alpha,u'),h' )
{\hat f}(\theta_{\alpha}, \omega, u',h')
\\
&=&
\frac{1}{{\widehat{\mathcal Z}}} \int_\Omega d{\mathbb P}\int
_{\omega_0}du
\int_{{\mathbb S}^{d-1}}dh\, {\hat g}(\omega,u,h)
\int_{\mathbb R}d \alpha
\int_{\omega_\alpha}du' \\
&&{} \times\int_{{\mathbb S}^{d-1}}dh'\,
{{\mathtt P}_t^{\theta_\alpha\omega}{}}
( (0,u'),-h';(-\alpha,u),-h )
{\hat f}(\theta_{\alpha} \omega, u',h')
\\
&=&
\frac{1}{{\widehat{\mathcal Z}}}
\int_{\mathbb R}d \alpha
\int_\Omega d{\mathbb P}\int_{\omega_{-\alpha}}du
\int_{{\mathbb S}^{d-1}}dh\, {\hat g}(\theta_{-\alpha},\omega,u,h)
\int_{\omega_0}du' \\
&&{} \times\int_{{\mathbb S}^{d-1}}dh'\,
{{\mathtt P}_t^{\omega}{}}
( (0,u'),-h';(-\alpha,u),-h )
{\hat f}( \omega, u',h')
\\
&=&
\frac{1}{{\widehat{\mathcal Z}}}
\int_{\mathbb R}d \alpha
\int_\Omega d{\mathbb P}\int_{\omega_{\alpha}}du
\int_{{\mathbb S}^{d-1}}dh\, {\hat g}(\theta_{\alpha},\omega,u,-h)
\int_{\omega_0}du' \\
&&{} \times
\int_{{\mathbb S}^{d-1}}dh'\,
{{\mathtt P}_t^{\omega}{}}
( (0,u'),h';(\alpha,u),h )
{\hat f}( \omega, u',-h')
\\&=& \langle{\breve f}, {\widehat{\mathcal P}}_t{\breve g} \rangle
_{{\widehat{\mathbb Q}}},
\end{eqnarray*}
where we used that the Lebesgue measure on ${\mathbb R}^d$ is product
to get the second line, quasi-reversibility for the third one,
Fubini and translation invariance of ${\mathbb P}$ for the fourth one, and
change of variables $(h,h',\alpha)$ to $(-h,-h',-\alpha)$ in the
fifth one.
\end{pf}
\subsection{Construction of the corrector}
\label{s_constr_corrector}
Now, we are going to construct the corrector function for the
random walk $\xi$.
Let us show that for any $g\in L^2({\mathfrak S})$,
\begin{equation}
\label{test_function}
\langle g, \Delta\rangle_{{\mathbb Q}} \leq\tfrac{1}{\sqrt
{2}}\langle b
\rangle_{{\mathbb Q}}^{1/2}\langle g, g \rangle_{1}^{1/2}.
\end{equation}
Indeed, from (\ref{def_drift}) we obtain
\begin{eqnarray*}
\langle g, \Delta\rangle_{{\mathbb Q}} &=& \frac{1}{{\mathcal Z}}\int
_{-\infty
}^{+\infty} \alpha\,
d\alpha\int_\Omega d{\mathbb P}
\int_{\Lambda^2}\mu^{\omega}_{0,\alpha}(u,v) g(\omega,u)
\Phi(0,u,\alpha,v)\\
&=& \frac{1}{{\mathcal Z}}\int_{-\infty}^{+\infty} \alpha
\,d\alpha\int_\Omega d{\mathbb P}
\int_{\Lambda^2}\mu^{\omega}_{-\alpha,0}(u,v)
g(\theta_{-\alpha}\omega,u)\Phi(-\alpha,u,0,v)\\
&=& -\frac{1}{{\mathcal Z}}\int_{-\infty}^{+\infty} \alpha
\,d\alpha\int_\Omega d{\mathbb P}
\int_{\Lambda^2}\mu^{\omega}_{0,\alpha}(u,v)
g(\theta_\alpha\omega,v)\Phi(0,u,\alpha,v),
\end{eqnarray*}
so
\begin{eqnarray}
\label{g_Delta}
\langle g, \Delta\rangle_{{\mathbb Q}} &=& \frac{1}{2{\mathcal Z}}\int
_{-\infty
}^{+\infty}
\alpha \,d\alpha\int_\Omega d{\mathbb P}\nonumber\\[-8pt]\\[-8pt]
&&{}\times\int_{\Lambda^2}\mu^{\omega}_{0,\alpha}(u,v)
\Phi(0,u,\alpha,v)\bigl(g(\omega,u)-g(\theta_\alpha\omega,v)\bigr).\nonumber
\end{eqnarray}
Using the Cauchy--Schwarz inequality in (\ref{g_Delta}), we obtain
\begin{eqnarray*}
\langle g, \Delta\rangle_{{\mathbb Q}} &\leq& \frac{1}{2}
\biggl[ \frac{1}{{\mathcal Z}}\int_{-\infty}^{+\infty} \alpha^2
\,d\alpha\int_\Omega d{\mathbb P}
\int_{\Lambda^2}\mu^{\omega}_{0,\alpha}(u,v) \Phi(0,u,\alpha,v)\\
&&\hspace*{11pt}{} \times\frac{1}{{\mathcal Z}}\int_{-\infty}^{+\infty} d\alpha
\int_\Omega d{\mathbb P}
\int_{\Lambda^2}\mu^{\omega}_{0,\alpha}(u,v) \Phi(0,u,\alpha,v)
\\
&&\hspace*{120.6pt}{}\times\bigl(g(\omega,u)-g(\theta_\alpha\omega,v)\bigr)^2 \biggr]^{1/2}\\
&=& \frac{1}{2} \langle b \rangle_{{\mathbb Q}}^{1/2}(2\langle g, g
\rangle
_{1})^{1/2},
\end{eqnarray*}
which shows (\ref{test_function}).
Note that, from (\ref{g_Delta}) with $g=1$ we obtain the
important property
\[
\langle\Delta\rangle_{{\mathbb Q}}=0.
\]
As shown in Chapter 1 of \cite{KLO}, we have the variational
formula
\begin{eqnarray*}
\langle(I-G)^{-1/2}\Delta, (I-G)^{-1/2}\Delta\rangle_{{\mathbb Q}} &=&
\langle\Delta, (I-G)^{-1}\Delta\rangle_{{\mathbb Q}}\\
&=&\sup\{\langle g, \Delta\rangle_{{\mathbb Q}} - \langle g, g
\rangle
_{1}, \langle g, g \rangle_{1}<\infty\}.
\end{eqnarray*}
Then provided that (\ref{finite_2nd_moment}) holds, inequality (\ref
{test_function}) implies that the
drift $\Delta$ belongs to the range of
$(I-G)^{1/2}$, and so the time-variance of $\Delta$ is finite.
At this point we mention that this already implies weaker
forms of the CLT, by applying \cite{KV}
(under the invariant measure,
or in probability with respect to the environment)
or \cite{DFGW} (under the annealed measure).
With this observation, we could have used the resolvent
method originally developed in \cite{KV,KLO}
to construct the corrector.
However, it is more direct to use the method of the orthogonal
projections on the potential subspace (cf. \cite{BP,M,MP}).
For $\omega\in\Omega$, $u\in\partial\omega_0$, define
\begin{eqnarray*}
{\mathsf V}^+_{\omega,u} &=& \{y\in\partial\omega\dvtx y\cdot e > 0,
K ((0,u),y )>0\},\\
{\mathsf V}^-_{\omega,u} &=& \{y\in\partial\omega\dvtx y\cdot e < 0,
K ((0,u),y )>0\}.
\end{eqnarray*}
Then, in addition to the space ${\mathfrak S}$, we define two spaces
${\mathfrak N}\subset{\mathfrak M}$ in the following way:
\begin{eqnarray*}
{\mathfrak N}&=& \{(\omega,u,y) \dvtx \omega\in\Omega,u\in\partial
\omega_0,
y\in{\mathsf V}^+_{\omega,u}\},\\
{\mathfrak M}&=& \{(\omega,u,y) \dvtx \omega\in\Omega,u\in\partial
\omega_0,
y\in\partial\omega\}.
\end{eqnarray*}
On ${\mathfrak N}$ we define the measure $K {\mathbb Q}$ with mass that
is less than 1
for which
a nonnegative function $f\dvtx{\mathfrak N}\mapsto{\mathbb R}$ has the
expected value
\begin{equation}
\label{df_ex_KQ}
\langle f \rangle_{{K{\mathbb Q}}} = \biggl\langle\int_{{\mathsf
V}^+_{\omega
,u}}f(\omega,u,y) K ((0,u),y )\, d\nu^{\omega}(y) \biggr\rangle_{{\mathbb Q}}.
\end{equation}
Two square-integrable functions $f,g\dvtx{\mathfrak N}\mapsto{\mathbb R}$ have
scalar product,
\begin{equation}
\label{df_sc_KQ}
\langle f, g \rangle_{{K{\mathbb Q}}} = \biggl\langle\int_{{\mathsf
V}^+_{\omega
,u}}f(\omega,u,y) g(\omega,u,y) K ((0,u),y ) \,d\nu^{\omega}(y)
\biggr\rangle_{{\mathbb Q}}.
\end{equation}
Also, define the gradient $\nabla$ as the map that transfers a
function $f\dvtx {\mathfrak S}\mapsto{\mathbb R}$
to the function $\nabla f \dvtx {\mathfrak N}\mapsto{\mathbb R}$, defined by
\begin{equation}
\label{df_nabla}
(\nabla f)(\omega,u,y) = f(\theta_{y\cdot e}\omega, {\mathcal U}y)
- f(\omega,u).
\end{equation}
Since ${\mathbb Q}$ is reversible for $G$, we can write
\begin{eqnarray*}
\langle(\nabla f)^2 \rangle_{{K{\mathbb Q}}} &=& \biggl\langle\int
_{{\mathsf V}
^+_{\omega,u}} \bigl(f(\theta_{y\cdot e}\omega, {\mathcal U}y) - f(\omega
,u) \bigr)^2
K ((0,u),y )\, d\nu^{\omega}(y) \biggr\rangle_{{\mathbb Q}}\\
&\leq& 2\biggl\langle\int_{\partial\omega} f^2(\theta_{y\cdot e}\omega
, {\mathcal U}y) K ((0,u),y ) \,d\nu^{\omega}(y) \biggr\rangle_{{\mathbb Q}}
\\
&&{} + 2\biggl\langle\int_{\partial\omega}f^2(\omega, u) K ((0,u),y )
\,d\nu^{\omega}(y) \biggr\rangle_{{\mathbb Q}}\\
&=& 2\langle Gf^2 \rangle_{{\mathbb Q}} + 2\langle f^2 \rangle
_{{\mathbb Q}}\\
&=& 4\langle f^2 \rangle_{{\mathbb Q}},
\end{eqnarray*}
so $\nabla$ is, in fact, a map from $L^2({\mathfrak S})$ to
$L^2({\mathfrak N})$.
Then, following \cite{BP}, we denote by $L^2_\nabla({\mathfrak N})$
the closure of the set of gradients of all
functions from $L^2({\mathfrak S})$.
We then consider the orthogonal decomposition of
$L^2({\mathfrak N})$
into the
``potential'' and the ``solenoidal'' subspaces:
$L^2({\mathfrak N})=L^2_\nabla({\mathfrak N})\oplus(L^2_\nabla
({\mathfrak N}))^\bot$. To
characterize the solenoidal subspace $(L^2_\nabla({\mathfrak N}))^\bot
$, we
introduce the divergence operator
in the following way. For $f\dvtx{\mathfrak N}\mapsto{\mathbb R}$, we have
$\operatorname{div}f \dvtx {\mathfrak S}
\mapsto{\mathbb R}$
defined by
\begin{eqnarray}\label{df_divergence}
(\operatorname{div}f)(\omega,u) &=& \int_{{\mathsf V}^+_{\omega,u}}K
((0,u),y )
f(\omega,u,y) \,d\nu^{\omega}(y)\nonumber\\[-8pt]\\[-8pt]
&&{} - \int_{{\mathsf V}^-_{\omega,u}}K ((0,u),y )
f \bigl(\theta_{y\cdot e}\omega,{\mathcal U}y,(|y\cdot e|,u) \bigr)\,
d\nu^{\omega}(y)\nonumber
\end{eqnarray}
[note that for $y\in{\mathsf V}^-_{\omega,u}$ we have
$(|y\cdot e|,u)\in{\mathsf V}^+_{\theta_{y\cdot e}\omega,{\mathcal U}y}$].
Now, we verify the following integration by parts formula:
for any $f\in L^2({\mathfrak S})$, $g\in L^2({\mathfrak N})$,
\begin{equation}
\label{gradient=-diverg}
\langle g, \nabla f \rangle_{{K{\mathbb Q}}} = -\langle f\operatorname
{div}g \rangle_{{\mathbb Q}}.
\end{equation}
Indeed, we have
\begin{eqnarray}\label{calc_g_nabla_f}\quad
\langle g, \nabla f \rangle_{{K{\mathbb Q}}} &=& \biggl\langle\int
_{{\mathsf V}
^+_{\omega,u}} K ((0,u),y )g(\omega,u,y)\nonumber\\
&&\hspace*{24.3pt}{}\times \bigl(f(\theta_{y\cdot e}\omega
,{\mathcal U}y) -f(\omega,u) \bigr) \,d\nu^{\omega}(y) \biggr\rangle_{{\mathbb
Q}}\nonumber\\[-8pt]\\[-8pt]
&=& - \biggl\langle\int_{{\mathsf V}^+_{\omega,u}} K ((0,u),y ) g(\omega
,u,y)f(\omega,u)\, d\nu^{\omega}(y) \biggr\rangle_{{\mathbb Q}}
\nonumber\\
&&{} + \biggl\langle\int_{{\mathsf V}^+_{\omega,u}} K ((0,u),y ) g(\omega,u,y)
f(\theta_{y\cdot e}\omega,{\mathcal U}y) \, d\nu^{\omega}(y) \biggr\rangle
_{{\mathbb Q}}.\nonumber
\end{eqnarray}
For the second term in the right-hand side
of (\ref{calc_g_nabla_f}), we obtain
\begin{eqnarray*}
&&\biggl\langle\int_{{\mathsf V}^+_{\omega,u}} K ((0,u),y )
g(\omega
,u,y) f(\theta_{y\cdot e}\omega,{\mathcal U}y) \,d\nu^{\omega}(y)
\biggr\rangle_{{\mathbb Q}}\\
&&\qquad= \frac{1}{{\mathcal Z}}\int_\Omega d{\mathbb P}\int_0^{+\infty
}d\alpha
\int_{\Lambda^2} d\mu^{\omega}_{0,\alpha}(u,v)\,
\Phi(0,u,\alpha,v)g (\omega,u,(\alpha,v) )
f(\theta_\alpha\omega,v)\\
&&\qquad= \frac{1}{{\mathcal Z}}\int_{-\infty}^0 d\alpha\int_\Omega
d{\mathbb P}
\int_{\Lambda^2} d\mu^{\omega}_{\alpha,0}(v,u)\,
\Phi(\alpha,v,0,u)g (\theta_\alpha\omega,v,(|\alpha|,u) )
f(\omega,u)\\
&&\qquad= \biggl\langle\int_{{\mathsf V}^-_{\omega,u}}f(\omega,u) g \bigl(\theta
_{y\cdot
e}\omega,{\mathcal U}y,(|y\cdot e|,u) \bigr) K ((0,u),y ) \,d\nu^{\omega
}(y) \biggr\rangle_{{\mathbb Q}},
\end{eqnarray*}
and so
\begin{eqnarray*}
\langle g, \nabla f \rangle_{{K{\mathbb Q}}} &=& - \biggl\langle\int
_{{\mathsf V}
^+_{\omega,u}} g(\omega,u,y)f(\omega,u)K ((0,u),y ) \,d\nu^{\omega}(y)
\biggr\rangle_{{\mathbb Q}}\\
&&{}+ \biggl\langle\int_{{\mathsf V}^-_{\omega,u}}f(\omega,u) g \bigl(\theta
_{y\cdot
e}\omega,{\mathcal U}y,(|y\cdot e|,u) \bigr) K ((0,u),y ) \,d\nu^{\omega
}(y) \biggr\rangle_{{\mathbb Q}
}\\
&=& -\langle f\operatorname{div}g \rangle_{{\mathbb Q}}
\end{eqnarray*}
and the proof of (\ref{gradient=-diverg}) is complete.
Analogously to Lemma 4.2 of \cite{BP}, we can characterize the
space $(L^2_\nabla({\mathfrak N}))^\bot$ as follows:
\begin{lmm}
\label{l_charact_solenoidal}
$g\in(L^2_\nabla({\mathfrak N}))^\bot$ if and only if $\operatorname
{div}g(\omega,u) = 0$
for ${\mathbb Q}$-almost all $(\omega,u)$.
\end{lmm}
\begin{pf}
This is a direct consequence of (\ref{gradient=-diverg}).
\end{pf}
A function $f\in L^2({\mathfrak N})$ can be interpreted as a flow by
putting formally
\[
f(\omega,u,y) := -
f \bigl(\theta_{y\cdot e}\omega,{\mathcal U}y, (|y\cdot e|,u) \bigr)
\]
for $y\in{\mathsf V}^-_{\omega,u}, \omega\in{\mathfrak S}$.
Then it is straightforward to obtain that every $f\in
L^2_\nabla({\mathfrak N})$ is \textit{curl-free}, which means that for
any loop
$y_0, y_1,\ldots,y_n\in\partial\omega$ with $y_0=y_n$ and
$K(y_i,y_{i+1})>0$ for $i=1,\ldots,n-1$, we have
\begin{equation}
\label{cocycle}
\sum_{i=0}^{n-1} f \bigl(\theta_{y_i\cdot e}\omega,{\mathcal U}y_i,
y_{i+1}-(y_i\cdot e)e \bigr) = 0.
\end{equation}
Every curl-free function $f$ can be integrated into a unique
function $\phi\dvtx {\mathfrak M}\mapsto{\mathbb R}$
which can be defined by
\begin{equation}
\label{assembling_phi}
\phi(\omega,u,y) = \sum_{i=0}^{n-1}
f \bigl(\theta_{y_i\cdot e}\omega,{\mathcal U}y_i,
y_{i+1}-(y_i\cdot e)e \bigr),
\end{equation}
where $y_0, y_1,\ldots,y_n \in\partial\omega$ is an arbitrary path
such that
$y_0=(0,u)$, $y_n=y$, and $K(y_i,y_{i+1})>0$ for $i=1,\ldots,n-1$.
Automatically, such a function $\phi$ satisfies the following
\textit{shift-covariance} property: for any $u\in\partial\omega_0$,
$x,y\in\partial\omega$,
\begin{equation}
\label{shift-covariance}
\phi(\omega,u,x) = \phi(\omega,u,y)
+ \phi\bigl(\theta_{y\cdot e}\omega,{\mathcal U}y,x-(y\cdot e)e \bigr).
\end{equation}
We denote by ${\mathcal H}({\mathfrak M})$ the set of all
shift-covariant functions
${\mathfrak M}\to{\mathbb R}$.
Note that, by taking $x=y=(0,u)$ in (\ref{shift-covariance}),
we obtain
\begin{equation}
\label{shift-cov_in_0}
\phi(\omega,u,(0,u) )=0 \qquad\mbox{for any } \phi\in
{\mathcal H}({\mathfrak M}).
\end{equation}
Also, for any $\phi\in{\mathcal H}({\mathfrak M})$, we define
$\operatorname{grad}\phi$ as the
unique function $f\dvtx{\mathfrak N}\to{\mathbb R}$,
from the shifts of which $\phi$ is assembled
[as in (\ref{assembling_phi})].
In view of (\ref{shift-cov_in_0}), we can write
\[
(\operatorname{grad}f)(\omega,u,y) = f(\omega,u,y) \qquad\mbox{for }
(\omega,u,y)\in{\mathfrak N}, f \in{\mathcal H}({\mathfrak M}).
\]
Let us define
an operator ${\mathcal L}$ which transfers a function $\phi\dvtx{\mathfrak
M}\mapsto{\mathbb R}$
to a function
$f\dvtx{\mathfrak S}\mapsto{\mathbb R}$, $f={\mathcal L}\phi$ with
\begin{equation}
\label{df_action_G_N}\quad
({\mathcal L}\phi)(\omega,u) = \int_{\partial\omega}
K ((0,u),y ) [\phi(\omega,u,y)-\phi(\omega,u,(0,u))
] \, d\nu^{\omega}(y).
\end{equation}
Note that, by (\ref{df_nabla}), we obtain ${\mathcal L}(\nabla f) = Gf-f$
for any $f \in L^2({\mathfrak S})$.
Then, using (\ref{shift-covariance}) and (\ref{shift-cov_in_0}),
we write, for $\phi\in{\mathcal H}({\mathfrak M})$,
\begin{eqnarray*}
(\operatorname{div}\operatorname{grad}\phi)(\omega,u) &=& \int
_{{\mathsf V}^+_{\omega,u}}K ((0,u),y
)\phi(\omega,u,y) \,d\nu^{\omega}(y)\\
&&{}-\int_{{\mathsf V}^-_{\omega,u}}K ((0,u),y )
\phi\bigl(\theta_{y\cdot e}\omega,{\mathcal U}y,(|y\cdot e|,u)\bigr) \,d\nu^{\omega}(y)\\
&=& \int_{{\mathsf V}^+_{\omega,u}\cup{\mathsf V}^-_{\omega,u}}K ((0,u),y
)\phi(\omega,u,y) \,d\nu^{\omega}(y).
\end{eqnarray*}
So, for any $\phi\in{\mathcal H}({\mathfrak M})$, we have
$\operatorname{div}\operatorname{grad}\phi= {\mathcal L}\phi$.
This observation together with Lemma \ref{l_charact_solenoidal}
immediately implies the following fact:
\begin{lmm}
\label{l_harmonic}
Suppose that $\phi\in{\mathcal H}({\mathfrak M})$ is such that
$\operatorname{grad}\phi\in(L^2_\nabla({\mathfrak N}))^\bot$.
Then $\phi$ is harmonic for the Knudsen random walk, that is,
$({\mathcal L}\phi)(\omega,u)=0$ for ${\mathbb Q}$-almost all
$(\omega,u)$.
\end{lmm}
Now, we are able to construct the corrector.
Consider the function\break $\phi(\omega,u,y)=y\cdot e$,
and observe that $\phi\in{\mathcal H}({\mathfrak M})$.
Let ${\hat\phi}=\operatorname{grad}\phi$. First, let us show that
\begin{equation}
\label{hatphi=b/2}
\langle{\hat\phi}^2 \rangle_{{K{\mathbb Q}}} = \tfrac{1}{2}\langle b
\rangle_{{\mathbb Q}},
\end{equation}
that is, if (\ref{finite_2nd_moment}) holds, then
${\hat\phi}\in L^2({\mathfrak N})$. Indeed,
\begin{eqnarray}\label{calculation_symmetry}
\langle{\hat\phi}^2 \rangle_{{K{\mathbb Q}}} &=& \biggl\langle\int
_{{\mathsf V}
^+_{\omega,u}} (y\cdot e)^2 K ((0,u),y ) \,d\nu^{\omega}(y) \biggr\rangle
_{{\mathbb Q}
}\nonumber\\
&=& \frac{1}{{\mathcal Z}}\int_0^{+\infty}\alpha^2\,
d\alpha\int_\Omega d{\mathbb P}\int_{\Lambda^2}
d\mu^{\omega}_{0,\alpha}(u,v)\,
\Phi(0,u,\alpha,v)\nonumber\\[-8pt]\\[-8pt]
&=& \frac{1}{{\mathcal Z}}\int_{-\infty}^0\alpha^2\,
d\alpha\int_\Omega d{\mathbb P}\int_{\Lambda^2}d
\mu^{\omega}_{\alpha,0}(v,u)\,
\Phi(\alpha,v,0,u)\nonumber\\
&=& \biggl\langle\int_{{\mathsf V}^-_{\omega,u}}(y\cdot e)^2 K ((0,u),y )\,
d\nu^{\omega}
(y) \biggr\rangle_{{\mathbb Q}}\nonumber
\end{eqnarray}
and so
\begin{eqnarray*}
\langle{\hat\phi}^2 \rangle_{{K{\mathbb Q}}} &=& \frac{1}{2}\biggl\langle
\int
_{{\mathsf V}^+_{\omega,u} \cup{\mathsf V}^-_{\omega,u}}(y\cdot e)^2
K ((0,u),y )\,
d\nu^{\omega}(y) \biggr\rangle_{{\mathbb Q}}\\
&=& \frac{1}{2}\langle b \rangle_{{\mathbb Q}}.
\end{eqnarray*}
Then, let $g$ be the orthogonal projection of $(-{\hat\phi})$
onto $L^2_\nabla({\mathfrak N})$.
Define $\psi\in{\mathcal H}({\mathfrak M})$ to be the unique function
such that
$g=\operatorname{grad}\psi$;
in particular,\break $\psi(\omega,u,(0,u) )=0$ for
$u\in\partial\omega_0$.
Then we have
\[
{\hat\phi}+g = \operatorname{grad}\bigl((y\cdot e)+\psi(\omega,u,y) \bigr)
\in
(L^2_\nabla({\mathfrak N}))^\bot,
\]
so Lemma \ref{l_harmonic} implies that for ${\mathbb Q}$-a.a.
$(\omega,u)$, $\psi$ is the corrector in the sense that
\begin{equation}
\label{psi_is_cr}
{\mathtt E}_{\omega}\bigl((\xi_1-\xi_0)\cdot e + \psi(\omega,u,\xi_1)
-\psi(\omega,u,\xi_0)\mid\xi_0=(0,u) \bigr)=0
\end{equation}
[recall that, by (\ref{shift-cov_in_0}), the term
$\psi(\omega,u,\xi_0)$ can be dropped from (\ref{psi_is_cr})].
Now, denote
\[
J^\omega_x = {\mathtt E}_{\omega}\bigl((\xi_1-\xi_0)\cdot e
+ \psi\bigl(\theta_{\xi_0\cdot e}\omega,{\mathcal U}\xi_0,
\xi_1-(\xi_0\cdot e)e\bigr)\mid\xi_0=x \bigr).
\]
By the translation invariance of ${\mathbb P}$, (\ref{psi_is_cr})
and (\ref{differentials}), we can write
\begin{eqnarray*}
0 &=& \int_{-\infty}^{+\infty}d\alpha
\frac{1}{{\mathcal Z}}\int_\Omega d{\mathbb P}\int_{\Lambda}d\mu
^{\omega}_\alpha(u)\,
\kappa^{-1}_{\alpha,u}\bigl|J^\omega_{(\alpha,u)}\bigr|\\
&=& \frac{1}{{\mathcal Z}}\int_\Omega d{\mathbb P}\int_{\partial
\omega}
|J^\omega_x| \,d\nu^{\omega}(x)
\end{eqnarray*}
and this implies that $J_x^\omega=0$ for
$\nu^\omega\otimes{\mathbb P}$-a.e.
$(\omega,x)$.
From (\ref{shift-covariance}), we have
\[
\psi(\omega,u,y)-\psi(\omega,u,x)=
\psi\bigl(\theta_{x\cdot e}\omega,{\mathcal U}x,y-(x\cdot e)e\bigr),
\]
which does not depend on $u$. We summarize this in:
\begin{prop}
\label{Prop_corrector}
For ${\mathbb P}$-almost all $\omega$, it holds
\begin{equation}
\label{psi_is_corrector}
{\mathtt E}_{\omega}\bigl((\xi_1-\xi_0)\cdot e + \psi(\omega,u,\xi_1)
-\psi(\omega,u,\xi_0)\mid\xi_0=x \bigr)=0
\end{equation}
for all $u\in\partial\omega_0$
and $\nu^{\omega}$-almost all $x\in\partial\omega$.
\end{prop}
\subsection{Sequence of reference points and properties of
the corrector}
\label{s_refpoints}
Let $\chi$ be a random variable with uniform distribution in
$[-1/2,1/2]$,
independent of everything. Note that $(\chi+n, n\in{\mathbb Z})$
is then a stationary point process on the real line.
For a fixed environment $\omega$ define the sequence of
conditionally
independent random variables $\zeta_n\in\Lambda$, $n\in{\mathbb Z}$,
with $\zeta_n$ uniformly distributed on $\partial\omega_{\chi+n}$,
\begin{equation}
\label{distr_zeta}
{\mathtt P}_{\omega}[\zeta_n\in B] = \frac{\mu^{\omega}_{\chi
+n}(B)}{\mu^{\omega}_{\chi+n}
(\partial\omega_{\chi+n})}.
\end{equation}
We denote by $\mathrm{E}^{\zeta}$ the expectation with respect to
$\zeta$
and $\chi$ (with fixed $\omega$),
and by $\bar{\mathrm{E}}^{\zeta}$ the expectation with respect to
$\zeta$
conditioned on $\{\chi=0\}$.
Then by (\ref{shift-covariance})
we have the following decomposition:
\begin{equation}
\label{decomp_corr}
\psi(\theta_\chi\omega,\zeta_0,(n,\zeta_n) ) =
\sum_{i=0}^{n-1}\psi(\theta_{\chi+i}\omega,\zeta_i,
(1,\zeta_{i+1}) )
\end{equation}
so that $\psi(\theta_\chi\omega,\zeta_0,(n,\zeta_n) )$
is a partial sum of a stationary ergodic sequence.
By Condition \ref{ConditionL}, there exists ${\tilde\gamma}_1>0$ such
that $\mu^{\omega}_n(\partial\omega_n)\geq{\tilde\gamma}_1$
${\mathbb P}$-a.s.
Hence, since ${\mathbb P}$ is stationary and
$\kappa_{0,u} \in[0,1]$, we obtain for
$f \geq0$,
\begin{eqnarray}\label{IP<IQ}
\langle{\mathrm E}^{\zeta}f(\theta_\chi\omega,\zeta_0) \rangle
_{{\mathbb P}} &=& \langle
\bar{\mathrm{E}}^{\zeta}f(\omega,\zeta_0) \rangle_{{\mathbb
P}}\nonumber\\
&=& \int_\Omega d{\mathbb P}\frac{1}{\mu^{\omega}_0(\partial\omega_0)}
\int_\Lambda d\mu^{\omega}_0(u)\,f(\omega,u)\nonumber\\[-8pt]\\[-8pt]
&\leq&\frac{1}{{\tilde\gamma}_1}\int_\Omega d{\mathbb P}
\int_\Lambda d\mu^{\omega}_0(u)\, \kappa_{0,u}^{-1}f(\omega,u)
\nonumber\\
&=& \frac{{\mathcal Z}}{{\tilde\gamma}_1}\langle f \rangle_{{\mathbb
Q}},\nonumber
\end{eqnarray}
which implies that
\[
\mbox{if }f\in L^2({\mathbb Q}) \qquad\mbox{then }
\langle{\mathrm E}^{\zeta}f^2(\theta_\chi\omega,\zeta_0) \rangle
_{{\mathbb P}}<\infty.
\]
To proceed, we need to show that the random tube satisfies a
uniform local D\"{o}blin condition.
Denote ${\widetilde K}^{(n)} := K+K^{(2)}+\cdots+K^{(n)}$.
\begin{lmm}
\label{l_local_Doeblin}
Under Condition \ref{ConditionP}, there exist $N$ and ${\hat\gamma}>0$ such that
for all $x,y\in{\mathcal R}_{\omega}$ with $|(x-y)\cdot e|\leq2$ it
holds that
${\widetilde K}^{(N)}(x,y)\geq{\hat\gamma}$, ${\mathbb P}$-a.s.
\end{lmm}
\begin{pf*}{Proof of Lemma \protect\ref{l_local_Doeblin}}
Indeed, with the notation used in Condition \ref{ConditionP} and $n=N-1$,
\begin{eqnarray*}
{\widetilde K}^{(N)}(x,y) &\geq& K^{(n+1)}(x,y)\\
&\geq& \int_{B_1}K(x,z_1) \,d\nu^{\omega}(z_1) \\
&&{} \times\int_{B_2}K(z_1,z_2) \,d\nu^{\omega}(z_2)\cdots
\int_{B_n}K(z_{n-1},z_n)K(z_n,y) \,d\nu^{\omega}(z_n) \\
&\geq& \delta^n\varepsilon^{n+1}\\
&\geq& \delta^{N-1}\varepsilon^N.
\end{eqnarray*}
\upqed\end{pf*}
Next, we state some integrability and centering properties
which will be needed later.
\begin{lmm}
\label{l_resume1617}
We have
\begin{eqnarray}
\label{EQ_corr2<infty}
\langle{\mathrm E}^{\zeta}\psi^2 (\omega,u,(\chi,\zeta_0) )
\rangle_{{\mathbb Q}} &<&
\infty,
\\
\label{E_corr=0}
\langle{\mathrm E}^{\zeta}\psi(\theta_\chi\omega,\zeta
_0,(1,\zeta_1) ) \rangle
_{{\mathbb P}} &=&
\langle\bar{\mathrm{E}}^{\zeta}\psi(\omega,\zeta_0,(1,\zeta_1)
) \rangle_{{\mathbb P}} = 0.
\end{eqnarray}
\end{lmm}
\begin{pf*}{Proof of Lemma \protect\ref{l_resume1617}}
We start proving that
\begin{equation}
\label{E_corr2<infty}
\langle{\mathrm E}^{\zeta}\psi^2 (\theta_\chi\omega,\zeta
_0,(1,\zeta_1) )
\rangle_{{\mathbb P}}
< \infty.
\end{equation}
We know that $\operatorname{grad}\psi\in L^2({\mathfrak N})$, that is,
$\langle(\operatorname{grad}\psi)^2 \rangle_{{K{\mathbb Q}}}<\infty$.
Analogously to the proof of the symmetry
relation (\ref{calculation_symmetry}), we obtain [note also that,
by (\ref{gradient=-diverg}), $\langle\operatorname{div}g \rangle
_{{\mathbb Q}}=0$
for all $g\in L^2({\mathfrak N})$]
\begin{eqnarray*}
\langle(\operatorname{grad}\psi)^2 \rangle_{{K{\mathbb Q}}} &=&
\biggl\langle\int_{{\mathsf V}
^+_{\omega,u}} \psi^2(\omega,u,y)K ((0,u),y ) \,d\nu^{\omega}(y)
\biggr\rangle
_{{\mathbb Q}} \\
&=& \biggl\langle\int_{{\mathsf V}^-_{\omega,u}} \psi^2(\omega,u,y)K
((0,u),y )\,
d\nu^{\omega}(y) \biggr\rangle_{{\mathbb Q}} \\
&=& \frac{1}{2} \bigl\langle{\mathtt E}_{\omega}\bigl(\psi^2(\omega,u,\xi
_1)\mid\xi
_0=(0,u)\bigr) \bigr\rangle_{{\mathbb Q}}.
\end{eqnarray*}
Then, using (\ref{cocycle}) we write
\[
\psi^2(\omega,u,\xi_n) \leq n\psi^2(\omega,u,\xi_1)
+ n\sum_{j=1}^{n-1}
\psi^2 \bigl(\theta_{\xi_j\cdot e}\omega,{\mathcal U}\xi_j,
\xi_{j+1}-(\xi_j\cdot e)e \bigr).
\]
Since ${\mathbb Q}$ is reversible for $G$, this implies that
for any $n$
\begin{equation}
\label{corr_in_L2}
\biggl\langle\int_{\partial\omega}\psi^2(\omega,u,y) K^{(n)} ((0,u),y
) \,d\nu^{\omega}(y) \biggr\rangle_{{\mathbb Q}} < \infty,
\end{equation}
where $K^{(n)}(x,y)$ is the $n$-step transition density.
Let us define
\[
F_n^\omega= \{x\in\partial\omega\dvtx x\cdot e \in(n-1/2,n+1/2]
\}.
\]
Now we are going to use (\ref{corr_in_L2})
and Lemma \ref{l_local_Doeblin} to prove (\ref{E_corr2<infty}).
Note that, by Condition \ref{ConditionL}, there are positive constants
$C_1,C_2$ such that
\[
C_1 \leq\nu^{\omega}(F_1^\omega) \leq C_2,\qquad \mbox{${\mathbb P}$-a.s.}
\]
Using (\ref{cocycle}), we write on $\{\chi=0\}$
\begin{eqnarray*}
&&\psi^2 (\omega,\zeta_0,(1,\zeta_1) )\\
&&\qquad= \frac{1}{\nu^{\omega}(F_1^\omega)}\int_{F_1^\omega}
\psi^2 (\omega,\zeta_0,(1,\zeta_1) ) \,d\nu^{\omega}(y)\\
&&\qquad \leq\frac{2}{\nu^{\omega}(F_1^\omega)} \int_{F_1^\omega}
\bigl(\psi^2(\omega,\zeta_0,y)
+\psi^2(\theta_1\omega,\zeta_1,y-e) \bigr)\, d\nu^{\omega}(y)\\
&&\qquad\leq\frac{2}{{\hat\gamma}C_1} \biggl(\int_{\partial\omega}
{\widetilde K}^{(N)} ((0,\zeta_0),y )
\psi^2(\omega,\zeta_0,y) \,d\nu^{\omega}(y)\\
&&\qquad\quad\hspace*{26.6pt} {}+ \int_{\partial\omega}
{\widetilde K}^{(N)} ((1,\zeta_1),y )
\psi^2(\theta_1\omega,\zeta_1,y-e)\,
d\nu^{\omega}(y) \biggr).
\end{eqnarray*}
Using the stationarity of $\zeta$ under ${\mathbb P}$, we obtain that
\[
\langle{\mathrm E}^{\zeta}\psi^2 (\theta_\chi\omega,\zeta
_0,(1,\zeta_1) )
\rangle_{{\mathbb P}}
= \langle\bar{\mathrm{E}}^{\zeta}\psi^2 (\omega,\zeta_0,(1,\zeta
_1) ) \rangle_{{\mathbb P}},
\]
then, again by stationarity,
\begin{eqnarray*}
&&\biggl\langle\bar{\mathrm{E}}^{\zeta}\int_{\partial\omega}
{\widetilde K}^{(N)}
((1,\zeta_1),y ) \psi^2(\theta_1\omega,\zeta_1,y-e) \,d\nu^{\omega}(y)
\biggr\rangle_{{\mathbb P}} \\
&&\qquad= \biggl\langle\bar{\mathrm{E}}^{\zeta}\int_{\partial\omega}
{\widetilde K}^{(N)}
((0,\zeta_0),y ) \psi^2(\omega,\zeta_0,y) \,d\nu^{\omega}(y)
\biggr\rangle_{{\mathbb P}}.
\end{eqnarray*}
So, (\ref{E_corr2<infty}) follows from (\ref{IP<IQ})
and (\ref{corr_in_L2}).
Analogously, it is not difficult to prove that
(\ref{EQ_corr2<infty}) holds.
Indeed,
similarly to (\ref{IP<IQ}),
we have
\begin{eqnarray*}
{\mathrm E}^{\zeta}\psi^2 (\omega,u,(\chi,\zeta_0) ) &=&
\int_{-1/2}^{1/2}d\alpha
\frac{1}{\mu^{\omega}_\alpha(\partial\omega_\alpha)}
\int_\Lambda d\mu^{\omega}_\alpha(v)\,\psi^2 (\omega,u,(\alpha,v)
)\\
&\leq&\frac{1}{{\tilde\gamma}_1}\int_{-1/2}^{1/2}d\alpha
\int_\Lambda d\mu^{\omega}_\alpha(v)\,\kappa_{\alpha,v}^{-1}
\psi^2 (\omega,u,(\alpha,v) )\\
&=& \frac{1}{{\tilde\gamma}_1}\int_{F_0^\omega}
\psi^2(\omega,u,y) \,d\nu^{\omega}(y),
\end{eqnarray*}
where we used (\ref{differentials}) in the last equality.
So, by Lemma \ref{l_local_Doeblin},
\[
{\mathrm E}^{\zeta}\psi^2 (\omega,u,(\chi,\zeta_0) ) \leq
\frac{1}{{\hat\gamma}{\tilde\gamma}_1}
\int_{\partial\omega}{\widetilde K}^{(N)} ((0,u),y )
\psi^2(\omega,u,y) \,d\nu^{\omega}(y)
\]
and (\ref{EQ_corr2<infty}) follows from (\ref{corr_in_L2}).
Finally, let us prove (\ref{E_corr=0}).
The first equality follows from the stationarity of ${\mathbb P}$.
Then, since $\operatorname{grad}\psi\in L^2_\nabla({\mathfrak N})$,
there is a sequence
of functions $f_n\in L^2({\mathfrak S})$ such that $\nabla f_n\to
\operatorname{grad}\psi$
in the sense of the $L^2({\mathfrak N})$-convergence.
Note that,
in fact, when proving (\ref{E_corr2<infty}), we proved that for
any function $g\in{\mathcal H}({\mathfrak M})$ such that
$\operatorname{grad}g \in L^2_\nabla({\mathfrak S})$,
we have for some $C_3>0$,
\[
\langle{\mathrm E}^{\zeta}g^2 (\theta_\chi\omega,\zeta_0,(1,\zeta
_1) ) \rangle
_{{\mathbb P}} <
C_3\langle(\operatorname{grad}g)^2 \rangle_{{K{\mathbb Q}}}.
\]
Then, (\ref{E_corr=0}) follows from the
above fact applied to $g$
assembled from shifts of $\operatorname{grad}\psi- \nabla f_n$,
since then we can then write
\[
\langle\psi(\theta_\chi\omega,\zeta_0,(1,\zeta_1) ) \rangle
_{{\mathbb P}}
= \lim_{n\to\infty} [\langle f_n(\theta_{\chi+1} \omega,\zeta_1)
\rangle_{{\mathbb P}} - \langle f_n(\theta_{\chi} \omega,\zeta_0)
\rangle
_{{\mathbb P}} ]=0
\]
by the stationarity of ${\mathbb P}$.
\end{pf*}
\section{Proofs of the main results}
\label{s_proofs}
\subsection{\texorpdfstring{Proof of Theorem
\protect\ref{t_q_invar_princ}}{Proof of Theorem 2.1}}
\label{s_proof_inv_pr}
In this section, we apply the machinery of
Section~\ref{s_environment} in order to prove the invariance
principle
for the (discrete time) motion of a single particle.
\begin{pf*}{Proof of Theorem \protect\ref{t_q_invar_princ}}
Denote
\[
\Theta_n = \xi_n \cdot e +
\psi(\theta_\chi\omega,\zeta_0,\xi_n-\chi e).
\]
Observe that by (\ref{psi_is_corrector}), $\Theta$ is a martingale
under the quenched law ${\mathtt P}_{\omega}$.
By shift-covariance (\ref{shift-covariance}) the increments of
$\Theta_n$ do not depend of $\chi$ and $\zeta$. With the notation
\[
h(\omega,u)= {\mathtt E}_{\omega}[ (\Theta_1-\Theta_0)^2 \mid\xi_0=(0,u)],
\]
the bracket of the martingale $\Theta_n$ is given by
\[
\langle\Theta\rangle_n = \sum_{i=0}^{n-1}
h( \theta_{\xi_i\cdot e}\omega, {\mathcal U}\xi_{i}).
\]
By the ergodic theorem,
\begin{equation}
\label{def:sigma}
\frac{1}{n} \langle\Theta\rangle_n \longrightarrow
\sigma^2 \stackrel{\mathrm{def}}{=} \langle h(\omega,u) \rangle
_{{\mathbb Q}},
\end{equation}
a.s. as $n \to\infty$.
Clearly, $\sigma^2 \in(0,\infty)$. Moreover, for all $\varepsilon>0$,
\begin{equation}
\label{eq:cnrs1}
\sum_{i=0}^{n-1} {\mathtt P}_{\omega}[ |\Theta_{i+1}-\Theta_{i}|
\geq
\varepsilon n^{1/2} \mid\xi_i ] \to0
\end{equation}
for ${\mathbb P}$-a.e. $\omega$ and ${\mathtt P}_{\omega}$-a.e. path.
To show this,
define for any $a>0$ and all $n\geq1$,
\[
h^{(a)}_n(\omega) = {\mathtt E}_{\omega}\bigl((\Theta_n-\Theta_{n-1})^2
{\mathbb I}{\{|\Theta_n-\Theta_{n-1}|\geq a \}} \mid\xi_{n-1} \bigr).
\]
Using the ergodicity of the process of the environment
viewed from the particle, we obtain
\[
\frac{1}{n} \sum_{i=1}^n h^{(a)}_i
\longrightarrow
\bigl\langle{\mathtt E}_{\omega}\bigl((\Theta_1-\Theta_0)^2{\mathbb I}{\{
|\Theta _1-\Theta_0|\geq a\}}
\mid\xi_0 = (0,u) \bigr) \bigr\rangle_{{\mathbb Q}}
\]
as $n \to\infty$
for ${\mathbb P}$-almost all $\omega$ and ${\mathtt P}_{\omega}$-almost
all trajectories of the walk. Note that, when $a$ is replaced
by $\varepsilon n^{1/2}$,
the left-hand side is, by
Bienaym\'{e}--Chebyshev inequality, an upper bound of the left-hand
side of (\ref{eq:cnrs1}) multiplied by $\varepsilon^2$.
Hence (\ref{eq:cnrs1}) follows by taking $a$ arbitrarily large.
Combining (\ref{def:sigma}) and (\ref{eq:cnrs1}),
we can apply the central limit theorem for martingales
(cf., e.g., Theorem 7.7.4 of \cite{D})
to show that
\begin{equation}
\label{conv_to_BM}
n^{-1/2}\Theta_{[n\cdot]}
\stackrel{\mathrm{law}}{\longrightarrow}
\sigma B(\cdot)\qquad
\mbox{as $n\to\infty$},
\end{equation}
where $B(\cdot)$ is the Brownian motion.
Then the idea is the following:
using (\ref{E_corr=0}) and the ergodic theorem, we
obtain that the
corrector $\psi(\omega,u,x)$ behaves sublinearly in $x$
which implies the convergence of $n^{-1/2}\xi_{[nt]}\cdot e$.
More precisely, we can write, with $m_j:=[1/2+\xi_j\cdot e]$ and
using (\ref{shift-covariance}),
\begin{eqnarray}\label{decomp_mart}
\frac{\Theta_{[nt]}}{n^{1/2}}
&=& \frac{\xi_{[nt]}\cdot e +\psi(\theta_\chi\omega,\zeta_0,
(m_{[nt]},\zeta_{m_{[nt]}}) )}
{n^{1/2}}\nonumber\\[-8pt]\\[-8pt]
&&{} - \frac{\psi(
\theta_{\xi_{[nt]}\cdot e}\omega,{\mathcal U}\xi_{[nt]},
(\chi+m_{[nt]}-\xi_{[nt]}\cdot e,\zeta_{m_{[nt]}})
)}{n^{1/2}}.\nonumber
\end{eqnarray}
Let us prove that the second term in the right-hand side
converges to $0$ in ${\mathtt P}_{\omega}$-probability for ${\mathbb P}$-almost
all $\omega$ and almost all $(\chi,\zeta)$.
Suppose, for the sake of simplicity, that $t=1$.
Then, by the stationarity of the process $ ((\chi+n,\zeta_n),
n\in{\mathbb Z})$ and (\ref{IQ_is_invariant}) together
with (\ref{EQ_corr2<infty}), we have for all $i\geq0$,
\begin{eqnarray*}
&&\bigl\langle{\mathrm E}^{\zeta}{\mathtt E}_{\omega}\bigl[\psi^2
\bigl(\theta_{\xi_i\cdot e}\omega, {\mathcal U}
\xi_i, (\chi+m_i-\xi_i\cdot e,\zeta_{m_i}) \bigr)\mid\xi_0=(0,u) \bigr]
\bigr\rangle_{{\mathbb Q}}
\\
&&\qquad=\langle{\mathrm E}^{\zeta}\psi^2 (\omega,u,(\chi,\zeta_0) )
\rangle_{{\mathbb Q}}\\
&&\qquad<\infty,
\end{eqnarray*}
so, by the ergodic theorem,
\begin{eqnarray*}
&&\frac{1}{n}\sum_{i=1}^n
{\mathtt E}_{\omega}\bigl(\psi^2 (\theta_{\chi+\xi_i\cdot e}\omega
,{\mathcal U}\xi_i,
(m_i,\zeta_{m_i}) )\\
&&\hspace*{17.6pt}\qquad{} - \psi^2 (\theta_{\chi+\xi_{i-1}\cdot e}\omega,
{\mathcal U}\xi_{i-1}, (m_{i-1},\zeta_{m_{i-1}}) ) \bigr) \to0
\end{eqnarray*}
as $n\to\infty$ which implies that
\begin{equation}
\label{2nd_to_0}
\frac{1}{n}{\mathtt E}_{\omega}\psi^2 (\theta_{\chi+\xi_n\cdot
e}\omega,
{\mathcal U}\xi_n,(m_n,\zeta_{m_n}) )
\to0
\end{equation}
for ${\mathbb P}$-almost all $\omega$ and almost all $(\chi,\zeta)$.
Now, let us prove that the limit of the first term
in the right-hand side of (\ref{decomp_mart})
is the same as the limit of $n^{-1/2}\xi_{[nt]}\cdot e$; for this,
we have to prove that
\begin{equation}
\label{psi_to_0}
\frac{\psi(\theta_\chi\omega,\zeta_0,(m_{[nt]},
\zeta_{m_{[nt]}}) )}{n^{1/2}}
\to0 \qquad\mbox{as }n\to\infty, \mbox{ in ${\mathtt P}_{\omega}$-probability}.
\end{equation}
Using (\ref{decomp_corr}), (\ref{E_corr=0}), and the ergodic
theorem, we obtain that for ${\mathbb P}$-almost all $\omega$
$m^{-1}\psi(\theta_\chi\omega,\zeta_0,(m,\zeta_m) )\to0$
for almost all $(\chi,\zeta)$, as $|m| \to\infty$.
This means that, for any $\varepsilon>0$ there exists $H$
(depending on $\omega,\zeta,\chi$)
such that
\begin{equation}
\label{psi_sublinear}
|\psi(\theta_\chi\omega,\zeta_0,(m,\zeta_m) ) |
\leq H+\varepsilon|m|.
\end{equation}
Denote
\[
\Psi_j = \xi_j\cdot e +
\psi(\theta_\chi\omega,\zeta_0,(m_j,\zeta_{m_j}) ).
\]
From (\ref{psi_sublinear}) we see that
\begin{eqnarray*}
|\psi(\theta_\chi\omega,\zeta_0,(m_j,\zeta_{m_j}) )
| &\leq& H+\varepsilon|m_j|\\
&\leq& H+\frac{\varepsilon}{2}+\varepsilon|\xi_j\cdot e|\\
&\leq& H+\frac{\varepsilon}{2}+\varepsilon\bigl(|\Psi_j|
+ |\psi(\theta_\chi\omega,
\zeta_0,(m_j,\zeta_{m_j}) ) | \bigr),
\end{eqnarray*}
so for $\varepsilon<1/2$ we obtain
\[
|\psi(\theta_\chi\omega,\zeta_0,(m_j,\zeta_{m_j}) )
| \leq2H+\varepsilon+2\varepsilon|\Psi_j|.
\]
Using (\ref{conv_to_BM}) and (\ref{2nd_to_0})
in (\ref{decomp_mart}), we obtain
\[
\max_{j\leq n} \frac{|\Psi_j|}{n^{1/2}}
\stackrel{\mathrm{law}}{\longrightarrow} \sigma
{\max_{s\in[0,1]}}|B(s)|.
\]
So by the portmanteau theorem (cf. Theorem 2.1(iii)
of \cite{Bil}),
\[
\limsup_{n\to\infty} {\mathtt P}_{\omega}\Bigl[{\max_{j\leq n}}
|\psi(\theta_\chi\omega,\zeta_0,(m_j,\zeta_{m_j}) )
|\geq an^{1/2} \Bigr]
\leq P \biggl[{\max_{s\in[0,1]}}|B(s)|\geq\frac{a \sigma}{2\varepsilon}
\biggr],
\]
which converges to $0$ for any $a$ as $\varepsilon\to0$.
This concludes the proof of Theorem~\ref{t_q_invar_princ}.
\end{pf*}
\subsection{On the finiteness of the second moment}
\label{s_b_finite}
In this section, we prove the results which concern the
finiteness of $\langle b \rangle_{{\mathbb Q}}$.
First, we present a (quite elementary)
proof of Proposition \ref{pr_suff_2nd_moment} in the case $d\geq4$.
\begin{pf*}{Proof of Proposition \protect\ref{pr_suff_2nd_moment}
\textup{(case $d\geq4$)}}
First of all, note that
\[
|\{s\in{\mathbb S}^{d-1}\dvtx x+hs\in{\mathbb R}\times\Lambda\}| = O\bigl(h^{-(d-1)}\bigr)
\qquad\mbox{as } h\to\infty,
\]
uniformly in $x\in{\mathbb R}\times\Lambda$.
So, since $\omega\subset{\mathbb R}\times\Lambda$,
there is a constant $C_1>0$, depending only
on ${\widehat M}=\operatorname{diam}(\Lambda)/2$ and the dimension,
such that for ${\mathbb P}$-almost all~$\omega$
\begin{equation}
\label{bound_d>=4}
{\mathtt P}_{\omega}[|(\xi_1-\xi_0)\cdot e| > h \mid\xi_0=x] \leq
C_1 h^{-(d-1)}
\end{equation}
for all $x\in\partial\omega$, $h\geq1$.
Inequality (\ref{bound_d>=4}) immediately implies that $b$
is uniformly bounded for $d\geq4$.
\end{pf*}
Unfortunately, the above proof does not work in the case $d=3$.
To treat this case, we need some results concerning induced chords
which in some sense generalize
Theorems 2.7 and 2.8 of \cite{CPSV1}. So the rest of this section
is organized as follows. After introducing some notation, we prove
Proposition \ref{p_cosine_int} which is a generalization of the
result about the induced chord in a convex subdomain (Theorem 2.7
of \cite{CPSV1}). This will allow us to prove
Proposition \ref{pr_infinite_d=2}.
Then, using Theorem 2.8 of \cite{CPSV1} (the result about induced
chords in a general subdomain) we prove
Proposition~\ref{p_induced_chords}---a property of random
chords induced in a smaller random tube by
a random chord in a bigger random tube.
This last result will allow us to
prove Proposition \ref{pr_suff_2nd_moment}.
Let $S\subset\Lambda$ be an open convex set, and denote
by ${\widehat S}= {\mathbb R}\times S$ the straight cylinder generated
by $S$.
Assuming that ${\widehat S}\subset\omega$, we let ${\mathcal I}$ be
the event that the
trajectory of the first jump (i.e., from $\xi_0$ to $\xi_1$)
intersects ${\widehat S}$:
\[
{\mathcal I}= \{\mbox{there exists }t\in[0,1]\mbox{ such that }\xi_0
+(\xi_1-\xi_0)t\in{\widehat S}\}.
\]
For any $u\in\partial S$ such that $\partial S$ is differentiable
in $u$, define ${\hat{\mathbf n}}_u$ to be the normal vector
with respect to $\partial{\widehat S}$ at the point $(0,u)$; clearly,
we have ${\hat{\mathbf n}}_u\cdot e=0$ (if $\partial S$ is not differentiable
in $u$, define ${\hat{\mathbf n}}_u$ arbitrarily). Fix some family
$(U_v, v\in
\partial S)$ of unitary linear operators with the property $U_v e =
{\hat{\mathbf n}}_v$ for all $v\in\partial S$. Now, on the event
${\mathcal I}$ we may
define the conditional law of intersection of $\partial{\widehat S}$. Namely,
for $x,y\in\partial\omega$, let
\begin{equation}
\label{df_t_xy}
t_{x,y} = \inf\{t\in[0,1]\dvtx x+(y-x)t \in\partial{\widehat S}\}
\end{equation}
with the convention $\inf\varnothing=\infty$.
Then, we define the (projected) location of the crossing
of $\partial{\widehat S}$
by
\[
{\mathsf L}(x,y)= \cases{
{\mathcal U}\bigl(x+(y-x)t_{x,y}\bigr), &\quad if $t_{x,y} \in[0,1]$,\cr
\infty, &\quad otherwise,}
\]
and the relative direction of the crossing by
\[
{\mathsf Y}(x,y)= \cases{
\displaystyle U_{{\mathsf L}(x,y)}^{-1}\frac{y-x}{\|y-x\|}, &\quad if $t_{x,y}
\in[0,1]$,\vspace*{2pt}\cr
0, &\quad otherwise,}
\]
(see Figure \ref{f_cylinder}).
\begin{figure}
\includegraphics{504f03.eps}
\caption{On the definition of ${\mathsf L}$ and ${\mathsf Y}$: we have
${\mathsf L}(x,y)={\mathcal U}z$ and ${\mathsf
Y}(x,y)=U^{-1}_{{\mathcal U}z}v$.}
\label{f_cylinder}
\end{figure}
Here, in the case when there is no intersection, for formal
reasons we still assign values for ${\mathsf L}$ and ${\mathsf Y}$;
note, however,
that in the case $t_{x,y} \in[0,1]$, we have
${\mathsf L}(x,y)\in\partial S$ and ${\mathsf Y}(x,y)\in{\mathbb S}_e$.
Before proving Proposition \ref{pr_infinite_d=2}, we obtain a
remarkable fact which is
closely related to the invariance properties of random chords (cf.
Theorems 2.7 and 2.8 of \cite{CPSV1}).
We have that, conditioned on ${\mathcal I}$, the annealed law of
the pair of random variables
$({\mathsf L}(\xi_0,\xi_1),{\mathsf Y}(\xi_0,\xi_1))$ can be described
as follows: ${\mathsf L}(\xi_0,\xi_1)$ and ${\mathsf Y}(\xi_0,\xi
_1)$ are
independent, ${\mathsf L}(\xi_0,\xi_1)$ is uniform
on $\partial S$ and ${\mathsf Y}(\xi_0,\xi_1)$ has the cosine distribution.
More precisely, we formulate and prove the following result.
\begin{prop}
\label{p_cosine_int}
Let $d \geq2$.
It holds that $\langle{\mathtt P}_{\omega}[{\mathcal I}] \rangle
_{{\mathbb Q}}={|\partial S|}/{{\mathcal Z}
}$. Moreover,
for any measurable $B_1\subset\partial S, B_2\subset{\mathbb S}_e$
we have
\begin{eqnarray}
\label{eq_cosine_int}
&&\bigl\langle{\mathtt E}_{\omega}\bigl({\mathbb I}{\{{\mathsf L}(\xi_0,\xi
_1)\in B_1, {\mathsf Y}(\xi_0,\xi_1)\in B_2\}}\mid\xi_0=(0,u) \bigr)
\bigr\rangle_{{\mathbb Q}}\nonumber\\[-8pt]\\[-8pt]
&&\qquad= \frac{|\partial S|}{{\mathcal Z}} \frac{|B_1|}{|\partial S|}
\gamma_d \int_{B_2} h\cdot e \,dh.\nonumber
\end{eqnarray}
\end{prop}
\begin{pf}
First, we prove (\ref{eq_cosine_int}).
Define ${\tilde F}^\omega_s = \{x\in\partial\omega:
x\cdot e\in[-s,s]\}$ for
$s>0$. By the translation invariance and (\ref{differentials}),
we have
\begin{eqnarray}\label{conta_inv*}\quad
&&\bigl\langle{\mathtt E}_{\omega}\bigl({\mathbb I}{\{{\mathsf L}(\xi
_0,\xi _1)\in B_1, {\mathsf Y}(\xi_0,\xi _1)\in B_2\}}\mid\xi
_0=(0,u) \bigr) \bigr\rangle_{{\mathbb Q}}
\nonumber\\
&&\qquad= \frac{1}{{\mathcal Z}}\int_\Omega d{\mathbb P}
\int_\Lambda d\mu^{\omega}_0(u)\,\kappa_{0,u}^{-1}\nonumber\\
&&\qquad\quad{} \times\int_{\partial
\omega}
d\nu^{\omega}(y)\,K ((0,u),y ){\mathbb I}{\{{\mathsf L}((0,u),y) \in B_1, {\mathsf
Y}((0,u),y)\in B_2\}}\nonumber\\
&&\qquad= \frac{1}{2s{\mathcal Z}}\int_\Omega d{\mathbb P}\int_{-s}^s ds
\int_\Lambda d\mu^{\omega}_s(u)\,\kappa_{s,u}^{-1}\\
&&\qquad\quad{} \times\int_{\partial
\omega}
d\nu^{\omega}(y)\,K ((s,u),y )
{\mathbb I}{\{{\mathsf L}((s,u),y) \in B_1, {\mathsf
Y}((s,u),y)\in B_2\}}\nonumber\\
&&\qquad= \frac{1}{2s{\mathcal Z}}\int_\Omega d{\mathbb P}\int_{{\tilde
F}^\omega_s}
d\nu^{\omega}(x)\nonumber\\
&&\qquad\quad{}\times\int_{\partial\omega}d\nu^{\omega}(y)\, {\mathbb
I}{\{{\mathsf L}(x,y)\in B_1, {\mathsf Y}(x,y)\in
B_2\}}K(x,y).\nonumber
\end{eqnarray}
Define the domain ${\mathcal D}_s^\omega$ by
\[
{\mathcal D}_s^\omega= \{x\in\omega\dvtx x\cdot e \in[-s,s]\}
\]
and note that $\partial{\mathcal D}_s^\omega= {\tilde F}^\omega
_s\cup
(\{-s\}\times\omega_{-s})\cup(\{s\}\times\omega_{s})$.
For $x,y\in\partial{\mathcal D}_s^\omega$ let ${\hat K}(x,y)$ be defined
as in (\ref{def_K}), but with ${\mathcal D}_s^\omega$ instead
of $\omega$. Note that ${\hat K}(x,y) = K(x,y)$ when
$x,y\in{\tilde F}^\omega_s$.
Next, we show that the random chord in $\omega$ with the first
point in ${\tilde F}^\omega_s$ has roughly the same
law as the random chord in ${\mathcal D}_s^\omega$: for any
$\varepsilon>0$
there exists $s_0$ such that for all $s\geq s_0$ [with some abuse of
notation, we still denote by $\nu^{\omega}(\partial{\mathcal
D}_s^\omega)$ the
$(d-1)$-dimensional Hausdorff measure of $\partial{\mathcal
D}_s^\omega$]
\begin{eqnarray}\label{conta_inv**}\hspace*{20pt}
&& \biggl| \frac{1}{\nu^{\omega}({\tilde F}^\omega_s)}
\int_{{\tilde F}^\omega_s} d\nu^{\omega}(x)\int_{\partial\omega
}d\nu^{\omega}(y)\,
{\mathbb I}{\{{\mathsf L}(x,y)\in B_1, {\mathsf Y}(x,y)\in B_2\}}K(x,y)
\nonumber\\
&&\qquad{} - \frac{1}{\nu^{\omega}(\partial{\mathcal D}_s^\omega)}
\int_{(\partial{\mathcal D}_s^\omega)^2}
d\nu^{\omega}(x)\,d\nu^{\omega}(y)\\
&&\,\hspace*{130.8pt}{}\times{\mathbb I}{\{{\mathsf L}(x,y)\in
B_1, {\mathsf Y}(x,y)\in B_2\}}
{\hat K}(x,y) \biggr| < \varepsilon\nonumber
\end{eqnarray}
[in the second term, we suppose that ${\mathsf L}(x,y)=\infty,
{\mathsf Y}(x,y)=0$ when $x\in(\{-s\}\times S)\cup(\{s\}\times S)$].
Indeed, we have
\begin{equation}
\label{poverhnosti}
\nu^{\omega}({\tilde F}^\omega_s) \leq\nu^{\omega}(\partial
{\mathcal D}_s^\omega)
\leq\nu^{\omega}({\tilde F}^\omega_s)+2|\Lambda|
\end{equation}
and, by Condition \ref{ConditionL}, there exists $C_4>0$ such that
\begin{equation}
\label{poverhnost'_Fs}
\nu^{\omega}({\tilde F}^\omega_s) \geq C_4 s, \qquad{\mathbb P}\mbox{-a.s.}
\end{equation}
Also, since $\omega\subset{\mathbb R}\times\Lambda$, for any
$\varepsilon>0$
there exists $C_5>0$ such that
for all $x\in\partial\omega$
\begin{equation}
\label{chord_not_too_long}
\int_{\{y\in\partial\omega\dvtx |(x-y)\cdot e|>C_5\}}
K(x,y) \,d\nu^{\omega}(y) < \varepsilon,\qquad
{\mathbb P}\mbox{-a.s.}
\end{equation}
Now, (\ref{conta_inv**}) follows from
(\ref{poverhnosti})--(\ref{chord_not_too_long}) and
a coupling argument: choose the first point uniformly
on $\partial{\mathcal D}_s^\omega$; with
big probability, it will fall on ${\tilde F}^\omega_{s-C_5}$
(and so it can be used
as the first point of the random chord in $\partial\omega$).
Then, choose the second point according
to the cosine law; by (\ref{chord_not_too_long}), with big
probability it will belong to ${\tilde F}^\omega_s$, and so the
probability that the coupling is successful converges to $1$
as $s\to\infty$.
Then, recall Theorem 2.7 from \cite{CPSV1}: in a finite domain,
the induced random chord in a convex subdomain has the same
uniform${}\times{}$cosine law. So
\begin{eqnarray*}
&&\frac{1}{\nu^{\omega}(\partial{\mathcal D}_s^\omega)}
\int_{\partial{\mathcal D}_s^\omega\times\partial{\mathcal
D}_s^\omega}
d\nu^{\omega}(x)\,d\nu^{\omega}(y)\,{\mathbb I}{\{{\mathsf L}(x,y)\in
B_1, {\mathsf Y}(x,y)\in B_2\}}
{\hat K}(x,y)
\\
&&\qquad = {\mathtt P}_{\omega}[{\mathcal I}_s] \frac{|B_1|}{|{\mathbb
S}_e|} \gamma_d \int_{B_2}
h\cdot e \,dh,
\end{eqnarray*}
where ${\mathcal I}_s$ is the event that the random chord of
$\partial{\mathcal D}_s^\omega$
crosses the set $[-s,s]\times\partial S$.
By formula (47) of \cite{CPSV1}
[see also formula (17) in Theorem 2.8 there], we have
\begin{equation}
\label{ver_peresech}
{\mathtt P}_{\omega}[{\mathcal I}_s] = \frac{2s|\partial
S|}{|\partial{\mathcal D}_s^\omega|}
= \frac{2s|\partial S|}{\nu^{\omega}({\tilde F}^\omega_s)
+|\omega_{-s}|+|\omega_s|}.
\end{equation}
Since, by the ergodic theorem, $|{\tilde F}^\omega_s|/(2s)\to
{\mathcal Z}$
as $s\to\infty$, (\ref{ver_peresech}) implies that
${\mathtt P}_{\omega}[{\mathcal I}_s]\to|\partial S|/{\mathcal Z}$ as
$s\to\infty$.
We obtain (\ref{eq_cosine_int}) using (\ref{conta_inv*})
and (\ref{conta_inv**}), and sending $s$ to $\infty$.
Finally, the fact that $\langle{\mathtt P}_{\omega}[{\mathcal I}]
\rangle_{{\mathbb Q}}={|\partial
S|}/{{\mathcal Z}}$
follows from (\ref{eq_cosine_int})
(take $B_1=\partial S, B_2={\mathbb S}_e$).
\end{pf}
Now, using Proposition \ref{p_cosine_int}, it is
straightforward to obtain Proposition \ref{pr_infinite_d=2}.
\begin{pf*}{Proof of Proposition \protect\ref{pr_infinite_d=2}}
Suppose that $\omega$ contains an infinite straight
cylinder ${\widehat S}$ (more precisely, a strip, since we
are considering the case $d=2$) of height $r>0$, ${\mathbb P}$-a.s.
Keep the notation $t_{x,y}$ from (\ref{df_t_xy}), and define also
\[
t'_{x,y} = \sup\{t\in[0,1]\dvtx x+(y-x)t \in\partial{\widehat S}\}.
\]
On the event ${\mathcal I}$, define the random points $\Upsilon_0,
\Upsilon_1\in\partial{\widehat S}$
by
\begin{eqnarray*}
\Upsilon_0 &=& \xi_0+(\xi_1-\xi_0)t_{x,y},\\
\Upsilon_1 &=& \xi_0+(\xi_1-\xi_0)t'_{x,y},
\end{eqnarray*}
so that $(\Upsilon_0, \Upsilon_1)$ is the random chord of ${\widehat S}$
induced by the first crossing. On ${\mathcal I}^c$, define
$\Upsilon_0=\Upsilon_1=0$. By Proposition \ref{p_cosine_int},
conditioned on ${\mathcal I}$, the random chord $(\Upsilon_0, \Upsilon
_1)$ has
the cosine law, that is, the density of a direction is proportional to
the cosine of the angle between this direction and the normal vector
(which, in this case, is perpendicular to $e$).
Let $P[\cdot]:=\frac{{\mathcal Z}}{2}\langle{\mathtt P}_{\omega
}[\cdot{\mathbb I}{\{\mathcal I\}}] \rangle_{{\mathbb Q}
}$ be the annealed
probability conditioned on the intersection;
since $d=2$ and $S$ is a bounded interval, $|\partial S|=2$.
With $\eta:=(\xi_1-\xi_0)/\|\xi_1-\xi_0\|$ and ${\hat{\mathbf
n}}$ the inner
normal vector to the cylinder at $\Upsilon_0$,
\begin{figure}
\includegraphics{504f04.eps}
\caption{($d=2$) Computing the distribution of
$|(\Upsilon_1-\Upsilon_0)\cdot e|$.}
\label{f_2dim}
\end{figure}
we have (see Figure \ref{f_2dim})
\begin{eqnarray*}
P [|(\Upsilon_1-\Upsilon_0)\cdot e| > x ] &=&
P \biggl[\eta\cdot{\hat{\mathbf n}}< \frac{r}{\sqrt{r^2+x^2}} \biggr]\\
&=& \int_{\arccos\frac{r}{\sqrt{r^2+x^2}}}^{\pi/2}\cos z \,dz\\
&=& 1-\frac{x}{\sqrt{r^2+x^2}},
\end{eqnarray*}
so the conditional density of the random variable
$|(\Upsilon_1-\Upsilon_0)\cdot e|$ is $f(x) =
\frac{r^2}{(r^2+x^2)^{3/2}}$ on
${\mathbb R}^+$.
Then we have
\begin{eqnarray*}
\langle b \rangle_{{\mathbb Q}} &=&
\bigl\langle{\mathtt E}_{\omega}\bigl(|(\xi_1-\xi_0)\cdot e|^2 [{\mathbb I}{\{
{\mathcal I}\}}+{\mathbb I}{\{{\mathcal I}^c\}}] \mid\xi
_0=(0,u) \bigr) \bigr\rangle_{{\mathbb Q}}\\
&\geq&
\bigl\langle{\mathtt E}_{\omega}\bigl(|(\xi_1-\xi_0)\cdot e|^2 {\mathbb I}{\{
{\mathcal I}\}} \mid\xi_0=(0,u) \bigr)
\bigr\rangle_{{\mathbb Q}}\\
&\geq& \langle{\mathtt E}_{\omega}|(\Upsilon_1-\Upsilon_0)\cdot
e|^2 \rangle_{{\mathbb Q}
} \times
\langle{\mathtt P}_{\omega}[{\mathcal I}] \rangle_{{\mathbb Q}}\\
&=& \frac{2}{{\mathcal Z}} \int_0^{+\infty} x^2
\frac{r^2}{(r^2+x^2)^{3/2}} \,dx = +\infty,
\end{eqnarray*}
which concludes the proof of Proposition \ref{pr_infinite_d=2}.
\end{pf*}
Let us observe that if a stationary ergodic random tube is
almost surely convex,
then necessarily it has the form ${\mathbb R}\times S$ for some convex
(and nonrandom) set $S\subset\Lambda$. This shows that
Proposition \ref{p_cosine_int} is indeed a generalization of
Theorem~2.7 of \cite{CPSV1}. Now our goal is to obtain an analogue
of a more general Theorem 2.8 of~\cite{CPSV1}. For this we consider
a pair of stationary ergodic random tubes
$(\omega,\omega')\in\Omega^2$,
let $\widetilde{{\mathbb P}}$ be their joint law and ${\mathbb
P},{\mathbb P}'$ be
the corresponding marginals. Suppose also that $\omega$ is
contained in $\omega'$ $\widetilde{{\mathbb P}}$-a.s.
We keep the notation such as $\kappa_x, K(x,y), \ldots$
for $x,y \in\partial\omega'$ as well, when it creates no
confusion; for the measures $\mu$ and $\nu$ we usually indicate in
the upper index whether they refer to $\omega$ or $\omega'$.
Denote also ${\mathcal Z}' = \int_{\Omega} d{\mathbb P}'\int_\Lambda
\kappa^{-1}_{0,u} \,d\mu_0^{\omega'}(u)$.
If $(\xi'_0,\xi'_1)$ is a chord in $\omega'$, we denote by
$(\xi_0^{(1)},\xi_1^{(1)}),
\ldots, (\xi_0^{(\iota)},\xi_1^{(\iota)})$ the induced random
chords in $\omega$
(see Figure \ref{f_many_chords}). Here, $\iota\in\{0,1,2,\ldots\}$
is a random variable which denotes the number of induced chords
in $\omega$ so that $\iota=0$ when the chord $(\xi'_0,\xi'_1)$
has no intersection with $\omega$.
\begin{figure}
\includegraphics{504f05.eps}
\caption{Random chords induced in a random tube $\omega$ by a
random chord in a
random tube $\omega'$ (in this particular case, we have $\iota=4$).}
\label{f_many_chords}
\end{figure}
The generalization of Theorem 2.8 of \cite{CPSV1} that we
want to obtain is the following fact:
\begin{prop}
\label{p_induced_chords}
For any bounded function $f\dvtx{\mathfrak M}\mapsto{\mathbb R}$ we have
\begin{eqnarray}\label{eq_induced_chords}\quad
&&\bigl\langle{\mathtt E}_{\omega}\bigl(f(\omega, {\mathcal U}\xi_0,
\xi_1)\mid\xi_0=(0,u)
\bigr) \bigr\rangle_{{\mathbb Q}}\nonumber\\
&&\qquad= \frac{{\mathcal Z}'}{{\mathcal Z}}\times\frac{1}{{\mathcal Z}'}
\int_{\Omega^2}d\widetilde{{\mathbb P}}(\omega,\omega')
\int_\Lambda d\mu_0^{\omega'} (u)\,\kappa_{0,u}^{-1} \\
&&\qquad\quad{} \times
{\mathtt E}_{\omega,\omega'} \Biggl(\sum_{k=1}^\iota
f \bigl(\theta_{\xi_0^{(k)}\cdot e}\omega, {\mathcal U}\xi_0^{(k)},
\xi_1^{(k)} - \bigl(\xi_0^{(k)}\cdot e\bigr)e \bigr)
\biggm| \xi'_0=(0,u) \Biggr).\nonumber
\end{eqnarray}
\end{prop}
\begin{pf}
We keep the notation from the proof of
Proposition \ref{p_cosine_int} (with the obvious modifications
in the case when $\omega'$ is considered instead of $\omega$).
Without restriction of generality, we suppose that $f$
is nonnegative.
First, analogously to (\ref{conta_inv*}),
we obtain that the right-hand side of (\ref{eq_induced_chords})
may be rewritten as
\begin{eqnarray} \label{mnogo_chords2}
&&\frac{1}{2s{\mathcal Z}}
\int_{\Omega^2}d\widetilde{{\mathbb P}}(\omega,\omega')
\int_{{\tilde F}^{\omega'}_s}d\nu^{\omega'} (x)
\int_{\partial\omega'}d\nu^{\omega'} (y)\,K(x,y)\nonumber\\[-8pt]\\[-8pt]
&&\qquad{} \times\sum_{k=1}^{\iota(x,y)}
f \bigl(\theta_{x^{(k)}\cdot e}\omega, {\mathcal U}x^{(k)},
y^{(k)} - \bigl(x^{(k)}\cdot e\bigr)e \bigr) =: T_1,\nonumber
\end{eqnarray}
where $(x^{(1)},y^{(1)}),\ldots, (x^{(\iota(x,y))},
y^{(\iota(x,y))})$
are the chords induced in $\omega$ by the chord $(x,y)$
in $\omega'$.
Let us denote ${\tilde F}^\omega_{h,h'} =
\{x\in\partial\omega\dvtx x\cdot e\in[h,h']\}$
(so that ${\tilde F}^\omega_{s}={\tilde F}^\omega_{-s,s}$).
Define ${\hat\iota}_n(x,y)$ as the number of intersections
of the chord $(x,y)$ with ${\tilde F}^\omega_{s-n,s-n+1}$.
To proceed, we need the following fact: let $A$ be a
subset of $\partial{\mathcal D}_s^\omega$ and $x\in\partial
{\mathcal D}_s^{\omega'}$.
Then we have
\[
\mathtt{P}_{\omega'}[\mbox{random chord beginning at $x$
crosses $A$}]
\leq\nu^{\omega}(A)\sup_{y\in A}{\hat K}(x,y).
\]
Also, by decomposing $A$ into pieces that may have at most one
intersection with the chord starting from $x$ and using the above
inequality, we obtain
\begin{eqnarray}\label{cross_a_piece}
&&\mathtt{E}_{\omega'}[\mbox{number of intersections of the
random chord from $x$
with $A$}]\nonumber\\[-8pt]\\[-8pt]
&&\qquad \leq\nu^{\omega}(A)\sup_{y\in A}{\hat K}(x,y).\nonumber
\end{eqnarray}
Using Condition \ref{ConditionL}
one obtains that $\nu^{\omega}({\tilde F}^\omega_{s-n,s-n+1})$ is bounded
from above by a constant [see the argument before (\ref{IP<IQ})].
From (\ref{def_K}) we know that $K(z,z')\leq
\frac{\gamma_d}{\|z-z'\|}$,
so for any $x\in\{s\}\times\omega'_s$ it is straightforward
to obtain that
\begin{equation}
\label{number_inters}
\int_{\partial{\mathcal D}_s^{\omega'}}{\hat\iota}_n(x,y)K(x,y)\,
d\nu^{\omega'}(y) \leq
\frac{C_6\nu^{\omega}({\tilde F}^\omega_{s-n,s-n+1})}{n}
\leq\frac{C_7}{n}.
\end{equation}
Suppose, without restriction of generality, that $s$ is an integer
number.
Since $\iota(x,y) \leq1+\sum_{n=1}^{2s}{\hat\iota}_n(x,y)$,
we obtain that
\begin{eqnarray}\label{laterals_not_count}
&&\frac{1}{s}\int_{\Omega^2}d\widetilde{{\mathbb P}}(\omega,\omega')
\int_{\{s\}\times\omega'_s}d\nu^{\omega'} (x)
\int_{\partial{\mathcal D}_s^{\omega'}} d\nu^{\omega'} (y)\,
{\hat K}(x,y)\iota(x,y)
\nonumber\\
&&\qquad\leq\frac{1}{s} \Biggl(1+\sum_{n=1}^{2s}\frac{C_7}{n} \Biggr)
\\
&&\qquad\leq\frac{C_8\ln s}{s}\nonumber
\end{eqnarray}
and the same bound also holds if we change $\{s\}\times\omega'_s$
to $\{-s\}\times\omega'_{-s}$ in the second integral above.
Note that, by the ergodic theorem, we have that
\[
\frac{\nu^{\omega}(\partial{\mathcal D}_s^{\omega})}{2s}\to
{\mathcal Z},\qquad
\frac{\nu^{\omega'} (\partial{\mathcal D}_s^{\omega'})}{2s}\to
{\mathcal Z}'\qquad
\mbox{as $s\to\infty$, $ \widetilde{{\mathbb P}}$-a.s.}
\]
Then, analogously to (\ref{conta_inv**}),
using (\ref{laterals_not_count})
together with the fact that $f$ is a bounded function,
we obtain that for any $\varepsilon>0$ there exists $s_0$ such that
for all $s\geq s_0$ [recall (\ref{mnogo_chords2})],
\begin{equation}
\label{difference_Ts}
T_2-T_1<\varepsilon,
\end{equation}
where
\begin{eqnarray} \label{mnogo_chords3}
&&T_2:=\frac{1}{\nu^{\omega'} (\partial{\mathcal
D}_s^{\omega'})}
\int_{(\partial{\mathcal D}_s^{\omega'})^2}d\nu^{\omega'} (x)\,
d\nu^{\omega'} (y)\,{\hat K}(x,y)\nonumber\\[-8pt]\\[-8pt]
&&\qquad{} \times\sum_{k=1}^{\iota(x,y)}
f \bigl(\theta_{x^{(k)}\cdot e}\omega, {\mathcal U}x^{(k)},
y^{(k)} - \bigl(x^{(k)}\cdot e\bigr)e \bigr).\nonumber
\end{eqnarray}
Then, by Theorem 2.8 of \cite{CPSV1}, we have
\begin{equation}
\label{apply_Th.2.8}\hspace*{28pt}
T_2 = \frac{1}{\nu^{\omega}(\partial{\mathcal D}_s^{\omega})}
\int_{(\partial{\mathcal D}_s^{\omega})^2}d\nu^{\omega}(x)\, d\nu
^{\omega}(y)\,
{\hat K}(x,y) f \bigl(\theta_{x\cdot e}\omega, {\mathcal U}x,
y - (x\cdot e)e \bigr).
\end{equation}
Again, it is straightforward to obtain that for any $\varepsilon>0$
there exists $s_0$ such that for all $s\geq s_0$,
\begin{eqnarray}\label{difference_others}\hspace*{22pt}
&& \biggl| \frac{1}{\nu^{\omega}(\partial{\mathcal D}_s^{\omega})}
\int_{(\partial{\mathcal D}_s^{\omega})^2}d\nu^{\omega}(x)\, d\nu
^{\omega}(y)\,
{\hat K}(x,y) f \bigl(\theta_{x\cdot e}\omega, {\mathcal U}x,
y - (x\cdot e)e \bigr)\nonumber\\
&&\qquad{}- \frac{1}{2s{\mathcal Z}}
\int_{{\tilde F}^\omega_s}d\nu^{\omega}(x)\\
&&\hspace*{85.7pt}{}\times\int_{\partial\omega} d\nu^{\omega}(y)\,
K(x,y) f \bigl(\theta_{x\cdot e}\omega, {\mathcal U}x,
y - (x\cdot e)e \bigr) \biggr| < \varepsilon.\nonumber
\end{eqnarray}
By the ergodic theorem, we have that ${\mathbb P}$-a.s.
\begin{eqnarray*}
&&\lim_{s\to\infty}\frac{1}{2s{\mathcal Z}}
\int_{{\tilde F}^\omega_s}d\nu^{\omega}(x)
\int_{\partial\omega} d\nu^{\omega}(y)
K(x,y) f \bigl(\theta_{x\cdot e}\omega, {\mathcal U}x,
y - (x\cdot e)e \bigr)\\
&&\qquad
= \bigl\langle{\mathtt E}_{\omega}\bigl(f(\omega, {\mathcal U}\xi_0, \xi
_1)\mid\xi_0=(0,u) \bigr)
\bigr\rangle_{{\mathbb Q}},
\end{eqnarray*}
so, using (\ref{difference_Ts}), (\ref{apply_Th.2.8})
and (\ref{difference_others}), we obtain,
abbreviating for a moment
\[
\mathfrak{A}:=\sum_{k=1}^\iota
f \bigl(\theta_{\xi_0^{(k)}\cdot e}\omega, {\mathcal U}\xi_0^{(k)},
\xi_1^{(k)} - \bigl(\xi_0^{(k)}\cdot e\bigr)e \bigr),
\]
that
\begin{eqnarray}\label{ineq_induced_chords1}
&&\bigl\langle{\mathtt E}_{\omega}\bigl(f(\omega, {\mathcal U}\xi_0, \xi
_1)\mid\xi_0=(0,u) \bigr) \bigr\rangle
_{{\mathbb Q}}\nonumber\\[-8pt]\\[-8pt]
&&\qquad\leq\frac{{\mathcal Z}'}{{\mathcal Z}}\times\frac{1}{{\mathcal Z}'}
\int_{\Omega^2}d\widetilde{{\mathbb P}}(\omega,\omega')
\int_\Lambda d\mu_0^{\omega'} (u)\,\kappa_{0,u}^{-1}
{\mathtt E}_{\omega,\omega'} \bigl(\mathfrak{A}
\mid\xi'_0=(0,u) \bigr).\nonumber
\end{eqnarray}
The other inequality is much easier to obtain.
Fix an arbitrary ${\tilde c}>0$, and consider
$\mathfrak{A} {\mathbb I}{\{\mathfrak{A}\leq{\tilde c}\}}$
instead of $\mathfrak{A}$. Since $\mathfrak{A} {\mathbb I}{\{
\mathfrak{A} \leq{\tilde c}\}}$ is bounded, we now have no
difficulties relating
the integrals on ${\tilde F}^{\omega'}_s\times\partial\omega'$
to the corresponding integrals on $(\partial{\mathcal D}_s^{\omega'})^2$.
In this way we obtain that for any ${\tilde c}$,
\begin{eqnarray*}
&&\bigl\langle{\mathtt E}_{\omega}\bigl(f(\omega, {\mathcal U}\xi_0, \xi
_1)\mid\xi_0=(0,u) \bigr) \bigr\rangle
_{{\mathbb Q}}\\
&&\qquad\geq\frac{{\mathcal Z}'}{{\mathcal Z}}\times\frac{1}{{\mathcal Z}'}
\int_{\Omega^2}d\widetilde{{\mathbb P}}(\omega,\omega')
\int_\Lambda d\mu_0^{\omega'} (u)\,\kappa_{0,u}^{-1}
{\mathtt E}_{\omega,\omega'}
\bigl(\mathfrak{A} {\mathbb I}{\{\mathfrak{A}\leq{\tilde c}\}}
\mid\xi'_0=(0,u) \bigr).
\end{eqnarray*}
We use now the monotone convergence theorem
and (\ref{ineq_induced_chords1}) to conclude the proof of
Proposition \ref{p_induced_chords}.
\end{pf}
Using Proposition \ref{p_induced_chords}, we are now
able to prove Proposition \ref{pr_suff_2nd_moment} for all
$d\geq3$.
\begin{pf*}{Proof of Proposition \protect\ref{pr_suff_2nd_moment}}
We apply Proposition \ref{p_induced_chords} with $\omega'$
being the straight cylinder, $\omega'={\mathbb R}\times\Lambda$.
For the random chord in a straight tube, using the fact that
the cosine density vanishes in the directions orthogonal to the
normal vector, we obtain that (for any starting point $\xi'_0$)
$\phi_0:= \mathtt{E}_{\omega'}((\xi'_1-\xi'_0)\cdot e)^2 < \infty$.
Now consider the function
$f_{\tilde c}(\omega,u,y)=(y\cdot e)^2{\mathbb I}{\{(y\cdot e)^2\leq
{\tilde c}\}}$.
Since
\[
\sum_{k=1}^\iota
f_{\tilde c} \bigl(\theta_{\xi_0^{(k)}\cdot e}\omega, {\mathcal U}\xi_0^{(k)},
\xi_1^{(k)} - \bigl(\xi_0^{(k)}\cdot e\bigr)e \bigr)
\leq\bigl((\xi'_1-\xi'_0)\cdot e\bigr)^2,
\]
we obtain that for any ${\tilde c}$,
\[
\bigl\langle{\mathtt E}_{\omega}\bigl(f_{\tilde c}(\omega, {\mathcal U}\xi_0,
\xi_1)\mid\xi
_0=(0,u) \bigr) \bigr\rangle_{{\mathbb Q}} \leq\phi_0.
\]
Using the monotone convergence theorem, we conclude
the proof of Proposition~\ref{pr_suff_2nd_moment}.
\end{pf*}
\textit{Remarks.}
(i) Observe from the definitions of $\phi_0$ above
and (\ref{def_Lambda}) of $\Lambda$ that $\phi_0({\widehat M})
\stackrel{\mathrm{def}}{=}
\phi_0={\widehat M}^2 \phi_0(1)$.
Then we have shown the universal bound
\[
\langle b \rangle_{{\mathbb Q}} \leq{\widehat M}^2 C(d)
\]
for all random tubes with a vertical section included in the
sphere $\Lambda$ of radius ${\widehat M}$ where
$C(d)=\phi_0(1)$ corresponds to the straight cylinder
with spherical section of radius ${\widehat M}=1$.
(ii) For $k\geq1$, denote by
\[
b^{(k)}(\omega,u) =
{\mathtt E}_{\omega}\bigl(|(\xi_1-\xi_0)\cdot e|^k \mid\xi_0=(0,u)\bigr)
\]
the $k$th absolute moment of the projection of the first jump to the
horizontal direction. Then, similarly to the proof of
Propositions \ref{pr_suff_2nd_moment}
and \ref{pr_infinite_d=2}, one can
obtain, for the $d$-dimensional model, that
$\langle b^{(d)} \rangle_{{\mathbb Q}}=+\infty$ in the case when the random
tube contains
a straight cylinder and that $\langle b^{(d-\delta)} \rangle
_{{\mathbb Q}
}<\infty$
for any $\delta>0$.
\subsection{\texorpdfstring{Proof of Theorem
\protect\ref{t_q_invar_princ_cont}}{Proof of Theorem 2.2}}
\label{s_proof_inv_pr_cont}
We start by obtaining a formula for the mean length of the
first jump, at equilibrium.
\begin{lmm}
\label{l_chord_length}
We have
\begin{equation}
\label{eq_chord_length}
\langle{\mathtt E}_{\omega}\|\xi_1-\xi_0\| \rangle_{{\mathbb Q}} =
\frac{\pi^{1/2}
\Gamma(({d+1})/{2})d}{\Gamma({d}/{2}+1)}\times
\frac{1}{{\mathcal Z}}\int_\Omega|\omega_0| \,d{\mathbb P}.
\end{equation}
\end{lmm}
\begin{pf}
Recall the notation ${\tilde F}^\omega_s$,
${\mathcal D}_s^\omega$, ${\hat K}(x,y)$
from the proof of Proposition~\ref{p_cosine_int}.
The strategy of the proof will be similar to that of the proof of
Proposition~\ref{p_induced_chords}.
Analogously to (\ref{conta_inv*}), we write
\begin{eqnarray}\label{conta_dlina_chord}\qquad
\langle{\mathtt E}_{\omega}\|\xi_1-\xi_0\| \rangle_{{\mathbb Q}}
&=& \frac{1}{{\mathcal Z}}\int_\Omega d{\mathbb P}
\int_\Lambda
d\mu^{\omega}_0(u)\,\kappa_{0,u}^{-1}\nonumber\\
&&{}\times\int_{\partial\omega}d\nu
^{\omega}(y)\,
K ((0,u),y )\|(0,u)-y\|\nonumber\\
&=& \frac{1}{2s{\mathcal Z}}\int_\Omega d{\mathbb P}\int_{-s}^s ds
\int_\Lambda d\mu^{\omega}_s(u)\,\kappa_{s,u}^{-1}\\
&&{} \times\int_{\partial\omega}d\nu^{\omega}(y)\,
K ((s,u),y )
\|(s,u)-y\|\nonumber\\
&=& \frac{1}{2s{\mathcal Z}}\int_\Omega d{\mathbb P}\int_{{\tilde
F}^\omega_s}
d\nu^{\omega}(x)\int_{\partial\omega}d\nu^{\omega}(y) \|y-x\|K(x,y).\nonumber
\end{eqnarray}
By Theorem 2.6 of \cite{CPSV1}, we know that
\begin{equation}
\label{finite_mean_chord}
\int_{(\partial{\mathcal D}_s^\omega)^2} d\nu^{\omega}(x)\, d\nu
^{\omega}(y)\,
{\hat K}(x,y) \|x-y\|
= \frac{\pi^{1/2}\Gamma(({d+1})/{2})d}
{\Gamma({d}/{2}+1)} |{\mathcal D}_s^\omega|.
\end{equation}
Denote by $D_\ell= \{-s\}\times\omega_{-s}$ and
$D_r = \{s\}\times\omega_{s}$ the left and
right vertical pieces of $\partial{\mathcal D}_s^\omega$, so that
$\partial{\mathcal D}_s^\omega= {\tilde F}^\omega_s\cup D_\ell\cup D_r$.
From (\ref{conta_dlina_chord})
we obtain [recall also that ${\hat K}(x,y)={\hat K}(y,x)$ for all
$x,y\in\partial{\mathcal D}_s^\omega$]
\begin{eqnarray*}
\langle{\mathtt E}_{\omega}\|\xi_1-\xi_0\| \rangle_{{\mathbb Q}}
&\geq&\frac{1}{2s{\mathcal Z}
}\int_\Omega d{\mathbb P}
\int_{({\tilde F}^\omega_s)^2}
d\nu^{\omega}(x)\, d\nu^{\omega}(y) \|y-x\|K(x,y) \\
&\geq&\frac{1}{2s{\mathcal Z}}\int_\Omega d{\mathbb P}
\biggl(\int_{(\partial{\mathcal D}_s^\omega)^2}
d\nu^{\omega}(x)\, d\nu^{\omega}(y) \|y-x\|{\hat K}(x,y) \\
&&\hspace*{54.8pt}{}
- 2 \int_{(D_\ell\cup D_r) \times
\partial{\mathcal D}_s^\omega}
d\nu^{\omega}(y) \|y-x\|{\hat K}(x,y) \biggr).
\end{eqnarray*}
Observe that [recall (\ref{def_Lambda})] for all
$x,y\in{\mathbb R}\times\Lambda$ it holds that
$\|x-y\|\leq|(x-y)\cdot e|+2{\widehat M}$.
So by (\ref{bound_d>=4}), there exists $C_1>0$ such that
for all $s$ we have
\[
\int_{(D_\ell\cup D_r) \times\partial{\mathcal D}_s^\omega}
d\nu^{\omega}(y) \|y-x\|{\hat K}(x,y) \leq C_1 \ln s + 2{\widehat M},
\]
and, using (\ref{finite_mean_chord}), we obtain
\begin{eqnarray}
\label{oc_snizu_mean_chord_lim}
&&\langle{\mathtt E}_{\omega}\|\xi_1-\xi_0\| \rangle_{{\mathbb Q}}
\nonumber\\[-8pt]\\[-8pt]
&&\qquad\geq\frac{1}{2s{\mathcal Z}
}\int_\Omega d{\mathbb P}
\biggl(\frac{\pi^{1/2}\Gamma(({d+1})/{2})d}
{\Gamma({d}/{2}+1)}|{\mathcal D}_s^\omega|-C_1 \ln s
- 2{\widehat M} \biggr)\,d{\mathbb P}.\nonumber
\end{eqnarray}
Since, by the ergodic theorem,
\[
\frac{1}{2s}|{\mathcal D}_s^\omega| \to\int_\Omega|\omega_0|\,
d{\mathbb P}\qquad
\mbox{a.s., as $s\to\infty$},
\]
and sending $s$ to $\infty$
we obtain from (\ref{oc_snizu_mean_chord_lim}) that
\begin{equation}
\label{oc_snizu_mean_chord}
\langle{\mathtt E}_{\omega}\|\xi_1-\xi_0\| \rangle_{{\mathbb Q}}
\geq\frac{\pi^{1/2}
\Gamma(({d+1})/{2})d}{\Gamma({d}/{2}+1)}\times
\frac{1}{{\mathcal Z}}\int_\Omega|\omega_0| \,d{\mathbb P}.
\end{equation}
Now, fix ${\tilde c}>0$ and write analogously
to (\ref{conta_dlina_chord})
\begin{eqnarray*}
&&\langle{\mathtt E}_{\omega}\|\xi_1-\xi_0\|{\mathbb I}{\{\|
\xi_1-\xi _0\| \leq {\tilde c}\}} \rangle_{{\mathbb Q}} \\
&&\qquad= \frac{1}{2s{\mathcal Z}}\int_\Omega d{\mathbb P}\int_{{\tilde
F}^\omega_s}
d\nu^{\omega}(x)\int_{\partial\omega}d\nu^{\omega}(y) \|y-x\|
{\mathbb I}{\{\|y-x\| \leq{\tilde c}\}} K(x,y).
\end{eqnarray*}
In this situation
$\|\xi_1-\xi_0\|{\mathbb I}{\{\|\xi_1-\xi_0\|\leq{\tilde c}\}}$ is bounded.
So, analogously to the proof of Proposition \ref{p_cosine_int} and
again using (\ref{finite_mean_chord}), by a coupling argument it is
elementary to obtain that for any ${\tilde c}$,
\begin{eqnarray*}
&&\langle{\mathtt E}_{\omega}\|\xi_1-\xi_0\|{\mathbb I}{\{\|\xi
_1-\xi_0\|\leq {\tilde c}\}}
\rangle_{{\mathbb Q}} \\
&&\qquad\leq
\frac{\pi^{1/2}\Gamma(({d+1})/{2})d}{\Gamma({d}/{2}+1)}
\times
\frac{1}{{\mathcal Z}}\int_\Omega|\omega_0| \,d{\mathbb P}.
\end{eqnarray*}
Using the monotone convergence theorem
and (\ref{oc_snizu_mean_chord}),
we conclude the proof of Lemma \ref{l_chord_length}.
\end{pf}
With Lemma \ref{l_chord_length} at hand,
we are now ready to prove Theorem \ref{t_q_invar_princ_cont}.
\begin{pf*}{Proof of Theorem \protect\ref{t_q_invar_princ_cont}}
Define $n(t)=\max\{n\dvtx\tau_n\leq t\}$.
We have
\[
t^{-1/2} X_t\cdot e = t^{-1/2} \xi_{n(t)}\cdot e
+ t^{-1/2}\bigl(X_t-\xi_{n(t)}\bigr)\cdot e.
\]
Let us prove first that the second term goes to $0$.
Indeed, by definition of the continuous-time process we have
\begin{equation}
\label{eq_cont_clt}
t^{-1} \bigl(\bigl(X_t-\xi_{n(t)}\bigr)\cdot e \bigr)^2
\leq\frac{1}{n(t)} \bigl(\bigl(\xi_{n(t)+1}-\xi_{n(t)}\bigr)\cdot e
\bigr)^2.
\end{equation}
But then from the stationarity of $\xi$ we obtain that
\[
n^{-1} {\mathtt E}_{\omega}\bigl(\bigl(\xi_{n+1}-\xi_n\bigr)\cdot e \bigr)^2 \to0
\]
as $n\to\infty$ for ${\mathbb P}$-almost all $\omega$
[this is analogous to the derivation of (\ref{2nd_to_0})
in the proof of Theorem \ref{t_q_invar_princ}].
Now, the first term in the right-hand side of (\ref{eq_cont_clt})
equals
\[
\biggl(\frac{n(t)}{t} \biggr)^{1/2} \times
\frac{1}{n(t)^{1/2}}\xi_{n(t)}\cdot e.
\]
For the second term in the above product, apply
Theorem \ref{t_q_invar_princ}.
As for the first term, since
\[
\frac{n(t)}{\tau_{n(t)+1}} \leq\frac{n(t)}{t}
\leq\frac{n(t)}{\tau_{n(t)}},
\]
by the ergodic theorem and Lemma \ref{l_chord_length}
we have, almost surely,
\begin{eqnarray*}
\lim_{t\to\infty} \frac{n(t)}{t} &=&
\lim_{n\to\infty}\frac{n}{\tau_n}\\
& = &(\langle{\mathtt E}_{\omega}\|\xi_1-\xi_0\| \rangle_{{\mathbb
Q}} )^{-1}\\
& = & \frac{\Gamma({d}/{2}+1){\mathcal Z}}
{\pi^{1/2}\Gamma(({d+1})/{2})d}
\biggl(\int_\Omega|\omega_0|\, d{\mathbb P}\biggr)^{-1}.
\end{eqnarray*}
This concludes the proof of Theorem
\ref{t_q_invar_princ_cont}.\vspace*{-15pt}
\end{pf*}
\begin{appendix}\label{app}
\section*{Appendix}
\label{s_vertical_walls}
In this section we discuss the case when the map
$\alpha\mapsto\omega_\alpha$
is not necessarily continuous which corresponds to the case when
the random tube can have vertical walls.
The proofs contained here are given in a rather
sketchy way without going into much detail.
Define
\[
\varpi_\alpha= \{u\in\Lambda\dvtx (\alpha,u)\in\partial\omega\}
\]
to be the section of the boundary
by the hyperplane where the first coordinate is equal to $\alpha$.
Then let
\[
{\mathcal S}^{(0)} = \{\alpha\in{\mathbb R}\dvtx |\varpi_\alpha|\geq1\}
\]
and, for $n\geq1$,
\[
{\mathcal S}^{(n)} = \biggl\{\alpha\in{\mathbb R}\dvtx
|\varpi_\alpha|\in\biggl[\frac{1}{n+1},\frac{1}{n} \biggr) \biggr\}.
\]
Besides Condition \ref{ConditionR}, we have to assume something more.
Namely, we assume that for ${\mathbb P}$-almost all $\omega$,
$\nu^{\omega}$-almost all $(\alpha,u)\in\partial\omega$
are such that either $|\varpi_\alpha|>0$
(so that $\alpha\in{\mathcal S}^{(n)}$ for some $n$), or
$(\alpha,u)\in{\mathcal R}_{\omega}$ (recall the definition of
${\mathcal R}_{\omega}$ from
Section~\ref{s_notations}).
Also, we modify the definition of the measure $\mu^{\omega}_\alpha$
in the following way:
it is defined as in Section \ref{s_notations} when
$|\varpi_\alpha|=0$, and we put $\mu^{\omega}_\alpha\equiv0$
when $|\varpi_\alpha|>0$.
Observe that, for any $n\geq0$, ${\mathcal S}^{(n)}$ is a stationary point
process.
Note that, in contrast, the set $\bigcup_{n \geq0} {\mathcal S}^{(n)}$ may
\textit{not} be locally finite, which is the reason why we need to
introduce a sequence ${\mathcal S}^{(n)}$. Let ${\mathbb P}^{(n)}$
be the Palm version of ${\mathbb P}$ with respect to ${\mathcal
S}^{(n)}$, that is,
intuitively it is ${\mathbb P}$ ``conditioned on having a point of
${\mathcal S}^{(n)}$
at the origin.'' Observe that ${\mathbb P}^{(n)}$ is singular with respect
to ${\mathbb P}$, since, obviously,
\[
{\mathbb P}[|\varpi_0|>0] = 0.
\]
Now, define (after checking that the two limits below exist
${\mathbb P}$-a.s.)
\begin{eqnarray*}
q_0 &=& \biggl(\int_\Omega|\varpi_0| \,d{\mathbb P}^{(0)}
\biggr)^{-1}\\
&&{}\times
\lim_{a\to\infty}\frac{\nu^{\omega}(\{x\in\partial\omega\dvtx
x\cdot e\in[0,a], |\varpi_{x\cdot e}|\geq1\} )}
{a},\\
q_n &=& \biggl(\int_\Omega|\varpi_0| \,d{\mathbb P}^{(n)} \biggr)^{-1}
\\
&&{}\times
\lim_{a\to\infty}\frac{\nu^{\omega}(\{x\in\partial\omega\dvtx
x\cdot e\in[0,a],
|\varpi_{x\cdot e}|\in[{1}/({n+1}),
{1}/{n})\} )}{a}
\end{eqnarray*}
for $n\geq1$.
Then, we define the measure ${\mathbb Q}$ which is the reversible measure
for the environment seen from the particle
\begin{equation}\quad
\label{df_IQ_vert}
d{\mathbb Q}(\omega,u) = \frac{1}{{\mathcal Z}} \Biggl[\kappa_{0,u}^{-1}
\,d\mu^{\omega}_0(u)\,
d{\mathbb P}(\omega)
+ \sum_{n=0}^\infty q_n {\mathbb I}{\{u\in\varpi_0\}} \,du\,
d{\mathbb P}^{(n)}(\omega) \Biggr],
\end{equation}
where ${\mathcal Z}$ is the normalizing constant; as we will see below,
${\mathcal Z}$ still can be defined directly through the limit
\[
{\mathcal Z}= \lim_{a\to\infty}\frac{\nu^{\omega}(\{x\in\partial
\omega\dvtx
x\cdot e\in[0,a]\} )}{a}.
\]
The scalar product is now defined by
\begin{eqnarray*}
\langle f, g \rangle_{{\mathbb Q}} &=& \frac{1}{{\mathcal Z}} \Biggl[\int
_\Omega d{\mathbb P}
\int_{\Lambda}
d\mu^{\omega}_0(u)\,
\kappa_{0,u}^{-1}f(\omega,u)g(\omega,u) \\
&&\hspace*{15.4pt} {}
+ \sum_{n=0}^\infty q_n \int_\Omega d{\mathbb P}^{(n)}
\int_{\varpi_0} du\, f(\omega,u)g(\omega,u) \Biggr].
\end{eqnarray*}
Now we need a slightly different definition for the transition
density: define $\bar{K}(x,y)$ by formula (\ref{def_K})
but without the indicator functions that $|{\mathbf n}_{\omega
}(x)\cdot e|\neq1$ and
$|{\mathbf n}_{\omega}(y)\cdot e|\neq1$. Also, the transition
operator $G$ can be
written in the following way:
\begin{eqnarray*}
Gf (\omega,u) &=& {\mathtt E}_{\omega}\bigl(f(\theta_{\xi_1\cdot e}\omega
,{\mathcal U}\xi_1)
\mid\xi_0 = (0,u)\bigr)\\
&=& \int_{\partial\omega} \bar{K} ((0,u),x )
f(\theta_{x\cdot e}\omega,{\mathcal U}x)\, d\nu^{\omega}(x)
\\
&=& \int_{-\infty}^{+\infty} d\alpha\int_{\Lambda}
d\mu^{\omega}_\alpha(v)\,
\kappa_{\alpha,v}^{-1}
f(\theta_\alpha\omega,v) \bar{K} ((0,u),(\alpha,v) )
\\
&&{} + \sum_{n=0}^\infty\sum_{\alpha\in{\mathcal S}^{(n)}}
\int_{\varpi_\alpha} dv\,
f(\theta_\alpha\omega,v) \bar{K} ((0,u),(\alpha,v) ).
\end{eqnarray*}
Now, we have to prove the reversibility of $G$ with
respect to ${\mathbb Q}$.
The direct method adopted in the proof of
Lemma \ref{l_revers_discr} now seems to be to cumbersome to apply,
so we use another approach by taking advantage of stationarity.
For two bounded functions $f,g$, consider the quantity
\begin{eqnarray*}
{\mathfrak A}(a) &=& \frac{1}{{\mathcal Z}a}\int_{\{x\in\partial
\omega\dvtx
x\cdot e\in[0,a]\}^2}
d\nu^{\omega}(x)\,d\nu^{\omega}(y)\, \bar{K}(x,y)\\
&&\hspace*{91.3pt}{}\times f(\theta_{x\cdot
e}\omega,{\mathcal U}x)
g(\theta_{y\cdot e}\omega,{\mathcal U}y).
\end{eqnarray*}
Using (\ref{chord_not_too_long}),
it is elementary to obtain that (assuming for now that the
limit exists ${\mathbb P}$-a.s.)
\begin{eqnarray*}
\lim_{a\to\infty} {\mathfrak A}(a) &=& \lim_{a\to\infty}
\frac{1}{{\mathcal Z}a}\int_{\{x\in\partial\omega\dvtx x\cdot e\in
[0,a]\}}
d\nu^{\omega}(x)\,
f(\theta_{x\cdot e}\omega,{\mathcal U}x) \\
&&\hspace*{21.2pt}{} \times\int_{\partial\omega}d\nu^{\omega}(y)\,
\bar{K}(x,y)g(\theta_{y\cdot e}\omega,{\mathcal U}y)
\\
&=& \lim_{a\to\infty} \frac{1}{{\mathcal Z}a}\int_{\{x\in\partial
\omega\dvtx
x\cdot e\in[0,a]\}}d\nu^{\omega}(x)\,
f(\theta_{x\cdot e}\omega,{\mathcal U}x)\\
&&\hspace*{110.3pt}{}\times Gg(\theta_{x\cdot e}\omega
,{\mathcal U}x).
\end{eqnarray*}
Then we write, using the ergodic theorem,
\begin{eqnarray*}
&&\lim_{a\to\infty} \frac{1}{a} \int_0^a d\alpha
\int_\Lambda d\mu^{\omega}_\alpha(u)\, \kappa^{-1}_{\alpha,u}
f(\theta_\alpha\omega,u)Gg(\theta_\alpha\omega,u)\\
&&\qquad=\int_\Omega d{\mathbb P}\int_\Lambda d\mu^{\omega}_0(u)\, \kappa^{-1}_{0,u}
f(\omega,u)Gg(\omega,u),\qquad {\mathbb P}\mbox{-a.s.}
\end{eqnarray*}
Again, by the ergodic theorem, we have
\[
\lim_{a\to\infty} \frac{|{\mathcal S}^{(m)}\cap[0,a]|}{a} = q_m,\qquad
{\mathbb P}\mbox{-a.s.}
\]
so that we can write
\begin{eqnarray*}
&&\lim_{a\to\infty} \frac{1}{a}
\sum_{\alpha\in{\mathcal S}^{(m)}\cap[0,a]} \int_{\varpi_\alpha}du\,
f(\theta_\alpha\omega,u)Gg(\theta_\alpha\omega,u)\\
&&\qquad= q_m \int_\Omega d{\mathbb P}^{(m)}\int_{\varpi_0} du\,
f(\omega,u)Gg(\omega,u),\qquad {\mathbb P}\mbox{-a.s.}
\end{eqnarray*}
Thus we have for ${\mathbb P}$-almost all environments
\begin{eqnarray*}
\lim_{a\to\infty} {\mathfrak A}(a) &=&\lim_{a\to\infty}
\frac{1}{{\mathcal Z}a}
\Biggl[\int_0^a d\alpha\int_\Lambda
d\mu^{\omega}_\alpha(u)\, \kappa^{-1}_{\alpha,u}
f(\theta_\alpha\omega,u)Gg(\theta_\alpha\omega,u) \\
&&\hspace*{45.3pt}{} + \sum_{m=0}^\infty
\sum_{\alpha\in{\mathcal S}^{(m)}\cap[0,a]} \int_{\varpi_\alpha}du\,
f(\theta_\alpha\omega,u)Gg(\theta_\alpha\omega,u) \Biggr] \\
& =& \frac{1}{{\mathcal Z}} \Biggl[\int_\Omega d{\mathbb P}\int_\Lambda
d\mu^{\omega}_0(u)\,
\kappa^{-1}_{0,u}
f(\omega,u)Gg(\omega,u) \\
&&\hspace*{15pt}{} + \sum_{m=0}^\infty q_m \int_\Omega d{\mathbb P}^{(m)}
\int_{\varpi_0} du\,
f(\omega,u)Gg(\omega,u) \Biggr]\\
&=& \langle f, Gg \rangle_{{\mathbb Q}}.
\end{eqnarray*}
By symmetry, in the same way one proves that $\lim_{a\to\infty}
{\mathfrak A}(a) = \langle g, Gf \rangle_{{\mathbb Q}}$, so $G$ is still
reversible with
respect to ${\mathbb Q}$.
Now the crucial observation is that formula (\ref{IP<IQ}) is
still valid even in the case when ${\mathbb Q}$ is defined
by (\ref{df_IQ_vert}), since we still have, for any $f\geq0$,
\[
\langle f \rangle_{{\mathbb Q}} \geq\frac{1}{{\mathcal Z}}\int
_{\Omega}d{\mathbb P}
\int_{\Lambda} d\mu^{\omega}_0(u)\,
\kappa_{0,u}^{-1}
f(\omega,u),
\]
so one can see that the whole argument goes through in this
general case as well.
However, we decided to write the proofs for the case of random
tube without vertical walls to avoid complicating the calculations
which are already quite involved. Here is the (incomplete) list of
places that would require modifications (and strongly complicate the
exposition):
\begin{itemize}
\item the display after (\ref{calc_g_nabla_f})
[part of the proof of (\ref{gradient=-diverg})];
\item the proof of (\ref{hatphi=b/2});
\item the proof of Proposition \ref{Prop_corrector};
\item the proof of (\ref{EQ_corr2<infty});
\item calculations (\ref{conta_inv*})
and (\ref{conta_dlina_chord}).
\end{itemize}
\end{appendix}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,623
|
About one year ago I posted this entry about Animating overlay made easy with Flex 4 effects and skins. While the example does not provide the ultimate practical value, it is a decent didactic material for novices. Also not so long ago I also posted about dynamic skinparts, which reminded me about this old post and the fact that if I were to use it is not flexible enough. Every time I would like to add or remove item from the animated collection, it would require me going inside the project and add the new element inside the Overlay class and a new corresponding graphical representation inside the skin. Yack! There's gotta be a better way… Enter dynamic skin parts again. They provide a flexible way to manipulate skin parts at runtime.
So, how does this affects the old example?
3. Now skins parts are dynamic, so we need to keep track of how many they are. To spice things up a little bit, we declare a variable numGraphicElements and give it public access so it can be modified at runtime.
4. Creating and removing dynamic parts. The number of parts will vary according to numGraphicElements. In the example the default value for numGraphicElements is 3. However it can be modified at any time. Therefore the code that actually triggers the creation of skinparts is placed inside commitProperties() instead of createChildren(). Inside the latter we only set a "dirty" marker flag, to signal the need for creating children upon component instantiation. Alternatively the numGraphicElementsChanged can be initialized as dirty upon declaration, eliminating the need to override the createChildren() method.
The same commitProperties() holds the de code for destroying skinparts. Codes figures out if it needs to create or destroy a part by caching the old numGraphicElements and comparing it against its new value.
6. So far so good… Now we the effects targeting the elements needs to be created by hand in actionscript. Since the bulk of code will pretty much be similar for both skins, I moved most it inside a base class (OverlaySkinBase) which will be extended by the 2 skins. Additionally, I created an additional factory class (EffectsFactory) which is responsible for creating the effect instances.
OverlaySkinBase declares and instantiate the animator, the effects factory, starting/stopping the animation and provides hook methods for attaching/removing effects to the skin part. To achieve the latter the easiest way is to register for ElementExistenceEvent.ELEMENT_ADD / ElementExistenceEvent.ELEMENT_EVENT on the parenting group. Inside the handler effects targeting the element can be created or destroyed. For brevity only the code that adds/removes an effect is displayed below.
7. Now that the mechanism is hooked up in the base class, the 2 skins only need to override their specific parts. That means overriding createEffectForElement() and/or profiving additional factory method function for creating glow filters (if the case).
This is it, you can also DOWNLOAD the source/.fxp project.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 576
|
Justified: Smart Factory Investments
by Hadley Bauer and Michael Glessner
Digital initiatives and strategies create buzz words in every industry like 'millennial', 'autonomous', and 'smart connected'; but the buy in doesn't always follow. Sure, having a 'Smart Factory' sounds… well, smart, but the excitement and investment in smart factory sensors and processing capabilities is only justified as long as there is visible value provided that can be communicated in a meaningful way.
Meet Christy. Christy is an ambitious new process engineer immersed in research around Smart Factories and Industrie 4.0. She shared a few of her forward-thinking ideas amongst colleagues but met resistance because of the numerous times they were unsuccessful funding new technologies. Her colleagues have struggled to construct a business case that resonates with executives to include in pitches for smart factories funding.
Christy decides she is going to tackle justifying smart factory investments. She starts by investigating the line she was assigned to, which uses a mature process with a great deal of sensor data. To her understanding, process engineers in the plant pay little attention to the data unless a specific issue calls them to a particular point in the process. She wants to learn how to use that data in a meaningful way that is proactive rather than reactive.
Knowing there are several different systems on her line alone, she believes it could be extremely powerful to aggregate the data and construct a model of the process that could be built, validated and analyzed through existing data.
How can she justify the investment in this project to test her theories? Christy knows that executives will want to know the exact benefit before spending any of the limited budget. How will she begin to decode and unlock the potential value of Smart Factories to make it clear and actionable for her company?
Christy hears that one of her colleagues is a Lean Six Sigma Black Belt currently using a metric called Overall Equipment Effectiveness (OEE) on her line. She approaches him to learn more and realizes that her idea would be much easier to justify if she uses OEE in her executive conversation.
OEE is a known operational metric that will provide the structure and credibility that she was lacking in her current business case.
Using OEE as a framework, Christy analyzes the quality, performance and availability of her line to create a high impact proof of concept. As the diagram shows, OEE is a combination of quality and performance results that indicate sources of lost value. Since OEE is highly scalable, she leverages the data on her line to build a digital model using available analytical tools that could be applied to other areas on the plant. Despite the initial effort required, and even without the funding for the necessary tools, Christy works through the challenge to prove her point.
This model in turn yields insights into several aspects of performance such that Christy is able to turnaround the line performance based on her learnings. This experience proves to executives that the data from her line provides insights that moved OEE several percentage points when processed correctly. OEE turns the quality and line performance improvements into a measurable justification and opens the conversation to spark executive interest and buy in for an application of the tools needed to scale the effort.
With this proof of value, it is apparent that the same benefit could be applied more broadly to other areas of the plant. With the scalable nature of the OEE metric, she would be able to use this process to provide similar justification at a larger scale.
Now equipped with a valuable business case measured by OEE, Christy confidently prepares her pitch for a smart factory investment having cracked the code of justifying tools to enable Industrie 4.0.
Originally published on June 11th, 2018
Topics: analytics, data, digital, industrie 4.0, industry 4.0, innovation, oee, overall equipment effectiveness, sco, smart connected factory, smart connected operations, smart factory
Hadley Bauer
Driven by an entrepreneurial spirit, eye for design, and attention to the latest trends, Hadley has and will continue to develop her passion for service through innovation that proactively adapts to evolving consumer and client expectations.
More Viewpoints by Hadley Bauer
hadley.bauer@kalypso.com
Michael Glessner
Michael Glessner is a director with Kalypso and has worked extensively in the areas of business and innovation strategy, product development, portfolio management, smart connected operations, large-scale organizational change leadership, and the software systems that enable innovation. His industry experience includes life sciences, industrial and high technology companies. He is a frequent speaker and writer on innovation effectiveness, disruptive innovation and time-to-market reduction.
More Viewpoints by Michael Glessner
michael.glessner@kalypso.com
A Practical IoT Use Case: Smart Asset Management and Heads Up Displays for Industrial Manufacturers
Previously in High Technology
Three Ways Blockchain Technology Will Impact R&D Management
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,137
|
Need help? Get in touch now!
If at any time you have any questions regarding products, ordering, returns, repairs, replacements or general questions you can contact our Customer Services Department and we will gladly answer your questions for you.
During periods of high volume please leave a voicemail including your name and phone number and we will return your call. All calls made when we are closed are called back in a sequence to when we received them. Rest assured once our office is open you will be contacted. You can also email us and we'll get in touch as soon as possible.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,147
|
// *******************************************************
// MACHINE GENERATED CODE
// MUST BE CAREFULLY COMPLETED
//
// ABSTRACT METHODS MUST BE IMPLEMENTED
//
// Generated on 10/19/2014 13:46:12
// *******************************************************
package com.blastedstudios.freeboot.ai.bt.actions.execution;
import com.badlogic.gdx.math.Vector2;
import com.blastedstudios.gdxworld.util.Log;
import com.blastedstudios.gdxworld.util.Properties;
import com.blastedstudios.freeboot.world.WorldManager;
import com.blastedstudios.freeboot.world.being.Being;
import com.blastedstudios.freeboot.world.being.INPCActionExecutor;
import com.blastedstudios.freeboot.world.being.NPC;
import com.blastedstudios.freeboot.world.being.NPC.AIFieldEnum;
/** ExecutionAction class created from MMPM action ForestInit. */
public class ForestInit extends jbt.execution.task.leaf.action.ExecutionAction {
/**
* Constructor. Constructs an instance of ForestInit that is able to run a
* com.blastedstudios.freeboot.ai.bt.actions.ForestInit.
*/
public ForestInit(jbt.model.core.ModelTask modelTask,
jbt.execution.core.BTExecutor executor,
jbt.execution.core.ExecutionTask parent) {
super(modelTask, executor, parent);
if (!(modelTask instanceof com.blastedstudios.freeboot.ai.bt.actions.ForestInit)) {
throw new java.lang.RuntimeException(
"The ModelTask must subclass com.blastedstudios.freeboot.ai.bt.actions.ForestInit");
}
}
protected void internalSpawn() {
this.getExecutor().requestInsertionIntoList(
jbt.execution.core.BTExecutor.BTExecutorList.TICKABLE, this);
Log.debug(this.getClass().getCanonicalName(), "spawned");
}
protected jbt.execution.core.ExecutionTask.Status internalTick() {
final NPC self = (NPC) getContext().getVariable(AIFieldEnum.SELF.name());
final WorldManager world = (WorldManager) getContext().getVariable(AIFieldEnum.WORLD.name());
INPCActionExecutor executor = new INPCActionExecutor() {
@Override public Status execute(String identifier) {
if(identifier.equals("lunge")){
float aimAngle = Being.getAimAngle(self, world.getPlayer());
Vector2 lungeForce = new Vector2((float)Math.cos(aimAngle), (float)Math.sin(aimAngle)).scl(
Properties.getFloat("ai.forest.lunge.magnitude", 180f));
self.aim(aimAngle);
self.getRagdoll().applyForceAtCenter(lungeForce.x, lungeForce.y);
self.getRagdoll().applyLinearImpulse(lungeForce.x, lungeForce.y,
self.getRagdoll().getPosition().x, self.getRagdoll().getPosition().y);
}
return Status.SUCCESS;
}
};
getContext().setVariable(INPCActionExecutor.EXECUTE_CONTEXT_NAME, executor);
return Status.SUCCESS;
}
protected void internalTerminate() {}
protected void restoreState(jbt.execution.core.ITaskState state) {}
protected jbt.execution.core.ITaskState storeState() {
return null;
}
protected jbt.execution.core.ITaskState storeTerminationState() {
return null;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,578
|
Use the links below to choose your desired storefront. Specific user instructions are located on the corrosponding pages.
Be ready for the season with stationery for all sports. Pony Up!
The one stop shop for all faculty and staff.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 5,493
|
{"url":"https:\/\/rpg.stackexchange.com\/questions\/113936\/if-you-shove-an-enemy-towards-another-player-in-your-party-would-that-player-be","text":"If you shove an enemy towards another player in your party, would that player be able to make an opportunity attack? [duplicate]\n\nI'm playing a way of the open hand Monk, I use flurry of blows and using a ki point I can opt to shove my target up to 15 ft.\n\nIf I pushed it to within 5ft of a fighter in my party, could they use their reaction to make an attack of opportunity? Or do opportunity attacks only occur when leaving a characters reach?\n\nOpportunity attacks are only when an enemy leaves your reach\n\nYou can make an opportunity attack when a hostile creature that you can see moves out of your reach.\n\nThe exception to this is if you have the feat polearm master:\n\nWhile you are wielding a glaive, halberd, pike, or quarterstaff, other creatures provoke an opportunity attack from you when they enter the reach you have with that weapon.\n\nA shove will never provoke an opportunity attack regardless\n\nEven polearm master won't let you take an opportunity attack against the shoved enemy since in order to qualify for an opportunity attack the enemy has to move using their action, reaction, or movement:\n\nYou also don\u2019t provoke an opportunity attack when you\u00a0Teleport\u00a0or when someone or something moves you without using your\u00a0Movement, action, or reaction.\n\nA shoved enemy is moved by your action and without using any of their actions or movement. So it will not provoke an opportunity attack.","date":"2019-10-23 13:27:36","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.17354944348335266, \"perplexity\": 3439.25926230734}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570987833766.94\/warc\/CC-MAIN-20191023122219-20191023145719-00362.warc.gz\"}"}
| null | null |
{"url":"http:\/\/dave.thehorners.com\/tech-talk\/random-tech\/382-setting-up-video-conferences","text":"Dave Horner's Website - Yet another perspective on things...\n76 guests\nRough Hits : 3819927\nhow did u find my site?\n\nour entire universe; minuscule spec in gigantic multiverse which is mostly lethal.\n\n\u201cIn mathematics you don\u2019t understand things. You just get used to them.\u201d\n\u2013John Von Neumann\n$$e = \\sum_{n=0}^\\infty \\frac{1}{n!}$$\n\n# Setting up video conferences\n\nThursday, 07 August 2008 22:02\nI'd really like to get some software together to make video conferencing easier. There are video sip clients out there, but most cost money....or are proprietary\/closed.\n\nVLC - videolan client\nVideoLAN - Free and Open Source software and video streaming solutions for every OS!\nVLC is a powerful tool when dealing with video. It provides streaming functions...so it could be used for network video broadcasts. You can use it to stream your webcam using RTP.\nVideoLAN Streaming Howto\nChapter 4. Examples for advanced use of VLC's stream output (transcoding, multiple streaming, etc...)","date":"2019-07-20 20:35:53","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.3024284839630127, \"perplexity\": 7339.819955062927}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-30\/segments\/1563195526670.1\/warc\/CC-MAIN-20190720194009-20190720220009-00260.warc.gz\"}"}
| null | null |
Glasgow Events forum . A place to talk about Glasgow events.
Anyone on the site see Roger Waters ?
What events are you going to in Glasgow tonight ?
Who on the site will be going ?
Are there any Stevie McCrorie fans on the site ?
Did anybody see Bruno Mars in Glasgow ?
Is anybody going to see Shania Twain ?
Did anybody see Michael Mcintyre ?
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,668
|
The winning team will join us for Our GTZ Catering Event on Saturday November 30th catered by EAT CLEAN BRO.
-Members can participate for FREE.
-First time Non-Members can participate in the full 6-week challenge for $99.
-The winning team will be chosen based off of THE MOST AMOUNT OF RECORDS HELD in various exercises and challenges.
PICK BY CLICKING YOUR TEAM BELOW!
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,660
|
ConfigStackWidget::ConfigStackWidget(QWidget *parent) :
QStackedWidget(parent),
ui(new Ui::ConfigStackWidget)
{
ui->setupUi(this);
addWidget(new MiningSettings);
addWidget(new SmeltingSettings);
addWidget(new PumpjackSettings);
addWidget(new RefinerySettings);
addWidget(new ChemistrySettings);
addWidget(new AssemblingSettings);
addWidget(new RocketrySettings);
}
ConfigStackWidget::~ConfigStackWidget()
{
delete ui;
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 96
|
Q: J2ME power(double, double) math function implementation I want to implement math function power to double, can you advice algorithm for this?
I've reviewed sources of Java ME Open Source Software - Math but I want to implement it from the scratch.
Thank you!
A: I don't know J2ME well enough to know, but do you have Math.log() and Math.exp() ?
Then you can simply use this relation:
x^y = exp(y * log(x))
If you don't have the aforementioned two functions, then you should start by implementing those. As far as I know, the above relation is the only reasonable way to compute x^y.
Update: I see the paper linked in kusman's answer shows an alternative way to do pow using the idea of a fractional exponent. Quite cool! But the paper also shows the "normal" way to do things via multiplication of the log, and shows you how to implement Taylor series for exp() and log().
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,566
|
Q: How do I read input .in files in command line on windows I completed my code but the problem is I don't know how to test it based on instructions given.
The instructor provided us with 3 input files with the following values:
file1: 33 20
file2: 5 7
file3: 18 15
I'm supposed to take these values and create event objects with these stored values. Problem is the instructor is giving the testing method on Ubuntu and she displayed how to input file in command line like:
./sApp < simulationShuffled3.in
So i'm just really confused as to how I'm suppose to get it working. I am currently using Windows console, VStudios and sublime text with a terminal attachment.
The code I'm currently using that's following from an example from my course notes is
while (getline(cin >> ws, aLine)) { // while (there is data)
stringstream ss(aLine);
ss >> arrivalTime >> processingTime;
Event newEvent = Event('A',arrivalTime,processingTime);
eventPriorityQueue.enqueue(newEvent);
}
A: Read input from stdin in Windows [&/or] Linux
You can do this in three ways:
*
*In Command prompt (windows)
*In Powershell (windows/linux)
*In WSL & Linux
1: in Windows Cmd
type input.in | python file_requiring_input.py # in python
type input.in | go run file_requiring_input.go # in go
type input.in | node file_requiring_input.js # in js
javac file_requiring_input.java &&
type input.in | java file_requiring_input # in java
g++ file_requiring_input.cpp &&
type input.in | a.exe # in cpp
gcc file_requiring_input.c &&
type input.in | a.exe # in c
Another way
python file_requiring_input.py < input.in # in python
g++ file_requiring_input.cpp &&
a.exe < input.in # in cpp
2: in Powershell
gc .\input.in | python file_requiring_input.py # in python
g++ .\file_requiring_input.cpp ;
gc .\input.in | .\a.exe # in cpp
gc is short for Get-Content. Other aliases of gc are cat and type.
which means that all three names can be used as replacement or gc
3: use wsl for windows //Linux commands
cat input.in | python file_requiring_input.py # in python
g++ file_requiring_input.cpp &&
cat input.in | ./a.out # in cpp
another way
python file_requiring_input.py < input.in # in python
g++ file_requiring_input.cpp &&
./a.out < input.in # in cpp
have edited the code testing everything out hopefully. Do correct me if I am wrong or if anything more is to be added .
Also input.in is more generally a text file so you can create input.txt file as you wish and it would work the same
A: Well, as this is an assignment, I'm not going to provide you with a ready-made code. Rather, I'll just point you to the right direction.
In Windows, you can provide the arguments to your executable separated by space on Command Prompt like this:
C:\Assignment> Test.exe file1.in file2.in file3.in
And, it'll work on Ubuntu as well.
So, you need to study Command Line Arguments, File Handling, reading from file; and, you'll have to convert these strings read from files to integers.
Command Line Arguments: http://en.cppreference.com/w/c/language/main_function
File Handling: http://en.cppreference.com/w/cpp/io/basic_fstream
Here's a minimal example for reading from a file (std::ifstream):
I've a test file at C:\Test\Test.txt with the following contents:
11 22
12 23
23 34
Here's is main.cpp to test it:
#include <iostream>
#include <fstream>
#include <string>
int main( int argc, char *argv[] )
{
const std::string filename { R"(C:\Test\Test.txt)" };
std::ifstream ifs { filename };
if ( !ifs.is_open() )
{
std::cerr << "Could not open file!" << std::endl;
return -1;
}
int arrivalTime { 0 };
int processingTime { 0 };
while ( ifs >> arrivalTime >> processingTime )
{
std::cout << "Arrival Time : " << arrivalTime << '\n'
<< "Processing Time : " << processingTime << std::endl;
}
ifs.close();
return 0;
}
Output:
Arrival Time : 11
Processing Time : 22
Arrival Time : 12
Processing Time : 23
Arrival Time : 23
Processing Time : 34
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,662
|
Q: Facebook like button: hide text I just added a Facebook like button to my website, just the most basic one, but you can't select to hide the "Sign Up to see what your friends like." text.
Because the area for the button is so small, I don't want this text, as it overlaps with other text next to it.
Is there a way to hide this part?
I basically just want the like button, with the same functionality.
A: You would have probably figured it out by now but for others who haven't and reach this question, try data-layout="button_count".
You can play around here for more options: https://developers.facebook.com/docs/reference/plugins/like/
A: You can add layout="simple" (XFBML), or "data-layout"="simple" for HTML5 to the tag.
That'll show just a like button, with no count, faces or nonsense :)
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"redpajama_set_name": "RedPajamaStackExchange"
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I've made a transaction between my 2 cards issued by different Financial institutions (Banks). I've confirmed the transaction amount in 3DS window. But the total amount was decreased on a fee volume. This fee was billed by a Bank whose card was used to transfer from.
Is it required by 3DS standard to inform a cardholder about the net transfer value = amount - fee? Didn't my Bank break some of regulations - it informed me only about the amount without fee?
Transfer from MasterCard to Visa. Both Debit Cards.
I've consulted the Bank's stuff, they give the fillowing answer: 3DS service is used for verification only, it knows nothing about Banks fees. Also the tranfer was made from InternetBank client of target card Bank. It also knows nothing about source Banks fees.
In this situation unfortunately there were not technical possibility to inform me about fees.
It seems like you were both the merchant and consumer in this transaction. This is generally against the terms of service for credit cards.
That aside, merchants always pay a percent of the transaction as a fee. It's how credit cards work.
Not the answer you're looking for? Browse other questions tagged banking online-banking online-payment russia or ask your own question.
How to find information about ethical banking?
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"redpajama_set_name": "RedPajamaC4"
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\section{Introduction}
Spacetimes that approximate de Sitter space (dS) form the basis of inflationary early universe cosmology and also give a rough description of our current universe. One expects this description to further improve in the future as the cosmological expansion dilutes the various forms of matter, and that in tens of Gyrs it will become quite good indeed. Yet certain classic issues in gravitational physics, such as the construction of phase spaces and conserved charges, are less well developed in the de Sitter context than for asymptotically flat or asymptotically AdS spacetimes; see e.g.
\cite{ADM,ReggeTeitelboim,HenneauxTeitelboimAsympAdS,BrownHenneauxCentralCharge,AshtekarCVPS,CovarPhaseSpace}.
While there have been many discussions of de Sitter charges (see
\cite{CCStability,Banados:1998tb,Park:1998qk,Strominger:2001pn,balasubramaniandS,Shiromizu:2001bg,KastorCKV,JagerPhD,LuoPositiveMass,StromingerASG}) over a broad span of time,
most of these \cite{CCStability,Banados:1998tb,Park:1998qk,Strominger:2001pn,balasubramaniandS,JagerPhD,StromingerASG} do not construct a phase space in which the charges generate the associated diffeomorphisms while the remainder \cite{Shiromizu:2001bg,KastorCKV,LuoPositiveMass} define phase spaces in which many of the expected charges diverge. In particular, since~\cite{Strominger:2001pn,balasubramaniandS,JagerPhD,StromingerASG} fix the induced metric on future infinity the symplectic structure necessarily vanishes. We shall impose no such condition here.
This hole in the literature is presumably due, at least in part, to the fact that global de Sitter space admits a compact Cauchy surface of topology $S^{d-1}$. It is thus natural to define a phase space (which we call the $k=+1$ phase space, $\Gamma({\textrm{dS}_{k=+1}})$) which contains {\it all} solutions with an $S^{d-1}$ Cauchy surface. Since $S^{d-1}$ is compact, there is no need to impose further boundary conditions. The constraints then imply that all gravitational charges vanish identically. All diffeomorphisms are gauge symmetries and the asymptotic symmetry group is trivial.
On the other hand, it is natural in cosmological contexts to consider pieces of de Sitter space which may be foliated by either flat ($k=0$) or hyperbolic ($k=-1$) Cauchy surfaces. We call these patches $\dS$ and $\dSh$ respectively, see Figs.~\ref{conformalDiagram}, \ref{conformalDiagramHyp}. These Cauchy surfaces are non-compact, and boundary conditions are required in the resulting asymptotic regions. The purpose of this paper is to construct associated phase spaces (for both $k=0,-1$) of asymptotically de Sitter solutions in $d \ge 3$ spacetime dimensions for which the expected charges are finite and conserved.
As there are claims \cite{Kleppe:1993fz,Miao:2009hb,Miao:2010vs,Miao:2011fc,Miao:2011ng,Kahya:2011sy} in the literature that the so-called `dilatation symmetry' of the $k=0$ patch is broken at the quantum level (though see \cite{Allen:1986ta,Allen:1986dd,Allen:1986tt,Higuchi:1986py,Higuchi:1991tn,Higuchi:1991tk,Higuchi:2000ye,Higuchi:2001uv,Higuchi:2011vw}), it is particularly important to verify that this is indeed a symmetry of an appropriate classical gravitational phase space for $k=0$.
In most cases below the resulting asymptotic symmetry group (ASG) is the isometry group of the associated (flat- or hyperbolic-sliced) patch of dS, though for $k=-1$ and $d=3$ we find that the obvious rotational symmetry is enlarged to a (single) Virasoro algebra in the ASG. The structure is somewhat similar to that recently seen in the Kerr/CFT context \cite{Guica:2008mu,Bredberg:2011hp}, though in our present case the central charge vanishes due to a reflection symmetry in the angular direction. We also identify an interesting algebra somewhat larger than the ASG which contains two Virasoro algebras related by a reality condition and having imaginary central charges (in agreement with \cite{Fjelstad:2002wf,Balasubramanian:2002zh,Maldacena:2002vr,Ouyang:2011fs}). We note, however, that the extra generators (outside the ASG) have incomplete flows on our classical phase space. Thus real classical charges of this sort will not lead to self-adjoint operators at the quantum level.
We construct the phase spaces $\CVPS$ and $\CVPSh$ associated with $\dS$ and $\dSh$ below in sections \ref{k=0} and \ref{k=-1}. In each case, we find that our final expressions agree with the relevant charges of \cite{Strominger:2001pn,balasubramaniandS,StromingerASG}\footnote{We expect the same to be true of \cite {Banados:1998tb,Park:1998qk}. However, the fact that \cite{Banados:1998tb,Park:1998qk} used a Chern-Simons formulation makes direct comparison non-trivial; we will not attempt it here. We also make no direct comparison with ref. \cite{CCStability}, which worked perturbatively around dS, though we again expect agreement in the appropriate regime.}. This agreement provides a sense in which those charges generate canonical transformations on a well-defined phase space.
The case $d=3, k=-1$ merits special treatment. Despite the lack of local degrees of freedom, section \ref{wormholes} shows the phase space to be non-trivial due to a class of de Sitter wormholes. These solutions are $\Lambda > 0$ analogues of BTZ black holes and exhibit a corresponding mass gap. We close with some final discussion in section \ref{disc} which in particular compares our phase space with those of \cite{Shiromizu:2001bg,KastorCKV,LuoPositiveMass}.
\begin{figure}
\includegraphics[width=4.5in]{Figure1.pdf}
\caption{A conformal diagram of dS${}_d$. The region above the diagonal line is the $k=0$ cosmological patch. Each point represents an $S^{d-2}$. Our boundary conditions are applied at the $S^{d-2}$ labeled $i^0$, which we call spatial infinity. The dashed line shows a representative $(t= {\rm constant})$ slice.}
\label{conformalDiagram}
\end{figure}
\section{The phase space $\CVPS$}
\label{k=0}
Our first phase space
will consist of spacetimes asymptotic to the expanding spatially-flat ($k=0$) patch of de Sitter space (see figure \ref{conformalDiagram}) in $d\ge 3$ spacetime dimensions for which the metric takes the familiar form
\begin{equation}
\label{k=0dS}
ds^2 = - dt^2 + e^{2t/\ell} \delta_{ij} dx^i dx^j.
\end{equation}
Here $\delta_{ij}$ is a Kroenecker delta and $i,j$ range over the $d-1$ spatial coordinates.
We will refer to this patch as $\dS$ and the corresponding phase space as $\CVPS$. For future reference we note that the symmetries of $\dS$ are generated by three types of Killing fields (dilations, translations, and rotations) which take the following forms
\begin{eqnarray}
\label{k=0KVFs}
{\rm Dilations:} & \xi_D^a & = (\partial_t)^a - x^a/\ell ,\cr
{\rm Translations:} & \xi_{P^i}^a & = (\partial_i)^a, \cr
{\rm Rotations:} & \xi_{L^{ij}}^a & = (2x_{[i}\partial_{j]})^a.
\end{eqnarray}
Elements of our phase space are globally hyperbolic solutions to the Einstein equation in $d\ge3$ spacetime dimensions with positive cosmological constant
\begin{eqnarray}
\Lambda = \frac{(d-1)(d-2)}{2\ell^2}
\end{eqnarray}
and topology ${\mathbb R}^d.$ Introducing a time-function $t$ defines a foliation of ($t={\rm constant}$) spacelike slices $\Sigma$. Choosing coordinates $x^i \in {\mathbb R}^{d-1}$ on each slice, the metric may then be written in the form
\begin{eqnarray}
ds^2 = -N^2 dt^2 + h_{ij} (dx^i + N^i dt)(dx^j + N^j dt). \label{dSmetric}
\end{eqnarray}
We define $\CVPS$ to contain such spacetimes for which, on any $t = (\textrm{constant})$ slice $\Sigma$, the induced metric $h_{ij}$, the canonical momentum $\tilde{\pi}^{ij} = \sqrt{h} \pi^{ij}$, the lapse $N$, and the shift $N^i$ satisfy the boundary conditions\footnote{A study of the symplectic structure (eq. \eqref{SymplecticStructure} below) indicates that these boundary conditions can be significantly relaxed, presumably allowing radiation that falls off more slowly at large $r$. However, doing so requires non-trivial use of the equations of motion to make explicit the fact that the charges associated with \eqref{k=0KVFs} are finite. We have not attempted to complete such an analysis as we see no obvious advantage to weakening the boundary conditions \eqref{BoundaryConditions}.}
\begin{align} \label{BoundaryConditions}
\Delta h_{ij} &= h_{ij}^{(d-1)} + \order{r}{-(d-1+\epsilon)}, \cr
\Delta{\pi}^{ij} &= \pi^{ij}_{(d-2)} + \pi^{ij}_{(d-1)} + \order{r}{-(d-1+\epsilon)} \cr
N &= 1+ N^{(d-2)} + \order{r}{-(d-1)} \cr
N^i &= N^i_{(d-3)} + \order{r}{-(d-2)},
\end{align}
at large $r = \sqrt{\delta_{ij} x^i x^j}$, with
\begin{subequations}
\label{subh}
\begin{align}
h_{ij}^{(d-1)} = \frac{(\textrm{Any function of $\Omega$})_{ij}}{r^{d-1}}, \ \ & \\
\pi^{ij}_{(d-2)} = \frac{(\textrm{Odd function of $\Omega$})^{ij}}{r^{d-2}}, \ \ & \ \
\pi^{ij}_{(d-1)} = \frac{(\textrm{Any function of $\Omega$})^{ij}}{r^{d-1}} \\
N^{(d-2)} = \frac{(\textrm{Odd function of $\Omega$})}{r^{d-2}}, \ \ & \ \ N^i_{(d-3)} = \frac{(\textrm{Even function of $\Omega$})^i}{r^{d-3}}
\end{align}
\end{subequations}
where ${\Omega}$ denotes a set of angular coordinates on $r=(\textrm{constant})$ slices and where
\begin{align} \label{Deltahandpi}
\Delta h_{ij} = h_{ij} - e^{2t/\ell}\delta_{ij} = h_{ij} - \bar{h}_{ij}, \ \ \ \
\Delta \pi^{ij} = \pi^{ij} + \frac{(d-2) }{\ell}e^{-2 t/\ell}\delta^{ij} = \pi^{ij} - \bar{\pi}^{ij},
\end{align}
where $\bar{h}_{ij}$ and $\bar{\pi}^{ij}$ are the induced metric and momentum associated with~\eqref{k=0dS} (in general overbars will denote quantities associated with~\eqref{k=0dS}). We emphasize that, since the above conditions restrict the behavior only in the limit $r \rightarrow \infty$, they in no way restrict the induced (conformal) metric on future infinity at any finite $r$.
In order for time evolution to preserve~\eqref{BoundaryConditions} the lapse, shift and momentum must satisfy the additional relation
\begin{align} \label{lapseshiftcondition}
\pi_{ij}^{(d-2)} + \partial_{(i} N_{j)}^{(d-3)} + N^{(d-2)} \frac{\bar h_{ij}}{\ell} = 0.
\end{align}
This final condition was obtained by writing the equations of motion to leading order, imposing~\eqref{BoundaryConditions} and requiring that $\dot h^{(d-2)}_{ij}=0$ (no further condition is required to make $\dot \pi_{(d-2)}^{ij}$ odd). In all of the explicit examples we consider below this condition is satisfied trivially. We also assume that the $n$th derivative of the $\order{r}{-(d-1+\epsilon)}$ term in \eqref{BoundaryConditions} is $\order{r}{-(d-1+n+\epsilon)}$.
The definitions~\eqref{Deltahandpi} were chosen so that $\Delta h_{ij} = 0 = \Delta{\pi}^{ij}$ for exact de Sitter (Eq.~\eqref{k=0dS}). We also note that~\eqref{BoundaryConditions} together with the constraints~\eqref{constraints}, ensures that
\begin{align} \label{pitildeBC}
\Delta{\tilde\pi}^{ij} &= \frac{(\textrm{Odd function of $\Omega$})^{ij}}{r^{d-2}} + \mathcal{O}\left(r^{-(d-1)}\right),
\end{align}
with
\begin{align}
\Delta{\tilde\pi}^{ij} = \sqrt{h}\pi^{ij} - \sqrt{\bar h} \bar\pi^{ij}.
\end{align}
Let us now consider two tangent vectors $(\delta_1 h_{ij},\delta_1\tilde{\pi}^{ij})$ and $(\delta_2 h_{ij},\delta_2\tilde{\pi}^{ij})$ to $\CVPS$. In order for our phase space to be well defined we must show the symplectic product of these two tangent vectors to be finite and independent of the Cauchy surface on which it is evaluated, i.e. independent of $t$.
Our boundary conditions suffice to guarantee both of these conditions. Equations~\eqref{BoundaryConditions} and~\eqref{pitildeBC} imply convergence of the standard expression
\begin{eqnarray}
\omega(\delta_1 g,\delta_2 g) = \frac{1}{4\kappa} \int_\Sigma \left(\delta_1 h_{ij}\delta_2\tilde{\pi}^{ij} - \delta_2 h_{ij}\delta_1\tilde{\pi}^{ij}\right) \label{SymplecticStructure}
\end{eqnarray}
for the symplectic product (see e.g. \cite{PalmerSymplecticForm}). Furthermore, we will show in section \ref{CC} below that the (time-depenedent) Hamiltonian $H(\partial_t)$ (see~\eqref{Hz}) defined by some $N,N^i$ satisfying \eqref{BoundaryConditions} i) has well-defined variations and ii) generates an evolution that preserves the boundary conditions \eqref{BoundaryConditions} on $h_{ij}$ and $\tilde \pi^{ij}$. This in turn guarantees that $\omega(\delta_1 g,\delta_2 g)$ is time independent.\footnote{A finite well-defined Hamiltonian that preserves the phases space ensures that the Poisson bracket is conserved. Since the symplectic product is the inverse of the Poisson structure, it too must be conserved.\label{symfoot}}
Thus, we conclude that $\CVPS$ is well-defined. Below we compute asymptotic symmetries and conserved charges, largely following the approach of~\cite{ReggeTeitelboim,HenneauxTeitelboimAsympAdS,BrownHenneauxCentralCharge}.
\subsection{Asymptotic Symmetries}
We begin by using the fact that linearized diffeomorphisms generated by any element of our ASG must map~\eqref{k=0dS} onto a solution satisfying~\eqref{BoundaryConditions}. Consider the metric $\bar h_{ij}$ induced on a $t=(\textrm{constant})$ slice of~\eqref{k=0dS} and its pullback into the bulk spacetime which we call $\bar h_{ab}$. We also introduce $h^a_i$ which is the projector from the spacetime onto $\Sigma$. If $\xi$ is in our ASG then
\begin{eqnarray}
\delta_\xi \bar h_{ij} &\equiv& h^a_i h^b_j \pounds_\xi \bar h_{ab} \cr
&=& h^a_i h^b_j \left[\xi^c \bar\nabla_c (\bar h_{ab}) + 2 \bar h_{c(a}\bar\nabla_{b)} \xi^{c}\right] \cr
&=& 2 h^a_i h^b_j \bar\nabla_{(a} \xi_{b)} , \label{deltazetah}
\end{eqnarray}
must vanish as $r\rightarrow\infty$ fast enough so that $\bar h_{ij} + \delta_\xi \bar h_{ij}$ satisfies~\eqref{BoundaryConditions}. So, up to terms which vanish at $r\rightarrow\infty$, $\xi$ must satisfy
\begin{align}
\label{ckvf}
\partial_{(i} \vec\xi_{j)} = \frac{\xi_\perp e^{2t/\ell}}{\ell}\delta_{ij},
\end{align}
where we have defined the tangential and normal parts $\xi_\perp, \vec \xi^a$ to $\Sigma$ via the decomposition
\begin{equation}
\label{parts}
\xi^a = \xi_\perp n^a + \vec\xi^a.
\end{equation}
Note that \eqref{ckvf} is the conformal Killing equation for vectors $\vec\xi^i$ in Euclidean $\mathbb{R}^{d-1}$ with confromal factor $\xi_\perp e^{2t/\ell}/\ell$.
We wish to discard solutions to this equation which are either pure gauge ($\omega(\pounds_\xi g,\delta g)=0$) or do not preserve our boundary conditions. It is shown at the end of appendix \ref{finiteQ} that if $\xi$ vanishes as $r\rightarrow\infty$ then $\omega(\pounds_\xi g,\delta g)=0$. For $d>3$ the remaining solutions are the conformal group of $\mathbb{R}^{d-1}$. We find using~\eqref{LieDhpi} that our boundary conditions \eqref{BoundaryConditions} are not invariant under special conformal transformations\footnote{Specfically, acting on the Schwarzschild de Sitter solution \eqref{SdS2} below twice with a Lie derivative along the generator of special conformal transformations gives a term which violates our boundary conditions.}. Excluding such transformations leaves a group isomorphic to the isometries of $\dS$ (see \eqref{k=0KVFs}).
Due to the infinite-dimensional conformal group of the plane there are additional solutions to \eqref{ckvf} for $d=3$, each of which can be described by a potential satisfying Laplace's equation. Expanding this potential in sperical harmonics we obtain a set of symmetries which fall off with various powers of $r$. Vector fields with terms of order $r^2$ or higher violate our boundary conditions while those of order $r^{-1}$ or lower are pure gauge because they vanish at infinity. What remains are four vector fields (two of order $r^1$, two of order $r^0$) corresponding to the four isometries of $\dS$ for $d=3$.
We now show that our phase space is closed under the action of the expected symmetry group~\eqref{k=0KVFs}. To do so, we consider an arbitrary solution $(h_{ij},\tilde \pi^{ij})$ satisfying~\eqref{BoundaryConditions} and show that $(h_{ij} + \delta_\xi h_{ij},\tilde \pi^{ij} + \delta_\xi \tilde \pi^{ij})$ also satisfies~\eqref{BoundaryConditions} where $\xi$ is one of the vector fields~\eqref{k=0KVFs}.
First consider a purely spatial vector $\xi$, i.e. a translation or rotation. From the expressions
\begin{eqnarray}
\pounds_{\xi}h_{ij} &=& \vec\xi^k \partial_k \Delta h_{ij} + 2 \Delta h_{k(i} \partial_{j)} \vec\xi^k \cr
\pounds_{\xi}{\pi}^{ij} &=& \vec\xi^k \partial_k \Delta\pi^{ij} -2 \Delta \pi^{k(i} \partial_k \vec\xi^{j)}, \label{LieDhpi}
\end{eqnarray}
we can see that our boundary conditions are preserved by diffeomorphisms along these vector fields.
To see that $\xi_D$ preserves our boundary conditions note that
\begin{align}
\pounds_{\xi_D} = \pounds_{t} - \pounds_{x/\ell}.
\end{align}
Together with the canonical equations of motion, the boundary conditions \eqref{BoundaryConditions} and \eqref{lapseshiftcondition} ensure that $\pounds_{t}$ preserves $\CVPS$, and it is straightforward to verify that $\pounds_{x/\ell}$ does as well using~\eqref{LieDhpi}. Thus, our boundary conditions are also preserved by $\xi_D$. This completes our proof that the asymptotic symmetry group of $\CVPS$ is given by the isometries of $\dS$.
\subsection{Conserved Charges}
\label{CC}
Our next task is to construct a corresponding set of conserved charges.
As described by Regge and Teitelboim~\cite{ReggeTeitelboim}, the fact that any such charge $H(\xi)$ must generate diffeomorphisms along $\xi$ implies that $H(\xi)$ is a linear combination of the gravitational constraints determined by the relevant vector field $\xi$, together with certain surface terms chosen to ensure that the charges have well-defined variations with respect to $h_{ij}$ and $\tilde \pi^{ij}$. So long as the boundary conditions are sufficiently strong, the result takes the standard form
\begin{align}
H(\xi) &= \frac{1}{2\kappa} \int_\Sigma \sqrt{h} \left(\xi_\perp {\cal H} + \vec \xi^i {\cal H}_i \right) + \frac{1}{\kappa} \int_{\partial\Sigma} (dr)_i \vec \xi^j \left(\Delta\tilde\pi^{ik} h_{kj} + \tilde\pi^{ik} \Delta h_{kj} - \frac{\tilde\pi^{kl}\Delta h_{kl} }{2}{\delta^i}_j \right) \nonumber \\
&+ \frac{1}{2\kappa}\int_{\partial\Sigma} \sqrt{\sigma} \hat{r}_l G^{ijkl} \left(\xi_\perp D_k \Delta h_{ij} - \Delta h_{ij} D_k \xi_\perp\right), \label{Hz}
\end{align}
in terms of the Hamiltonian and momentum constraints
\begin{eqnarray}
\label{constraints}
{\cal H} &=& h^{-1} \left(\tilde{\pi}_{ij} \tilde{\pi}^{ij} - \frac{1}{d-2} \tilde{\pi}^2\right) -(\mathcal{R}-2\Lambda) , \cr
{\cal H}^i &=& - h^{-1/2} D_j (2 \tilde{\pi}^{ij}).
\end{eqnarray}
In \eqref{Hz},
\begin{align}
G^{ijkl} &= h^{i(k}h^{l)j} - h^{ij}h^{kl},
\end{align}
$\kappa = 8\pi G$, $\partial\Sigma$ is the limit of constant $r = \sqrt{\delta_{ij}x^i x^j}$ submanifolds in $\Sigma$ as $r\rightarrow\infty$, and $\sigma_{ij}$ and $\hat{r}^i$ are the induced metric on and the unit normal (in $\Sigma$) to $\partial\Sigma$.
The boundary conditions are strong enough for (\ref{Hz}) to hold when general variations of the above boundary terms can be computed by varying only
$\Delta h_{ij}$ and $\Delta \tilde \pi^{ij}$; i.e., all other terms in the general variation are too small to contribute in the $r \rightarrow \infty$ limit. Power counting shows that this is indeed implied by eqs. \eqref{BoundaryConditions}.
Now, naive power counting suggests that~\eqref{Hz} may diverge. But since~\eqref{BoundaryConditions} ensures that the symplectic structure is finite, the equations of motion must conspire to prevent these divergences. This fact is verified in appendix \ref{finiteQ}. We define
\begin{equation}
\label{Qk=0}
Q_D := H(-\xi_D), \ \ \ P^j := H(\xi_{P^j}), \ \ \ L^{jk} := H(\xi_{L^{jk}}).
\end{equation}
Note that in defining $Q_D$ we chose signs that would conventionally appear in the definition of an `energy,' while we defined $P^j$ and $L^{jk}$ with signs conventionally chosen in defining momenta. Interestingly, this choice of signs makes $Q_D$ negative for the de Sitter-Schwarzschild solution in agreement with \cite{balasubramaniandS}.
We may also consider a general Hamiltonian $H(\partial_t)$ for $\partial_t$ defined by lapse and shift of the form \eqref{BoundaryConditions}. Power counting and the boundary conditions~\eqref{BoundaryConditions} ensure that $H(\partial_t)$ is finite and that it has well-defined variations. The boundary conditions~\eqref{BoundaryConditions} and~\eqref{lapseshiftcondition} ensure that it generates an evolution which preserves the boundary conditions on $h_{ij}, \tilde \pi^{ij}$ and thus, as noted in footnote \ref{symfoot}, that the symplectic structure is conserved. It follows that the above charges are conserved as well.
In appendix~\ref{finiteQ} we explicitly show that that the conserved quantities~\eqref{Qk=0} are finite, and that with the boundary conditions~\eqref{BoundaryConditions} they take the following simple forms:
\begin{subequations} \label{Hk=0}
\begin{eqnarray}
Q_D &=& \frac{1}{\kappa}\int_{\partial\Sigma} \sqrt{\sigma} \frac{ \hat{r}_i \Delta^\prime \pi^{ij} x_j}{\ell} , \label{HDilatation} \\
P^j &=& \frac{1}{\kappa} \int_{\partial \Sigma} \sqrt{\sigma} \hat{r}_i \Delta^\prime \pi^{ij} , \label{Pi} \\
L^{jk} &=& \frac{1}{\kappa} \int_{\partial \Sigma} \sqrt{\sigma} \hat{r}_i 2\Delta^\prime \pi^{i[k} x^{j]}, \label{Li}
\end{eqnarray}
\end{subequations}
where
\begin{align}
\Delta^\prime \pi^{ij} = \pi^{ij} + \frac{d-2}{\ell} h^{ij}.
\end{align}
\subsection{Familiar Examples}
\label{FE}
We now consider some familiar spacetimes in order
to provide further intuition for the constructions above. In particular, for $d \ge 4$ we find coordinates in which our phase space contains the de-Sitter Schwarzschild solution and we compute the relevant charges. For $d=3$ we consider instead the spinning conical defect spacetimes, which describe gravity coupled to compactly supported matter fields.
In familiar static coordinates the $d \ge 4$ de Sitter-Schwarzschild solution takes the form
\begin{eqnarray}
ds^2 &=& - f(\rho) d\tau^2 + \frac{d\rho^2}{f(\rho)} + \rho^2 d\Omega^2 \label{dSschwarzMetric} \\
f(\rho) &=& 1-\frac{2GM}{\rho^{d-3}}-\frac{\rho^2}{\ell^2}.
\end{eqnarray}
In the region $\rho > \ell$ we introduce the coordinates $(t,\{x^i\})$ through the implicit expressions
\begin{subequations} \label{coordTrans}
\begin{eqnarray}
\tau &=& t + \int^\rho_\ell d\rho^\prime \frac{\sqrt{1-f(\rho^\prime)}}{f(\rho^\prime)} \\
\rho &=& e^{t/\ell}\sqrt{\sum_i (x^i)^2},
\end{eqnarray}
\end{subequations}
with the angular variables being related to $\{x^i\}$ in the usual way. After this change of coordinates \eqref{dSschwarzMetric} becomes
\begin{eqnarray}
\label{SdS2}
ds^2 = -dt^2 + e^{2t/\ell}\delta_{ij} \left(dx^i - \frac{ GM\ell x^i}{(e^{t/\ell}r)^{d-1}} dt \right) \left(dx^j - \frac{ GM\ell x^j}{(e^{t/\ell} r)^{d-1}} dt \right) + \mathcal{O}(r^{-(2d-3)}),
\end{eqnarray}
for $r \gg \ell e^{-t/\ell}$. As a result, we find
\begin{subequations} \label{dsSchwarzhandpi}
\begin{eqnarray}
\Delta h_{ij} &=& \mathcal{O}\left(r^{-(2d-3)}\right) \\
\Delta \pi^{ij} &=& \frac{e^{-2t/\ell} GM\ell }{(e^{t/\ell}r)^{d-1}} \left(\delta^{ij} - (d-1)\frac{x^i x^j}{r^2}\right) + \mathcal{O}\left(r^{-(2d-3)}\right).
\end{eqnarray}
\end{subequations}
Comparison with \eqref{BoundaryConditions} shows that \eqref{SdS2} does indeed lie in the phase space $\CVPS$.
The linear and angular momenta for this solution vanish by symmetry. Using~\eqref{HDilatation} to calculate the dilation charge yields
\begin{eqnarray}
\label{QDSdS}
Q_D &=& -\frac{(d-2)}{\kappa}GM \int_{\partial\Sigma} \sqrt{\gamma} d^{d-2}\theta \\
&=& -\frac{(d-2)\pi^{(d-3)/2}}{4\Gamma[(d-1)/2]}M,
\end{eqnarray}
where $\gamma$ is the determinant of the metric on the unit $S^{d-2}$ (so that the volume element on $S^{d-2}$ is $\sqrt{\gamma} d^{d-2}\theta$). In particular, we find $Q_D = -M$ for $d=4$ and $Q_D = -(3\pi/4) M$ for $d=5$. Up to a shift of the zero point of the energy for $d=5$ these results agree with the charges computed in \cite{balasubramaniandS} using a rather different approach (which did not involve constructing a phase space). We will show in section \ref{compare} below that this agreement holds more generally\footnote{ Because the counter-terms required by \cite{balasubramaniandS} proliferate in higher dimensions, section \ref{compare} considers only the cases $d=3,4,5$. We expect similar results for higher dimensions. The charges of \cite{Strominger:2001pn} also differ by an overall sign. }.
We now turn to the $d=3$ spinning conical defect solution \cite{Deser:1983nh} with defect angle $\theta_d$, which may be written in the form (see e.g. \cite{balasubramaniandS})
\begin{align}
ds^2 &= -f(\rho) d\tau^2 + \frac{d\rho^2}{f(\rho)} + \rho^2\left( \frac{8GMa}{2\rho^2} d\tau + d\phi\right)^2 \cr
f(\rho) &= 1 - 8GM - \frac{\rho^2}{\ell^2} + \frac{(8GMa)^2}{4\rho^2}, \label{ConicalDefect}
\end{align}
where the parameter $M=\theta_d/8\pi G$ is the mass that would be assigned to a conical defect in flat space with defect angle $\theta_d$~\cite{Deser:1983tn,Henneaux:1984ei}.\footnote{Our conventions are related to those of~\cite{balasubramaniandS} by $M\Rightarrow 1/8G - m$ and $aM \Rightarrow -J$.} After changing to the coordinates $(t,r)$ defined by
\begin{align}
\tau &= t - \frac{\ell}{2}\log \left(\frac{e^{2t/\ell} r^2}{\ell^2} - 1\right) \\
\rho &= e^{t/\ell} r,
\end{align}
we find $\Delta h_{ij}, \Delta \pi^{ij}\sim \order{r}{-2}$ so that the transformed solution lies in $\CVPS$, though $h^{(2)}_{ij} \neq0$. The non-vanishing results from \eqref{Hz} are $Q_D = -M$ and $L^{12}= aM$, in agreement with~\cite{balasubramaniandS} up to the expected shift in the zero point of $Q_D$ and in agreement with flat space results in the (here trivial) limit $\ell\rightarrow\infty$.
\subsection{Comparison with Brown-York methods at future infinity}
\label{compare}
Our discussion above closely followed the classic treatment of \cite{ReggeTeitelboim}. In contrast, refs. \cite{Strominger:2001pn,balasubramaniandS} took a rather different approach to the construction of charges in de Sitter gravity. They considered spacetimes for which the induced metric on {\it future} infinity $I^+$ (defined by a conformal compactification associated with a given foliation near $I^+$) agrees with some fixed metric $q_{ij}$.\footnote{In~\cite{balasubramaniandS} $q_{ij}$ is the flat metric, however one may clearly extend their results to allow non-flat $q_{ij}$ using a construction along the lines of~\cite{Henningson:1998gx}. Such a construction would involve adding logarithmically divergent terms to~\eqref{BYCounterterm} for $d=3$ and $d=5$. \label{logtermsFN}}
They then constructed an action $S$ for gravity subject to this Dirichlet-like boundary condition, choosing the boundary terms at future infinity so that variations of the action are well-defined. By analogy with the Brown-York stress tensor of \cite{BrownYork} (and with the anti-de Sitter case \cite{Henningson:1998gx,balasubramanianStressTensor}), refs. \cite{Strominger:2001pn,balasubramaniandS} defined a de Sitter `stress-tensor' $\tau^{ij}$ on a $t=(\textrm{constant})$ slice (with the intention of eventually taking $t\rightarrow\infty$) through
\begin{eqnarray}
\label{BYST}
\tau^{ij} = \frac{2}{\sqrt{h}} \frac{\delta S}{\delta h_{ij}} = \frac{\pi^{ij}}{\kappa} + \tau^{ij}_{ct},
\end{eqnarray}
where the first term results from varying the Einstein-Hilbert action with a Gibbons-Hawking-like boundary term $1/\kappa \int_{I^+} \sqrt{q} K $ and $\tau^{ij}_{ct}$ is the result of varying so-called counter-terms added to the action. Given a Killing field $\xi^i$ of $q_{ij}$ and any $d-2$ surface $B$ in $I^+$, \cite{Strominger:2001pn,balasubramaniandS} then define a charge
\begin{eqnarray}
Q_\xi(B) &=& \lim_{t\rightarrow\infty} \int_{B_t} \sqrt{\sigma} \left(\hat{b}_i \tau^{ij} \xi_j\right), \label{BYCharge}
\end{eqnarray}
where $\hat{b}^i$ and $\sqrt{\sigma}$ are the unit normal to and induced volume element on $B_t$ and $B_t$ is a $d-2$ surface on a constant $t$ slice that approaches $B$ as $t\rightarrow\infty$. Since $\xi^i$ is a Killing field of $q_{ij}$, the charge is in fact independent of $B$. For even $d$ one can show that $\tau^{ij}$ is traceless so that this $B$-independence also holds when this definition of charge is extended to conformal Killing fields $\xi^i$.
Because $q_{ij}$ is fixed, these boundary conditions force the symplectic flux through $I^+$ to vanish. So long as all other boundary conditions (e.g., at $r = \infty$) enforce conservation of symplectic flux, it follows immediately that this flux also vanishes on any Cauchy surface. As a result, the class of spacetimes for which $S$ is a valid variational principle does not form a phase space (though see \cite{Anninos:2011jp} for further discussion). On the other hand, as shown in \cite{StromingerASG}, the charges \eqref{BYCharge} agree with a natural construction that does not require the condition of fixed $q_{ij}$, but which is instead given by the covariant phase space prescription used by Wald and Zoupas \cite{Wald:1999wa} to define charges for the Bondi-Metzner-Sachs group in asymptotically flat space \cite{Bondi:1962px,Sachs:1962wk,Sachs:1962zza,Penrose:1962ij}.\footnote{This makes it clear that the charges of \cite{JagerPhD} also agree. These charges were constructed using Noether charge methods with fixed $q_{ij}$.} In this context, one takes $\xi^i$ above to be an arbitrary vector field on $I^+$ (and one generally expects $Q_\xi(B)$ to depend on $B$). Though it is not immediately clear in what sense such charges generate symmetries, this fact nevertheless suggests that the charges \eqref{BYCharge} are of interest even when $q^{ij}$ is not fixed. This is also suggested by the formal analogy with anti-de Sitter space.
In any case, we saw earlier that when $B$ is taken to be $i^0$ (as defined by figure \ref{conformalDiagram}) for $k=0$, $q_{ij}$ is taken to be the metric on the surface $t=\infty$, and $\xi^a$ is a generator of asymptotic symmetries for $\CVPS$, the charges \eqref{BYCharge} coincide with ours (up to a shift of the zero of energy) for the particular cases of $d=4,5$ de Sitter-Schwarzschild and the $d=3$ spinning conical defect in appropriate coordinates. It might seem natural to suppose that this equivalence extends to all of $\CVPS$. Such a correspondence is plausible since near $i^0$ the boundary conditions for $\CVPS$ require the spacetime to approach exact de Sitter space and the induced metric on $I^+$ becomes approximately fixed. We show below that in $d=3,4,5$ for generators of our asymptotic symmetries the charges \eqref{BYCharge} actually yield precisely \eqref{HDilatation}, \eqref{Pi}, \eqref{Li} (up to a possible shift of the zero points). They thus agree with our charges.
We wish to take $B$ to lie at $i^0$, which we will think of as the boundary $\partial \Sigma_\infty$ of the surface $\Sigma_\infty$ on which $t =\infty$. The unit normal to $\partial \Sigma_\infty$ in $\Sigma_\infty$ is thus $\hat b^i = \hat r^i$. We use the fact that, since any asymptotic symmetry $\xi^a$ preserves $I^+$, it defines a vector field $\xi^i_{I^+}$ on $I^+$. In fact, this $\xi^i_{I^+}$ is just the $t \rightarrow \infty$ limit of the part $\vec \xi^i$ of $\xi^a$ tangent to $\Sigma$ as defined by \eqref{parts}. We therefore use the notation $\vec \xi^i$ for this vector field below. It will further be useful to decompose $\vec \xi^i$ into parts normal and tangent to $\partial \Sigma_{\infty}$ according to
\begin{equation}
\label{2ndparts}
\vec \xi^i = \vec \xi_\perp \hat r^i + \vec {\vec \xi}^i.
\end{equation}
To compute the counter-term charges we recall from \cite{Strominger:2001pn,balasubramaniandS} that for $d=3, 4, 5$, (see footnote~\ref{logtermsFN})
\begin{eqnarray} \label{BYCounterterm}
\tau^{ij}_{CT} = \frac{1}{\kappa}\left(\frac{(d-2)h^{ij}}{\ell} + \frac{\ell}{d-3} \mathcal{G}^{ij} \right),
\end{eqnarray}
where $\mathcal{G}^{ij}$ is the Einstein tensor of $\Sigma_\infty$ and the $\mathcal{G}^{ij}$ term does not appear for $d=3$. It is then clear that first term in \eqref{BYCounterterm} combines nicely with the explicit $\pi^{ij}$ term in \eqref{BYST} to give a term involving $\Delta^\prime \pi^{ij}$; i.e., this piece of the counterterm cancels the contribution from the pure $\dS$ background. For $d=3$ we then see that
\eqref{BYCharge} precisely reproduces ~\eqref{HDilatation},~\eqref{Pi}, and~\eqref{Li}, and the same would be true for $d=4,5$ if the $\mathcal{G}^{ij}$ term in \eqref{BYCounterterm} can be ignored.
This is in fact the case, as we now show for $d=4,5$ that the $\mathcal{G}^{ij}$ term in \eqref{BYCounterterm} is independent of $(\Delta h_{ij},\Delta \pi^{ij})$ and thus yields at most an irrelevant shift of the zero point of the charge\footnote{By symmetry, such a shift is allowed only for the $Q_D$.}. To do so, recall that
$\hat r_i \mathcal{G}^{ij}$ can be expressed in terms of the Ricci scalar $\mathfrak{R}$ and the extrinsic curvature of $\partial \Sigma_\infty$ through the Gauss-Codacci equations. We will work with the pull-back $\theta_{ij}$ of this extrinsic curvature to $\Sigma_\infty$.
In particular, the contribution involving $\vec \xi_\perp$ is related to the `radial Hamiltonian constraint'
\begin{eqnarray}
\label{rH}
\mathcal{G}_{ij}\hat{r}^i \hat{r}^j = -\frac{1}{2}(\mathfrak{R} - \theta^2 + \theta_{ij}\theta^{ij}).
\end{eqnarray}
After expanding $h_{ij} = \bar h_{ij} + \Delta h_{ij}$,
power counting shows that only the (constant) background term and terms linear in $\Delta h_{ij}$ can contribute in the $r\rightarrow \infty$ limit. A bit of calculation (given in appendix \ref{details}) then shows
\begin{eqnarray}
\label{pp}
\frac{\hat r^i \ell \mathcal{G}_{ij} \vec{\xi}_\perp \hat r^j}{d-3} = -\frac{\ell \vec{\xi}_\perp}{2 r} \hat{r}^m \bar{h}^{jk} \left(D_j \Delta h_{km} - D_m \Delta h_{jk}\right) + (\text{constant}) + \dots,
\end{eqnarray}
where $\dots$ represents both higher order terms (that do not contribute as $r \rightarrow \infty$) and total divergences on $\partial \Sigma_\infty$. Power counting again then shows that the non-trivial term in \eqref{pp} vanishes by our boundary conditions.
We now turn to the counter-term contribution involving $\vec {\vec \xi}^i$, which is a combination of the `radial momentum constraints':
\begin{equation}
\label{mc}
\hat r_i \mathcal{G}^{ij} \vec {\vec \xi}_j = \mathcal D_i \left( \theta^{ij} - \theta \sigma^{ij} \right) \vec {\vec \xi}_j,
\end{equation}
where $\cal D$ is the derivative operator associated with $\sigma_{ij}$. We now treat the various asymptotic symmetries separately:
This term vanishes explicitly for dilations as they have $\vec {\vec \xi}^i =0$. For rotations, the symmetry of $\theta^{ij}$ and the fact that $\vec {\vec \xi}^i$ is a Killing field of $\partial \Sigma_\infty$ allow us to bring the factor of $\vec {\vec \xi}^i =0$ inside the parentheses and write \eqref{mc} as a total divergence on $\partial \Sigma$. Thus its integral over $\partial \Sigma$ (a closed manifold) must vanish. Finally for translations we use the fact that $\vec {\vec \xi}^i$ is a conformal Killing vector of $\partial\Sigma$ to write
\begin{align}
\hat r_i \mathcal{G}^{ij} \vec {\vec \xi}_j = \frac{(d-3)\theta}{r} \vec\xi_\perp.
\end{align}
The leading order contribution to this term vanishes upon integration due to the fact that $\vec\xi_\perp$ is odd. The remaining terms vanish by power counting. It follows that \eqref{mc} makes no contribution to the total charge and we see that, as previously claimed, the charges \eqref{BYCharge} are given up to a possible shift of the zero-point by \eqref{HDilatation}, \eqref{Pi}, \eqref{Li}.
\section{The $k=-1$ phase space}
\label{k=-1}
\begin{figure}
\includegraphics[width=4.5in]{Figure2.pdf}
\caption{A conformal diagram of dS${}_d$. The region above the diagonal line is the expanding hyperbolic patch. The $S^{d-2}$ labeled $i^0$ is the spatial infinity at which our boundary conditions are applied. The dashed line shows a representative $(T= {\rm constant})$ slice.}
\label{conformalDiagramHyp}
\end{figure}
We now construct two phase spaces of $d \ge 3$ spacetimes which asymptotically approach the hyperbolic ($k=-1$) patch of de Sitter space (see figure ~\ref{conformalDiagramHyp}) with metric
\begin{eqnarray}
ds^2 = -dT^2 + \sinh^2(T/\ell)\left(\delta_{ij} - \frac{1}{1+\ell^2/R^2}\frac{X_i X_j}{R^2}\right) dX^i dX^j, \label{dsHypVacuum}
\end{eqnarray}
where $X_i := \delta_{ij}X^j$. The Killing vectors then take the simple form
\begin{eqnarray}
\label{k=-1KVFs}
{\textrm {`Translations'}:} & \xi_{P^i}^a = \sqrt{R^2+\ell^2} (\partial_i)^a, \cr
{\rm Rotations:} & \xi_{L^{ij}}^a = (2X_{[i}\partial_{j]})^a.
\end{eqnarray}
These are precisely the Killing fields of $H^{d-1}$ and so generate the Lorentz group $SO(d-1,1)$. One might thus equally well refer to the hyperbolic `translations' as boosts.
The phase space $\CVPSh$ will be constructed in direct analogy to our treatment for $k=0$ in section \ref{k=0}. We again consider globally hyperbolic solutions to Einstein's equations in $d\ge 3$ spacetime dimensions with positive cosmological constant and topology $\mathbb{R}^d$. Introducing a foliation as before with coordinates $(T,\{X^i\})$ and a metric of the form \eqref{dSmetric}, we define $\CVPSh$ to contain spacetimes with induced metric $h_{ij}$ canonical momentum ${\pi}^{ij}$, lapse $N$, and shift $N^i$ on a $(T= {\rm constant})$ slice $\Sigma$ which satisfy
\begin{align}
\Delta h_{ij} &= h^{(d-2)}_{ij} + \order{h^{(d-2)}_{ij} R}{-1} \cr
\Delta {\pi}^{ij} &= \pi^{ij}_{(d-2)} + \order{\pi_{(d-2)}^{ij} R}{-1} \cr
N &= 1+ N^{(d-2)} + \order{R}{-(d-1)} \cr
N^i &= N^i_{(d-3)}+\order{N^i_{(d-3)}R}{-1}, \label{BoundaryConditionsh}
\end{align}
for large $R$ with $R=\sqrt{\delta_{ij}X^i X^j}$. The required falloff of $h^{(d-2)}_{ij}$, $\pi^{ij}_{(d-2)}$ and $N^i_{(d-3)}$ are most clearly expressed in spherical coordinates,\begin{subequations}
\begin{align}
\label{hdm2}
h_{RR}^{(d-2)} &= \frac{(\textrm{Function of $\Omega$})}{R^{2+(d-2)}} , & h_{R\theta}^{(d-2)} &= \frac{(\textrm{Function of $\Omega$})}{R^{(d-2)}} , & h_{\phi\theta}^{(d-2)} &= \frac{(\textrm{Function of $\Omega$})}{R^{-2+(d-2)}} \\
\pi^{RR}_{(d-2)} &= \frac{(\textrm{Function of $\Omega$})}{R^{-2+(d-2)}} , & \pi^{R\theta}_{(d-2)} &= \frac{(\textrm{Function of $\Omega$})}{R^{(d-2)}} , & \pi^{\phi\theta}_{(d-2)} &= \frac{(\textrm{Function of $\Omega$})}{R^{2+(d-2)}} \\
N^{(d-2)} &= \frac{(\textrm{Function of $\Omega$})}{R^{(d-2)}} , & N_{(d-3)}^R &= \frac{(\textrm{Function of $\Omega$})}{R^{(d-3)}} , & N_{(d-3)}^\theta &= \frac{(\textrm{Function of $\Omega$})}{R^{2+(d-3)}}
\end{align}
\end{subequations}
with $\theta$ and $\phi$ standing in for any angular coordinates. We define
\begin{subequations} \label{DeltahpiHyp}
\begin{eqnarray}
\Delta h_{ij} &=& h_{ij} - \sinh^2\left(T/\ell\right)\omega_{ij} \\
\Delta {\pi}^{ij} &=& {\pi}^{ij} + \frac{(d-2) \coth(T/\ell) \sinh^{-2}(T/\ell)}{\ell}{\omega}^{ij}.
\end{eqnarray}
\end{subequations}
Here we have introduced the metric $\omega_{ij}$ on the unit $H^{d-1}$:
\begin{eqnarray}
\omega_{ij} = \delta_{ij} - \frac{1}{1+\ell^2/R^2}\frac{X_i X_j}{R^2}.
\end{eqnarray}
The definitions \eqref{DeltahpiHyp} ensure that $\Delta h_{ij}=0=\Delta{\pi}^{ij}$ for $\dSh$. The boundary conditions~\eqref{BoundaryConditionsh} are sufficient to ensure that, in spherical coordinates,
\begin{align}
\Delta\tilde\pi^{ij} = \order{\Delta\pi_{(d-2)}^{ij}R}{d-3},
\end{align}
which makes the symplectic structure \eqref{SymplecticStructure} finite. We will show below that it is also conserved. Thus $\CVPSh$ is a well-defined phase space.
\subsection{Asymptotic Symmetries}
As in the $\dS$ case we know that any element of our ASG must map~\eqref{dsHypVacuum} onto a spacetime satisfying~\eqref{BoundaryConditionsh}. This means that the associated vector field must satisfy $h^a_i h^b_j \bar \nabla_{(a} \xi_{b)}~=~\mathcal{O}\left(R^{-(d-2)}\right)$, or
\begin{align}
D_{(i}\vec\xi_{j)} &= \partial_{(i}\vec\xi_{j)} + \frac{R \vec\xi_\perp}{\ell^2} \omega_{ij} = \frac{\sinh(T/\ell)\cosh(T/\ell)\xi_\perp}{\ell} \omega_{ij}, \label{ckvfHyp}
\end{align}
up to terms which vanish at infinity, where $D_i$ is the covariant derivative on $\Sigma$. For $d\ge 4$ we project this equation onto a $R~= ~(\text{constant})$ submanifold which gives
\begin{align}
\mathcal D_{(\underline i}\vec{\vec\xi}_{\underline{j})} &= \left(\frac{\sinh(T/\ell)\cosh(T/\ell)\xi_\perp}{\ell}-\frac{(1-R^2/\ell^2)\vec\xi_\perp}{R} \right) \sigma_{\underline{ij}} , \label{ckvfHypP}
\end{align}
where $\mathcal D_i$ is the covariant derivative on the $R= (\text{constant})$ subsurface of $\Sigma$. Since we consider here the metric \eqref{dsHypVacuum}, eqn. \eqref{ckvfHypP} is the conformal Killing equation on the unit $S^{d-2}$. The sphere is conformally flat, so the solutions to this equation are the generators of the $d-2$ dimensional Euclidean conformal group. For $d\ge 5$ this group is $SO(d-1,1)$ which is isomorphic to the group generated by \eqref{k=-1KVFs}. For $d=4$, \eqref{ckvfHypP} has an infinite number of solutions, however we are only interested in those solutions which are globally well defined on the sphere. These solutions form the subgroup $PSL(2,\mathbb{C})~\cong~SO(3,1)$, which is again isomorphic to the group generated by \eqref{k=-1KVFs}. We conclude that our $d \ge 4$ ASG can only contain symmetries which asymptotically approach the isometries \eqref{k=-1KVFs}. The case $d=3$ will be addressed below.
As before,~\eqref{LieDhpi} shows that our phase space is closed under the isometries of $\dSh$ (noting that $\vec\xi\sim R$ and $\xi_\perp = 0$). So we have shown that the asymptotic symmetry group of $\CVPSh$ is isomorphic to the isometries of $\dSh$ for $d\ge 4$. Using the same technique as in section \ref{CC} (and appendix~\ref{finiteQ}), we obtain conserved charges for the asymptotic symmetries of $\CVPSh$ and $d\ge4$,
\begin{eqnarray} \label{Qk=-1}
P^j &\equiv& H(\xi^a_{P^j}) = \frac{1}{\kappa}\int_{\partial\Sigma} \sqrt{\sigma} R \hat{R}_i\Delta^\prime \pi^{ik} h_{kj} \label{Phyp} \cr
L^{jk} &\equiv& H(\xi^a_{L^{jk}}) = \frac{1}{\kappa}\int_{\partial\Sigma} \sqrt{\sigma} 2 \hat{R}_i \Delta^\prime \pi^{im} \bar h_{ml} \delta^{l[k} X^{j]}, \label{Lhyp}
\end{eqnarray}
with
\begin{align}
\Delta^\prime \pi^{ij} = \pi^{ij} + \frac{(d-2) \coth(T/\ell) }{\ell} h^{ij}.
\end{align}
The charges~\eqref{Qk=-1} are finite by the boundary conditions~\eqref{BoundaryConditionsh}. As for $k=0$ one finds that $H(\partial_T)$ is finite, has well-defined variations, and generates an evolution that preserves the boundary conditions~\eqref{BoundaryConditionsh} on $h_{ij},\tilde \pi^{ij}$. (For $k=-1$ there is no need to introduce an analogue of \eqref{lapseshiftcondition}.) So we again conclude that the symplectic structure and the above charges are conserved on $\CVPSh$.
The case $d=3$ is special due to the infinite-dimensional conformal group in two dimensions. Since the hyperbolic plane is conformally flat, the solutions of~\eqref{ckvfHyp} define two commuting Virasoro algebras formally associated with charges $L_n$ and $\bar L_n$ for $n \in {\mathbb Z}$ satisfying $L_n^* = \bar L_{-n}$ where $*$ denotes complex conjugation and $n$ labels the angular momentum quantum number.
The details of the vector fields are given in appendix \ref{d=3ASG}.
The unfamiliar reality condition is due to the fact that the symmetries of the Lorentz-signature theory generate the 2d Euclidean-signature conformal group and was previous discussed in \cite{Fjelstad:2002wf,Balasubramanian:2002zh,Ouyang:2011fs}. With our conventions, the angular momentum (called $L_{ij}$ above in higher dimensions) is $J_0$ where $J_n = (L_n + \bar L_n)$. It is also useful to introduce $K_n = (L_n - \bar L_n)/i\ell$. We will see below that $K_0$ captures energy-like information about solutions.
As noted in section \ref{k=0}, expression \eqref{Hz} is valid only when second order terms in $\Delta h_{ij}, \Delta \pi^{ij}$ do not contribute to the variations. For the $J_n$ charges, this condition holds on all of $\CVPSh$. For the $K_n$ charges, it holds only when we use the gauge freedom to set $h^{(1)}_{ij} =0$. This is always possible for $d=3$ since $h_{ij}$ has only 3 independent components. With this understanding for $K_n$, we find
\begin{align}
J_n &\equiv H(\xi_{J_n}) = \frac{1}{\kappa}\int_{\partial\Sigma} \sqrt{\sigma} 2 \hat{R}_i\Delta^\prime \pi^{im} \bar h_{ml} \delta^{l[k} X^{j]} e^{i n \theta} \cr
K_n &\equiv H(-\xi_{K_n}) = \frac{1}{\kappa}\int_{\partial\Sigma} \sqrt{\sigma} \hat{R}_i \Delta^\prime \pi^{ik} \bar h_{kj} \frac{R^2\coth(T/\ell)}{\ell^2} (\partial_R)^j e^{in\theta} \cr
& \quad + \frac{1}{2\kappa} \int_{\partial\Sigma} \sqrt{\sigma} \hat{R}_l G^{ijkl} \left(-\frac{R}{\ell} D_k \Delta h_{ij}+\frac{\omega_k^R}{\ell} \Delta h_{ij} \right)e^{in\theta}. \label{V2}
\end{align}
In choosing sign conventions we have treated $J_n$ as a momentum and $K_n$ as an energy. Since appendix \ref{KnConservation} shows that the expression for $K_n$ above is invariant under gauge transformations that preserve $h^{(1)}_{ij} =0$, we may use \eqref{V2} to define $K_n$ as a gauge invariant charge on all of $\Gamma(dS_{k=-1})$.
From the Poincar\'e disk description of the 2d hyperbolic plane, one readily sees that diffeomorphisms associated with $J_n$ preserve the boundary while those associated with $K_n$ do not. A careful study of our boundary conditions \eqref{BoundaryConditionsh} similarly shows that the phase space $\CVPSh$ is invariant only under the $J_n$. As a result, the asymptotic symmetry group of either $\CVPSh$ or $\CVPSh_{gf}$ is given by a single Virasoro algebra
\begin{align}
[J_{n}, J_{_m} ] = (n-m) J_{n+m},
\end{align}
where $[A,B]$ denotes the commutator of the corresponding quantum mechanical charges (i.e., we have inserted an extra factor of $i$ relative to the classical Poisson Bracket). The central charge vanishes due to the symmetry $\theta \rightarrow - \theta$, which reflects the lack of a gravitational Chern-Simons term. Adding such a term to the action should lead to non-vanishing central charge.
Simple power counting shows that $J_n$ is finite on $\CVPSh$, and also that $H(\partial_T)$ is finite, has well-defined variations, and generates an evolution that preserves the boundary conditions~\eqref{BoundaryConditionsh} on $h_{ij},\tilde \pi^{ij}$. It follows that the symplectic structure and the $J_n$ charges are conserved on $\CVPSh$, and thus on $\CVPSh_{gf}$ as well. While the $K_n$ do not generate asymptotic symmetries, it turns out that expresion~\eqref{V2} is nevertheless finite, gauge invariant, and time independent on $\CVPSh$. The details of this argument are given in Appendix~\ref{KnConservation}.
We take these observations as motivation to consider further the full 2d conformal algebra. The associated central charges can be computed as in \cite{BrownHenneauxCentralCharge} and turn out to be non-zero:
\begin{align}
\label{ccharge}
[L_n, L_m] &= (n-m) L_{n+m} + i \frac{1}{12} \left(\frac{3\ell}{2 G}\right) n(n^2-1) \delta_{n,-m} \\
[\bar L_n, \bar L_m] &= (n-m) \bar L_{n+m} - i \frac{1}{12} \left(\frac{3\ell}{2 G}\right) n(n^2-1) \delta_{n,-m} \\
[L_n, \bar L_m] &= 0 ,
\end{align}
so that the left- and right-moving central charges are imaginary complex conjugates
in agreement with \cite{Balasubramanian:2002zh,Maldacena:2002vr,Ouyang:2011fs}.
It would be interesting to understand the unitary representations of (\ref{ccharge}) under the appropriate reality conditions. This question was briefly investigated in \cite{Balasubramanian:2002zh}. However, our analysis suggests that there is an additional subtlety: Because the flows generated by $K_n$ are not complete on our classical phase space, ``real'' elements of the algebra they generate (e.g., $K_0$) are unlikely to be self-adjoint on the quantum Hilbert space. Indeed, it is natural to expect behavior resembling that of $-i\frac{d}{dx}$ on the half-line, which admits complex eigenvalues. This in principle allows representations more general than those considered in \cite{Balasubramanian:2002zh}, though we will not pursue the details here.
For later use, we note that imposing the additional gauge condition
\begin{equation}
\label{ggh}
\Delta h_{ij} = h_{ij}^{(3)} + \order{h_{ij}^{(3)} R}{-\epsilon}
\end{equation}
further simplifies \eqref{V2} and yields:
\begin{align}
\label{simple}
J_n &= \frac{1}{\kappa}\int_{\partial\Sigma} \sqrt{\sigma} \hat R_i 2 \Delta^\prime \pi^{im} h_{ml} \delta^{l[k} X^{j]} e^{i n \theta} \cr
&= \frac{1}{\kappa}\int_{\partial\Sigma} \pi_{(2)}^{R\theta} R^2 \ell \sinh^4(T/\ell) e^{i n \theta} \cr
K_n &= \frac{1}{\kappa} \int_{\partial\Sigma} \sqrt{\sigma} \hat{R}_i \Delta^\prime \pi^{ik} h_{kj} \frac{R^2\coth(T/\ell)}{\ell^2} (\partial_R)^j e^{in\theta} \cr
&= \frac{1}{\kappa} \int_{\partial\Sigma} \pi_{(2)}^{RR} \sinh^3(T/\ell) \cosh(T/\ell) e^{in\theta}.
\end{align}
\subsection{Familiar Examples}
\label{exk=-1}
We now study two classes of familiar solutions -- the $d=4$ Kerr-de Sitter solution and the $d=3$ spinning conical defect. We find coordinates for which each solution lies in the phase space $\CVPSh$ and compute the appropriate charges. We consider the Kerr case (as opposed to just Schwarzschild) since spherical symmetry would force all $d=4$ charges to vanish.
Our first task is to transform the standard $d=4$ Kerr-de Sitter metric~\cite{carterKerrdS}
\begin{eqnarray}
ds^2 &=& -\frac{\Delta-\Sigma a^2\sin^2(\psi)}{\Omega} d\tau^2 + a\sin^2(\psi)\left(\frac{2GM\rho}{\Omega}+\frac{\rho^2+a^2}{\ell^2}\right) (dt d\gamma+d\gamma dt) + \frac{\Omega}{\Delta} d\rho^2 \cr
&+& \frac{\Omega}{\Sigma} d\psi^2 + \sin^2(\psi)\left(\frac{2GM\rho a \sin^2(\psi)}{\Omega}+\Delta+2GM\rho\right)d\gamma^2 \label{KdS} \cr
\Delta &=& (\rho^2 + a^2)\left(1-\frac{\rho^2}{\ell^2}\right)-2GM\rho \cr
\Omega &=& \rho^2+a^2\cos^2(\psi) \cr
\Sigma &=& 1+\frac{a^2}{\ell^2}\cos^2(\psi), \label{KerrMetric}
\end{eqnarray}
into coordinates for which it satisfies the boundary conditions \eqref{BoundaryConditionsh}.
We proceed by introducing coordinates $(s,\theta,\phi)$ through the expressions (c.f. appendix B of~\cite{HenneauxTeitelboimAsympAdS})
\begin{align}
s\cos(\theta) &= \rho\cos(\psi) \cr
\left(1+\frac{a^2}{\ell^2}\right)s^2 &= \rho^2+a^2\sin^2(\psi)+\frac{a^2}{\ell^2} \rho^2 \cos^2(\psi) \cr
\phi &= \left(1+\frac{a^2}{\ell^2}\right) \gamma + \frac{a}{\ell^2} \tau. \label{KerrcoordTrans}
\end{align}
In $(\tau,s, \theta, \phi)$ coordinates the metric \eqref{KdS} approaches exact de Sitter space in static coordinates as $M\rightarrow 0$. We then introduce further coordinates $T,R$ through
\begin{align}
\tau &= \ell \log\left(\frac{\cosh(T/\ell)+\sinh(T/\ell)\sqrt{1+R^2/\ell^2}} {|\sinh^2(T/\ell)R^2/\ell^2-1|^{1/2}}\right) \cr
s &= \sinh(T/\ell) R. \label{TRcoord}
\end{align}
By transforming \eqref{KdS} to $(T,R,\theta,\phi)$ coordinates we obtain a metric which approaches \eqref{dsHypVacuum} when $M \rightarrow 0$. The explicit form of the metric is unenlightening but yields $\Delta h_{ij},\Delta \pi_{ij}$
which satisfies \eqref{BoundaryConditionsh}. A similar calculation using the de Sitter-Schwarzschild solution in $d \ge 4$ yields fields with $h_{ij}^{(d-2)}=0=\pi^{ij}_{(d-2)}$ and which again satisfy \eqref{BoundaryConditionsh}. Thus we see that our phase spaces are non-trivial for $d \ge 4$. Note that in $d=4$ the leading order terms in $(\Delta h_{ij},\Delta \pi^{ij}$) for rotating black holes vanish as $a\rightarrow 0$. We expect the same to be true in higher dimensions, though with the rotating solutions still satisfying \eqref{BoundaryConditionsh}.
Returning to the Kerr-de Sitter solution, symmetry implies that the only non vanishing charge is $L^{12}$. From \eqref{Lhyp} we find
\begin{eqnarray}
L^{12} = \frac{aM}{(1+a^2/\ell^2)^2}. \label{KerrJ}
\end{eqnarray}
This differs from the analogous AdS result~\cite{HenneauxTeitelboimAsympAdS} only by the expected replacement $\ell\rightarrow i\ell$ and agrees with the analogous flat space result when $\ell\rightarrow\infty$.\footnote{Note that \cite{HenneauxTeitelboimAsympAdS} used a different sign convention for $a$.}
Finally, for $d=3$ we once again consider the conical defect solution~\eqref{ConicalDefect} of~\cite{BrownHenneauxCentralCharge,balasubramaniandS}. After transforming from static to $k=-1$ coordinates (through a transformation resembling~\eqref{TRcoord}) we find $\Delta h_{ij}, \Delta \pi^{ij} $ satisfy~\eqref{BoundaryConditionsh} with $h_{ij}^{(1)}=0$. Thus the transformed solution is in $\CVPSh$. We find $J_0 = aM$ and $K_0 = -M$. Note that this agrees with $Q_D$ as computed for the $k=0$ version of the conical defect in section \ref{FE}. As will be clear after we show equivalence to the counter-term charges in section \ref{comparehyp} below, this is due to the fact that $K_0$ and $Q_D$ correspond to the same element of the Euclidean conformal group on $I^+$.
\subsection{Asymptotically dS${}_{k=-1}$ wormhole spacetimes}
\label{wormholes}
We now turn to some more novel spacetimes asymptotic to dS${}_{k=-1}$. We consider pure $\Lambda > 0$ Einstein-Hilbert gravity, for which all solutions are quotients of dS${}_3$. As noted in \cite{Balasubramanian:2002zh}, quotients generated by a single group element fall into two classes (up to congujation): The first leads to the conical defects discussed above. For the 2nd class, the generator of the quotient group can be described simply in terms of the 3+1 Minkowski space $M^{3,1}$ into which dS${}_3$ is naturally embedded (as the set of points of proper distance $\ell$ from the origin). This generator then consists of a simultaneous boost (say, along the $z$-axis) and a commuting rotation (in the $xy$ plane). This class of quotients was not investigated in \cite{Balasubramanian:2002zh}, essentially because the resulting spacetimes are not asymptotically $\dSh$. Indeed, from the point of view of the $k=0$ patch the quotient spacetime is naturally interpreted as a cosmological solution in which space is a cylinder $(S^1 \times \mathbb{R})$ at each moment of time.
However, in appropriate coordinates this 2nd class of quotients also defines spacetimes asymptotic to the $k=-1$ patch and which in fact lie in $\CVPSh$. In this sense our quotient spacetimes may be thought of as $\Lambda > 0$ analogues of BTZ black holes \cite{Banados:1992wn,Banados:1992gq}. That the quotient lies in $\CVPSh$ is easy to see when the quotient generator is a pure boost (i.e., where the commuting rotation is set to zero) in which case the quotient group preserves the appropriate $k=-1$ patch. Indeed,
recall that for non-spinning BTZ black holes the associated quotient on AdS${}_3$ acts separately on each slice of constant global time, and that such surfaces are two-dimensional hyperbolic space $H^2$. Here the $T=(\text{constant})$ slices of \eqref{dsHypVacuum} are also $H^2$ and we apply the analogous quotient.
This amounts to defining new coordinates $(R,\theta)$ through
\begin{equation}
X = \frac{2\pi R}{\theta_0}, \ \ \
Y = \sinh\left(\frac{\theta_0}{2\pi} \theta\right) \sqrt{\left(\frac{2\pi R}{\theta_0}\right)^2 +\ell^2},
\end{equation}
and taking $\theta$ to be periodic with period $2\pi$. The $T= (\text{constant})$ slices are then topologically $S^1\times \mathbb{R}$ and the the metric is
\begin{align}
\label{nsw}
g_{ab} = -dT^2 + \sinh^2(T/\ell) \left(\frac{\ell^2 dR^2}{R^2 + (\theta_0\ell/2\pi)^2} + \left(R^2 + (\theta_0\ell/2\pi)^2\right) d\theta^2\right).
\end{align}
It is evident that \eqref{nsw} satisfies \eqref{BoundaryConditionsh} (in fact, with $h^{(1)}_{ij}=0$) and thus lies in $\CVPSh$. We refer to \eqref{nsw} as a `wormhole' since on a given constant $T$ surface the $\theta$ circle has a minimum size $ \theta_0 \ell \sinh(T/\ell)$ at $R=0$. These solutions have $J_0 =0$ and $K_0 = - \left(1+(\theta_0/2\pi)^2\right)/8G$. Since $K_0$ is an energy-like charge that vanishes for $dS_{k=-1}$, we find a mass gap analogous to that between AdS${}_3$ and the BTZ black holes.
When the commuting rotation is non-zero, the quotient group does not preserve the $k=-1$ patch of exact dS${}_3$. Yet it appears that the quotient can nevertheless be considered to lie in $\CVPSh$. Indeed, assuming a single rotational symmetry it is straightforward to solve the constraints \eqref{constraints} to find initial data for wormholes with angular momentum lying in $\dSh$. For data asymptotic to a $T= (\text{constant})$ surface we find
\begin{align} \label{sw}
h_{ij} &= \sinh^2(T/\ell) \left(
\begin{array}[c]{cc}
\dfrac{\ell^2}{R^2+(\theta_0\ell/2\pi)^2} & 0 \\
0 & R^2 +(\theta_0 \ell/2\pi)^2
\end{array} \right) \cr
\pi^{ij} &= -\frac{\coth(T/\ell)}{\ell} h^{ij} + \left(
\begin{array}[c]{cc}
\dfrac{\gamma(T,R)}{\ell\sinh^4(T/\ell)} & \dfrac{\alpha_0}{\left(R^2 + (\theta_0\ell/2\pi)^2\right) \sinh^4(T/\ell)} \\
\dfrac{\alpha_0}{\left(R^2 + (\theta_0\ell/2\pi)^2\right) \sinh^4(T/\ell)} & \beta(T,R) \coth^2(T/\ell)/\ell^3
\end{array}
\right), \cr
\end{align}
where
\begin{align}
\gamma &= \alpha(T,R) - \sqrt{\alpha(T,R)^2 - \alpha_0^2} \\
\beta &= \frac{ \alpha(T,R) \left( \sqrt{\alpha(T,R)^2 - \alpha_0^2 } - \alpha(T,R) \right)-\alpha_0^2}{ \alpha(T,R)^2 \sqrt{\alpha(T,R)^2 - \alpha_0^2} } ,
\end{align}
with
\begin{align}
\alpha(T,R) := \frac{R^2 + (\theta_0 \ell/2\pi)^2 }{\ell^2} \frac{\sinh(2T/\ell)}{2},
\end{align}
where $R$ ranges over $(-\infty, +\infty)$ though we must choose $ \alpha(T,R) > \alpha_0$. The above canonical data satisfies \eqref{BoundaryConditionsh} with $h_{ij}^{(1)}=0$ so we may readily compute the charges
\begin{eqnarray}
J_0 &=& \frac{\alpha_0 \ell}{4G} , \cr
K_0 &=& - \frac{1 + (\theta_0/2\pi)^2}{8G} .
\end{eqnarray}
Thus $\alpha_0$, $\theta_0$ are constant on any solution (at least when the lapse and shift have the fall off dictated by~\eqref{BoundaryConditionsh}). Indeed, using the Bianchi identities one may show that
$\dot{J}_0 = 0 = \dot{K}_0 $ (as evaluated in one asymptotic region) are precisely the conditions for \eqref{sw} to solve the canonical equations of motion with lapse and shift defined by solving any 3 independent sets of these equations.
The resulting lapse and shift can be chosen to satisfy
\begin{align}
N &= 1+ \frac{2\alpha_0^2 \ell^5}{5 \sinh^2(2T/\ell)R^4} + \order{R}{-5} \\
N^R &= \frac{2\alpha_0^2\ell^3}{5\sinh^3(T/\ell)\cosh(T/\ell)R^3} + \order{R}{-6} \\
N^\theta &= \frac{2 \alpha_0 \ell^2}{3 \sinh^2(T/\ell) R^3} + \order{R}{-2}
\end{align}
in one asymptotic region, though for the foliation defined by \eqref{sw} they then diverge in the second asymptotic region. It would be interesting to find a more well-behaved foliation of the spinning wormhole spacetime, or perhaps an analytic solution for the full spacetime metric. Such a solution can presumeably be found by considering the above-mentioned quotients of dS${}_3$ and taking the size of the commuting rotation to be determined by $\alpha_0$.
In the non-spinning case, it is clear that the above construction may be generalized to quotients by groups with more than one generator. In analogy with \cite{Aminneborg:1997pz,Aminneborg:1998si}, one may construct quotients for which the $T= (\text{constant})$ surface (and thus $I^+$) is an arbitrary Reimann surface with any number of punctures\footnote{For spheres, the number of punctures must be at least $2$.}, where each puncture describes an asymptotic region. In particular, one may construct solutions with only a single asymptotic region. We expect that angular momentum may be added to these solutions as above. The solution also depends on a choice of internal moduli when the Riemann surface is not a sphere.
\subsection{Comparison with Brown-York methods at future infinity}
\label{comparehyp}
We now compare our charges to those obtained in \cite{Strominger:2001pn,balasubramaniandS} using boundary stress tensors on $I^+$. We wish to evaluate~\eqref{BYCharge} for $k=-1$. We begin with the special case $d=3$ for which the counterterm is again simply $(d-2) h^{ij}/\ell \kappa$ which results in a term
\begin{align}
\Delta^{\prime\prime} \pi^{ij} = \pi^{ij} + \frac{(d-2)}{\ell} h^{ij},
\end{align}
which matches the $\Delta^\prime \pi^{ij}$ term in \eqref{V2} in the limit $T\rightarrow\infty$. Thus the $J_n$ agree with~\cite{Strominger:2001pn,balasubramaniandS} on $\CVPSh$.
The situation for $K_n$ is more subtle. While our $K_n$ are fully gauge invariant, the corresponding Brown-York charges~\eqref{BYCharge} fail to be invariant under all of our gauge transformations. From the perspective of \cite{Strominger:2001pn,balasubramaniandS}, this is simply because our gauge transformations act as conformal transformations on $I^+$ and thus generate conformal anomaly terms. These terms are large enough to contribute to the Brown-York versions of the $K_n$ and can even make them diverge. Under a general transformation that we consider to be gauge, the $K_n$ computed as in \cite{Strominger:2001pn,balasubramaniandS} thus transform by adding a term that depends on the gauge transformation but is otherwise independent of the solution on which it is evaluated; the term is a gauge-dependent $c$-number. On the other hand, if we impose the gauge \eqref{ggh} we may use \eqref{simple}. As a result, our $K_n$ charges then match those defined using~\eqref{BYCounterterm} as given by a flat boundary metric.
For $d=4,5$ we will also obtain a $\Delta^{\prime\prime} \pi^{ij} $ term which again reproduces the $\Delta^{\prime} \pi^{ij} $ term in \eqref{Qk=-1} when $T\rightarrow\infty$. Thus we must again show that the counterterm
\begin{align}
\frac{\ell}{d-3} \mathcal{G}^{ij}
\end{align}
can contribute only a constant (which must then vanish by symmetry for all charges). Using the same notation and conventions as in section \ref{compare} we first evaluate the contributions from radial momentum constrains. As in the $k=0$ case the contribution is a pure divergence for rotations. For translations the result is (see Appendix~\ref{details})
\begin{align}
\frac{\hat R_i \ell \mathcal{G}^{ij} \vec{\vec{\zeta}}_j}{d-3} = \frac{R \vec{\zeta}_\perp}{\ell} \hat{R}^k \sigma^{ij} D_k \Delta \sigma_{ij}. \label{radmomentumhyp}
\end{align}
The contribution from the radial Hamiltonian constraint is given by
\begin{align}
\frac{\hat R_i \ell \mathcal{G}^{ij} \vec{\zeta}_\perp \hat R_j}{d-3} = \frac{R \vec{\zeta}_\perp}{\ell} \hat{R}^k \sigma^{ij}\left( D_i \Delta \sigma_{jk} - D_k \Delta \sigma_{ij} \right). \label{radhamiltonianhyp}
\end{align}
This vanishes explicitly for rotations (for which $\zeta_\perp =0$). For translations, \eqref{radmomentumhyp} nicely cancels the second term in the radial Hamiltonian contribution leaving only
\begin{align}
\frac{\hat R_i \ell \mathcal{G}^{ij} \vec{\zeta}_j}{d-3} = \frac{R \vec{\zeta}_\perp}{\ell} \hat{R}^k \sigma^{ij} D_i \Delta \sigma_{jk}.
\end{align}
The leading order term vanishes because $\zeta_\perp$ is odd. Power counting now shows that the remaining terms vanish by~\eqref{BoundaryConditionsh}.
\section{Discussion}
\label{disc}
We have constructed phases spaces $\CVPS$ and $\CVPSh$ associated with spacetimes asymptotic to the planar- and hyperbolic-sliced regions $\dS$ and $\dSh$ of de Sitter space for $d \ge 3$. Our charges agree with those defined in \cite{balasubramaniandS,StromingerASG} when the latter are computed for our asymptotic Killing fields at the respective $i^0$, and using an appropriate conformal frame for $d=3, k=-1$. This establishes that (some of) the charges of \cite{Strominger:2001pn,balasubramaniandS,StromingerASG} generate diffeomorphisms in a well-defined phase space.
For $d \ge 4$ our phase spaces are non-trivial in the sense that they contain the de Sitter-Schwarzschild solution as well as spacetimes with generic gravitational radiation through $I^+$, provided only that this radiation falls off sufficiently quickly at $i^0$. For $d=3$ and $k=0$ the phase spaces become non-trivial when coupled to matter fields or point particles. Despite the lack of local degrees of freedom, the case $d=3$ with $k=-1$ is non-trivial even without matter due to both boundary gravitons and the family of wormhole spacetimes described in section \ref{wormholes}. These solutions are $\Lambda > 0$ analogues of BTZ black holes (and their generalizations \cite{Aminneborg:1997pz,Aminneborg:1998si}) and exhibit a corresponding mass gap. They are labeled by their angular momentum, an energy-like $K_0$ charge, and the topology of $I^+$, as well as internal moduli if the topology of $I^+$ is sufficiently complicated. The latter two are analogues of the parameters discussed in \cite{Aminneborg:1997pz,Aminneborg:1998si} for $\Lambda < 0$.
In most cases we found an asymptotic symmetry group (ASG) isomorphic to the isometries of $\dS$ or $\dSh$, though for $k=-1$ and $d=3$ the obvious rotational symmetry was enlarged to a (single) Virasoro algebra in the ASG. Since we do not include a gravitational Chern-Simons term, the central charge for this case vanishes due to reflection symmetry in the angular direction. While we expect a similar structure to arise for phase spaces asymptotic to general 2+1 dimensional $k=-1$ Friedmann-Lema\^itre-Robertson-Walker cosmologies, we leave such a general study for future work. We also identified a larger algebra containing two Virasoro sub-algebras with non-trivial imaginary central charges
$\pm i \left(\frac{3\ell}{2G}\right)$ in agreement with those expected from \cite{Maldacena:2002vr,Balasubramanian:2002zh} and computed in \cite{Ouyang:2011fs}.
While the classical reality conditions are those of \cite{Fjelstad:2002wf,Balasubramanian:2002zh,Ouyang:2011fs}, the fact that the additional generators $K_n$ do not preserve our phase space suggests that corresponding ``real'' elements of the algebra (e.g., $K_0$) do not define self-adjoint operators at the quantum level. Instead, we expect that these operators behave somewhat like $-i \frac{\partial}{\partial x}$ on the half-line and may have complex eigenvalues. While the $K_n$ charges do not generate symmetries, they are nevertheless gauge invariant and conserved on $\CVPSh$.
A similar extension to the full Euclidean conformal group may also be allowed for $d = 3, k=0$ and perhaps even in higher dimensions. However, reflection and rotation symmetries imply that the additional `charges' vanish for $d=3$ spinning conical defects, for $d=4$ Kerr-de Sitter, and for rotating de Sitter Myers-Perry black holes in higher dimensions. We have not investigated whether other solutions in our phase space (perhaps a `moving' black hole?) might lead to non-zero values of such charges.
It remains to compare our phase spaces with those of \cite{Shiromizu:2001bg,KastorCKV,LuoPositiveMass}. These references studied spacetimes asymptotic to $\dS$ in four spacetime dimensions, so we limit the comparison to our $\CVPS$ with $d=4$.
The focus in \cite{Shiromizu:2001bg,KastorCKV,LuoPositiveMass} was on proving positive energy theorems associated with a charge $Q[\partial_t]$ defined by the time-translation conformal Killing field $\partial_t$ of $\dS$.
Because $\partial_t$ defines only an asymptotic {\it conformal} symmetry, the value of $Q[\partial_t]$ depends on the Cauchy surface on which it is evaluated. I.e., it is time-dependent, and is thus not conserved in the sense in which we use the term here. The boundary conditions of~\cite{KastorCKV} for $d=4$ can be stated as follows. Define
\begin{equation} \label{KTbc}
\Delta^\prime h_{ij} = h_{ij} - e^{2t/\ell} \delta_{ij}= \Delta h_{ij}, \ \ \ \
\Delta^\prime K_{ij} = K_{ij} - \frac{h_{ij}}{\ell} \ne \Delta K_{ij}
\end{equation}
and require that there exist a foliation with vanishing shift on which
$\Delta^\prime h_{ij} = \mathcal{O}(r^{-1})$, $\Delta^\prime K_{ij} = \mathcal{O}(r^{-3})$.
These boundary conditions make $Q[\partial_t]$ finite and allow one to prove that $Q[\partial_t ] \ge0$. However, as the authors note, they do not appear to be sufficient to make finite the charges associated with the asymptotic Killing fields\footnote{One suspects that the boundary conditions of \cite{KastorCKV} can be tightened to make the Killing charges finite while keeping their $Q[\partial_t]$ finite and positive. It would be interesting to show this explicitly.}. In contrast, our boundary conditions were chosen specifically to make such `Killing charges' finite.
Luo et. al.~\cite{LuoPositiveMass} use boundary conditions that are similar to~\cite{KastorCKV}. They require also that a foliation be constructed with vanishing shift and
$\Delta^\prime h_{ij} = \mathcal{O}(r^{-1})$, $\Delta^\prime K_{ij} = \mathcal{O}(r^{-2})$.
A simple calculation yields
\begin{eqnarray}
\Delta^\prime \tilde{\pi}^{ij} = \Delta \tilde{\pi}^{ij} - \frac{\sqrt{\bar h}}{\ell} \left( 2 \Delta h^{ij} + \Delta {h^k}_k \bar h^{ij}\right) + \mathcal{O}(\Delta h^2).
\end{eqnarray}
Now in order for Eqs.~\eqref{BoundaryConditions} and the boundary conditions of either \cite{KastorCKV} or \cite{LuoPositiveMass} to be simultaneously satisfied, we must have at least $\Delta h_{ij} = \Delta^\prime h_{ij} = \mathcal{O}(r^{-2})$. Using the results of~\cite{LuoPositiveMass} (particularly Theorem 4.2) it can be shown that the only globally hyperbolic spacetime which satisfies both sets of boundary conditions on the same foliation is exact de Sitter space in the form \eqref{dsHypVacuum} (up to gauge transformations).\footnote{However it is possible for the same spacetime to admit two different foliations with one satisfying \eqref{BoundaryConditionsh} and the other satisfying the boundary conditions of \cite{KastorCKV,LuoPositiveMass}. This is in particular the case for the de Sitter--Schwarzschild solution; see \cite{KastorCKV,LuoPositiveMass}.} Our phase space thus has precisely one point in common with that of either \cite{KastorCKV} or \cite{LuoPositiveMass}. It is nevertheless interesting to ask whether the methods of \cite{KastorCKV,LuoPositiveMass} might be used to derive a bound on the charge $K_0$ for $d=3$.
We end with a brief comment on the related approach of Shiromizu et. al.~\cite{Shiromizu:2001bg}, which also imposes $\Delta^\prime h_{ij} = \mathcal{O}(r^{-1})$, $\Delta^\prime K_{ij} = \mathcal{O}(r^{-3})$ and in addition requires the sapcetime to admit a foliation by constant mean curvature slices with $h^{ij} \Delta^\prime K_{ij} = 0$. This last requirement is quite non-trivial, though it has been shown numerically that it continues to allow Schwarzschild-de Sitter black holes~\cite{Nakao:1990gw}. Results from the asymptotically flat case~\cite{Isenberg:1997re,FischerMoncrief1997} suggest that constructing a phase space of such solutions is non-trivial, but possible with the right understanding. Due to the similarities with \cite{KastorCKV,LuoPositiveMass}, we expect that our charges would again fail to be finite on such a phase space, but this remains to be shown in detail.
\section*{Acknowledgements}
We thank Tomas Andrad\'e, Curtis Asplund, Andy Strominger, Jennie Traschen, and David Kastor for interesting discussions concerning de Sitter charges. We also thank Alejandra Castro, Matthias Gaberdiel, and Alex Maloney for discussions related to the algebra \eqref{ccharge}. Finally we thank an anonymous referee for identifying an error in a previous draft. This work was supported in part by the National Science Foundation under Grant No PHY08-55415, and by funds from the University of California.
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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Q: Qt ODBC driver crashes on QDatabase::open() OS X While trying to connect to a MS SQL database the app crashes.
QSqlDatabase db = QSqlDatabase::addDatabase("QODBC");
db.setHostName("test");
db.setDatabaseName("test");
db.setUserName("test");
db.setPassword("test");
qDebug() << "Is driver available:" << db.isDriverAvailable("QODBC");
qDebug() << "Drivers:" << db.drivers();
qDebug() << "Db is valid:" << db.isValid();
qDebug() << "Last error:" << db.lastError();
if (!db.open()) // Crashes here
qDebug() << "Database error";
I saw some posts where unixODBC and FreeTDS is a solution but I was unable to get it working.
The output of qDebug() calls is:
Is driver available: true
Drivers: ("QSQLITE", "QMYSQL", "QMYSQL3", "QODBC", "QODBC3", "QPSQL", "QPSQL7")
Db is valid: true
Last error: QSqlError("", "", "")
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,807
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Lady Muriel Evelyn Vernon Paget CBE DStJ (19 August 1876 – 16 June 1938) was a British philanthropist and humanitarian relief worker, initially based in London, and later in Eastern and Central Europe. She was made an OBE in 1918 and promoted to CBE in 1938. She received awards in recognition of her humanitarian work from the governments of Belgium, Czechoslovakia, Estonia, Japan, Latvia, Lithuania, Romania, and Imperial Russia. In 1916 she was invested as a Dame of Grace of the Order of St John.
Family
Lady Muriel Finch-Hatton was the elder of the two children of Murray Finch-Hatton, 12th Earl of Winchilsea, of Haverholme Priory, Lincolnshire. She was educated privately at home. Her brother George, Viscount Maidstone, to whom she was greatly attached, died aged nine, in 1892.
She married Richard Arthur Surtees Paget (who later became the second Baronet Paget of Cranmore) on 31 May 1897. They had five children, the first of whom (Richard Hatton Harcourt Paget; 6 March 1898 – October 1898) died in infancy. The surviving children were:
Sylvia Mary Paget, Lady Chancellor (10 July 1901 – 29 October 1996); married Sir Christopher Chancellor
Pamela Winefred Paget, Lady Glenconner (7 August 1903 – 1989); married Christopher Tennant, Baron Glenconner
Angela Sibell Paget, Lady Debenham (14 November 1906 – 16 June 1965); married Sir Piers Debenham Bt.
Sir John Starr Paget (25 November 1914 – 1992); married Nancy Mary Parish, great-granddaughter of William Ewart Gladstone, four times Prime Minister of the United Kingdom.
The invalid kitchens of London
After an initial involvement in co-founding the Children's Order of Chivalry, a society that linked wealthy children with poor London children, Lady Muriel became involved in charity work when, in 1905, she responded to a suggestion made by an aunt that she might take up the post of honorary secretary of a charity seeking to establish a kitchen in Southwark (the Southwark Invalid Kitchen). The aim of this charity was to provide, at the nominal cost of 1d, well-prepared and nourishing meals for expectant and nursing mothers, sick children, and convalescents whose would otherwise have been unable to afford them. The kitchen was situated in Scovell Road, with meals being served between 12 noon and 1 p.m. Later on, the charity's rules were revised and the charges were assessed according to the earning capacity of each individual's family. The intention was that these meals would be provided to cases recommended by a doctor, a hospital, or by other approved agencies.
Through fundraising, similar kitchens were later founded in various other areas of London through the Invalid Kitchens of London movement (which evolved from the Southwark Invalid Kitchen), under the patronage of Queen Mary. After the outbreak of the First World War, it necessary to increase the number of kitchens dramatically, partly because so many hospital places had to be allocated for the treatment of wounded soldiers (which meant that other patients were obliged to convalesce at home), and partly because there were wounded soldiers who themselves were recovering at home rather than in the hospitals. In 1915, the number of kitchens increased from 17 to 29, although the numbers tended to fluctuate in proportion to the amount of funding available.
The work of the Invalid Kitchens of London continued after the War. A new kitchen was opened by the Duchess of Somerset at Windsor Street, Essex Road on 17 November 1920. Three thousand more dinners had been served in 1920 when compared with 1919, and a Christmas appeal for £10,000 was launched that December. Lady Muriel was still the honorary secretary of the organisation at that time.
War work in connection with the Eastern Front
In 1915, concerned by what she had learned of the situation on the Russian front, Lady Muriel traveled to Petrograd, where she and her friend Lady Sybil Grey set up the Anglo-Russian Hospital for treatment of wounded soldiers. This was based in the Dmitri Palace, and was formally opened on 19 January 1916 (O.S.). The Empress Alexandra Feodorovna was involved in the funding of this project, and other major donations came from the UK. In 1916 Lady Muriel also established a number of field hospitals and food kitchens in Ukraine.
In 1917, to raise funds for the Anglo-Russian hospitals, she organized a large Russian exhibition on the theme of "Russia in Peace and War" at the Grafton Galleries in London, which ran through May of that year. The exhibition included a series of Russian concerts (where Feodor Chaliapin sang to raise money for her), lectures on various Russian-related topics, dramatic performances of Anton Chekhov and Leo Tolstoy, etc. The opening ceremony, presided over by Lord French, was preceded by a Russian Orthodox religious service.
Shortly after the exhibition, she returned to Russia. However, in February 1918, in the wake of the Bolshevik coup d'état, the majority of the British staff at the Anglo-Russian Hospital in Petrograd returned to the UK, leaving a Russian Red Cross commission with supplies for a further six months. Lady Muriel remained in Ukraine, but she, along with three of her nursing sisters and a doctor, a number of British civilians, and the British diplomat John Picton Bagge, had to be evacuated from Russia very soon afterwards, traveling back to the UK via Moscow, Vladivostok, Tokyo (17 April), Toronto (7 May), and the United States. In the party with her was Dr. Thomas Marsdon, a pseudonym for Dr. Thomas Masaryk, who escaped incognito from Eastern Europe.
An account of what she had seen and experienced in the weeks following the revolution was published in the New York Times. She arrived in London on 9 July, and was received by the King and Queen a week later. She took the opportunity to call British attention to the urgent appeals for aid and assistance being made in the US by Lt.-Col. Maria Bochkareva, foundress of the Russian Women's Battalion of Death.
The years after World War I: an overview
Shortly after the end of the War, Lady Muriel returned to Russia to continue her work, and then in 1920, she directed a mission to Latvia, where she set up access to free kitchens, free medical aid and free clothing. She also inaugurated a system of travelling clinics for the benefit of those living in remote areas, and provided a new hospital at Daugavpils. During the following years, she performed similar work in Estonia, Lithuania, Poland, Czechoslovakia, and Romania, at the request of Queen Marie of Romania who became a good friend. She and her team of British nurses and volunteers laid particular emphasis on teaching the local populations the importance of taking precautions to prevent the outbreak and spread of diseases, and in some cases she arranged for nurses from these countries to receive medical training in Britain.
Czechoslovakia
In February 1919, following an urgent appeal from Dr. Alice Masaryková (a.k.a. Alice G. Masaryk), chair of the Czechoslovak Red Cross and daughter of the country's first president, Dr. Thomas Masaryk, a relief mission of the British Red Cross was dispatched with the aim of supplying Czechoslovakia with hospital necessities, milk, clothing and blankets. Lady Muriel left London on the night of 18/19 February for Prague, taking with her a consignment of medical supplies. By 12 March 1919 a new Anglo-Czech Relief Fund had been set up in London under the War Charities Act of 1916, and she remained in Prague to oversee the distribution of the goods which were sent.
To ascertain conditions in Czechoslovakia, Lady Muriel traveled over 3,000 miles by car over a six-week period to investigate. She later reported that some of the problems were caused by rampant inflation (the price of clothing, she maintained, was 1,000% higher, when compared with the pre-war rates); others had arisen because during the Russian occupation there had been widespread commandeering. Cultivation was poor, the potato crop had been destroyed, and some peasants had gone to Hungary to work there for the harvest season as was usual, only to find that they were taken prisoner by the Bolsheviks, with the result that their families at home were left without support.
Displaced British subjects in the USSR
A small number of British residents in the Soviet Union were unable (for example, because of age or infirmity or poverty) – or in a few cases, unwilling – to leave Russia after the October Revolution of 1917. Since many of these were associated, in the minds of the Soviet authorities, with the employment in which they had been engaged under the Old Regime (e.g. private tutors, governesses, technical or clerical staff with British companies), their position became highly vulnerable, even though they might have married into Russian families or (in certain instances) they may have been born and brought up in Russia and spoke little or no English at all.
The British Government contributed a small amount into a fund whose purpose was to provide assistance to these expatriates in cases of particularly urgent need, and a similarly small amount had, since 1924, been allocated from Lady Paget's fund with the same intention. Soon after diplomatic relations between Britain and the USSR resumed in October 1929 (they had been broken off in May 1927), Lady Muriel decided to go to Leningrad to bring assistance. She arrived there early in 1930.
As a result of her initiatives, which included the establishment in a British Subjects in Russia Relief Organization in England, a dacha was eventually built at Detskoye Selo. This small country house was intended to serve as a retirement and convalescent home for displaced British Subjects. After some delays, the dacha opened in 1933, and was placed under the supervision of a Mrs Morley (formerly a matron at Newnham College, Cambridge). Earlier a flat in Leningrad had been obtained for a similar purpose.
Rakovsky's statement – questions in the House of Commons
In March 1938 Christian Rakovsky, a former Soviet ambassador to the United Kingdom who was on trial in Moscow for treason, made a statement to the court in which he declared that he had first begun spying for Britain in 1924, and, furthermore, that he had recommenced his espionage activities in 1934 at the express request of Lady Muriel Paget. Rakovsky's statement prompted questions in the House of Commons. On 9 March 1938, Miss Ellen Wilkinson (Labour Party MP for Jarrow) claimed Lady Muriel had "been lecturing on (her) experiences as (a member) of the British Intelligence Services".
Prime Minister Chamberlain replied that Lady Muriel had "no experience in the British Intelligence Service" and stressed that her work was "thoroughly unselfish and humanitarian". Wilkinson retorted that "those who know something about her work have reason to doubt the statement just made by the Prime Minister", and Willie Gallacher (Communist Party member for Fife West) asserted that Rakovsky was telling the truth. Chamberlain reiterated that none of the British subjects' names mentioned at the trial had ever worked for British Intelligence services, and William Leach (Labour, Bradford Central) urged the Prime Minister to take steps "to protect the innocent victims of these fantastic stories". Shortly afterwards the dacha was closed.
Death
Lady Muriel Paget died of cancer in 1938, aged 61. She was buried at Cranmore, Somerset. Her home from 1901 to 1902, 10 Cornwall Terrace, Regent's Park, London is named Paget House after her.
References
Further reading
Blunt, Wilfrid, Lady Muriel: Lady Muriel Paget, her Husband, and her Philanthropic Work in Central and Eastern Europe. London, Methuen & Co., 1962. .
1876 births
1938 deaths
British philanthropists
British humanitarians
British women in World War I
Commanders of the Order of the British Empire
Dames of Grace of the Order of St John
Daughters of British earls
Deaths from cancer in England
People from North Kesteven District
Place of death missing
Wives of baronets
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import React from 'react';
import { HashRouter as Router } from 'react-router-dom';
import Navigation from './Navigation';
import Footer from './Footer';
import Main from './Main';
import AppWrapper from './AppWrapper';
const App = () => (
<Router>
<AppWrapper>
<Navigation />
<Main />
<Footer />
</AppWrapper>
</Router>
);
export default App;
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"redpajama_set_name": "RedPajamaGithub"
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{"url":"https:\/\/deepai.org\/publication\/detecting-conflicting-summary-statistics-in-likelihood-free-inference","text":"# Detecting conflicting summary statistics in likelihood-free inference\n\nBayesian likelihood-free methods implement Bayesian inference using simulation of data from the model to substitute for intractable likelihood evaluations. Most likelihood-free inference methods replace the full data set with a summary statistic before performing Bayesian inference, and the choice of this statistic is often difficult. The summary statistic should be low-dimensional for computational reasons, while retaining as much information as possible about the parameter. Using a recent idea from the interpretable machine learning literature, we develop some regression-based diagnostic methods which are useful for detecting when different parts of a summary statistic vector contain conflicting information about the model parameters. Conflicts of this kind complicate summary statistic choice, and detecting them can be insightful about model deficiencies and guide model improvement. The diagnostic methods developed are based on regression approaches to likelihood-free inference, in which the regression model estimates the posterior density using summary statistics as features. Deletion and imputation of part of the summary statistic vector within the regression model can remove conflicts and approximate posterior distributions for summary statistic subsets. A larger than expected change in the estimated posterior density following deletion and imputation can indicate a conflict in which inferences of interest are affected. The usefulness of the new methods is demonstrated in a number of real examples.\n\n## Authors\n\n\u2022 2 publications\n\u2022 3 publications\n\u2022 20 publications\n\u2022 9 publications\n\u2022 ### Non-linear regression models for Approximate Bayesian Computation\n\nApproximate Bayesian inference on the basis of summary statistics is wel...\n09\/24\/2008 \u2219 by M. G. B. Blum, et al. \u2219 0\n\n\u2022 ### On deletion diagnostic statistic in regression\n\nA brief review about choosing a normalizing or scaling matrix for deleti...\n12\/28\/2020 \u2219 by Myung Geun Kim, et al. \u2219 0\n\n\u2022 ### A Comparison of Likelihood-Free Methods With and Without Summary Statistics\n\nLikelihood-free methods are useful for parameter estimation of complex m...\n03\/03\/2021 \u2219 by Christopher Drovandi, et al. \u2219 0\n\n\u2022 ### Towards constraining warm dark matter with stellar streams through neural simulation-based inference\n\nA statistical analysis of the observed perturbations in the density of s...\n11\/30\/2020 \u2219 by Joeri Hermans, et al. \u2219 5\n\n\u2022 ### On Model Selection with Summary Statistics\n\nRecently, many authors have cast doubts on the validity of ABC model cho...\n03\/28\/2018 \u2219 by Erlis Ruli, et al. \u2219 0\n\n\u2022 ### Robust and integrative Bayesian neural networks for likelihood-free parameter inference\n\nState-of-the-art neural network-based methods for learning summary stati...\n02\/12\/2021 \u2219 by Fredrik Wrede, et al. \u2219 12\n\n\u2022 ### Parameter inference and model comparison using theoretical predictions from noisy simulations\n\nWhen inferring unknown parameters or comparing different models, data mu...\n09\/21\/2018 \u2219 by Niall Jeffrey, et al. \u2219 0\n\n##### This week in AI\n\nGet the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.\n\n## 1 Introduction\n\nOften scientific knowledge relevant to statistical model development comes in the form of a possible generative process for the data. Computation of the likelihood is sometimes intractable for models specified in this way, and then likelihood-free inference methods can be used if simulation of data from the model is easily done. A first step in most likelihood-free inference algorithms is to reduce the full data set to a low-dimensional summary statistic, which is used to define a distance for comparing observed and simulated data sets. The choice of this summary statistic must be done carefully, balancing computational and statistical considerations (Blum et al., 2013). Once summary statistics are chosen, Bayesian likelihood-free inference can proceed using a variety of techniques, such as approximate Bayesian computation (ABC) (Marin et al., 2012; Sisson et al., 2018a) synthetic likelihood (Wood, 2010; Price et al., 2018) or regression based approaches (Beaumont et al., 2002; Blum and Fran\u00e7ois, 2010; Fan et al., 2013; Raynal et al., 2018).\n\nSometimes different components of the summary statistic vector bring conflicting information about the model parameter. This can arise due to model deficiencies that we wish to be aware of, and can complicate summary statistic choice. Furthermore, it can lead to computational difficulties when observed summary statistics are hard to match under the assumed model. We develop some diagnostics for detecting when this problem occurs, based on a recent idea in the interpretable machine learning literature. The suggested diagnostics are used in conjunction with regression-based approaches to likelihood-free inference.\n\nThe following example of inference on a Poisson mean, which is discussed in Sisson et al. (2018b), illustrates the motivation for our work. Here the likelihood is tractable, but the example is useful for pedagogical purposes. Suppose data are observed, and that we model as a Poisson random sample with mean . For Bayesian inference we use a prior density for . The gamma prior is conjugate, and the posterior density is , where is the sample mean of . Letting\n\ndenote the sample variance of\n\n, both and are point estimates of , since for the Poisson model the mean and variance are equal to ; furthermore, is a minimal sufficient statistic.\n\nConsider a standard rejection ABC method for this problem, which involves generating values from the prior, generating summary statistics under the model conditional on the generated values, and then keeping the values which lead to simulated summary statistics closest to those observed. See Sisson et al. (2018b) for further discussion of basic ABC methods. Consider first the summary statistic , and apply rejection ABC with prior samples and retaining of these in the ABC rejection step. This gives a very close approximation to the true posterior (Figure 1).\n\nThe computations were implemented using the default implementation of rejection ABC in the R package abc (Csill\u00e9ry et al., 2012). Reduction of the full data to involves no loss of information, as is sufficient.\n\nSince we observe values of and , these summaries bring conflicting information about , since they are both point estimates of and take quite different values. If we consider the summary statistic , and apply the same rejection ABC algorithm as before with prior samples and accepted samples, the estimated posterior density changes appreciably \u2013 see Figure 1. Although is still sufficient, and the corresponding posterior is the same as the posterior given , the ABC computational algorithm performs poorly because the observed summary statistic is hard to match with a reasonable fixed computational budget. Simultaneously observing and is unusual under the assumed model for any value of the model parameter. This results in accepting parameter samples having simulated summary statistic values far away from the observed value of . Also shown in Figure 1 is the posterior conditional on , which is even further from the true posterior than the posterior conditional on .\n\nThe conflicting information in the summary statistics and may indicate a model failure, motivating a more flexible model than the Poisson, such as negative binomial, in which the mean and variance are not required to be equal. Sisson et al. (2018b) considered this example partly as a demonstration of the difficulties which arise in greedy algorithms for summary statistic choice. An analyst following a policy of adding one summary statistic at a time, and stopping when the posterior density no longer changes appreciably, would incorrectly judge to be a better summary statistic than . Our example illustrates that if different parts of a summary statistic vector are conflicting, then detecting this can be insightful about model failures and can suggest model improvements. This is the motivation for the conflict detection diagnostics developed here.\n\nThe structure of the paper is as follows. In the next Section we describe regression approaches to likelihood-free inference. Section 3 then discusses a recent suggestion in the literature on interpretable machine learning, which has the goal of explaining how a flexible classifier makes the class prediction it does for a certain observation. This method is based on deletion of part of a feature vector, followed by imputation of what was deleted and assessment of how evidence for the observed class changes following the deletion and imputation process. In regression approaches to computing likelihood-free inferences, where regression models are considered with simulated parameters as the response values and simulated summary statistics as features, we show that a similar approach can be used to estimate the changes in a posterior distribution under sequential updating for summary statistic subsets. If the change in the posterior density is larger than expected when a subset of summary statistics is deleted, this may indicate that different parts of the summary statistic vector carry conflicting information about the parameter.\n\nIn Section 4, our diagnostics are formalized and placed in the broader framework of Bayesian model checking. We make connections with the literature on prior-data conflict, suggest a method of calibration, and also review related literature on model checking for likelihood-free methods. Section 5 considers three examples. First we revisit the pedagogical example above and show how our diagnostics apply in that simple case, before considering two further real examples. The first real example considers data on stereological extremes, where the model is not flexible enough to fit well in both the lower and upper tails. The second example concerns an ecological time series model. An analysis of these data using summary statistics derived from an auxiliary threshold autoregressive model is first considered, where the summary statistics can be thought of as capturing the different dynamic behaviour of the time series at high and low levels. Conflicts between summary statistic subsets for different regimes are insightful for understanding deficiencies in the original model. An analysis of these data without summary statistics is also considered, where the regression model is based on a convolutional neural network, and the feature vector consists of the whole time series. Here we explore temporally localized parts of the series not fitted well by the model. Section 6 gives some concluding discussion.\n\n## 2 Regression approaches to likelihood-free inference\n\nConsider a Bayesian inference problem with data\n\nand a parametric model for\n\nwith density , with parameter . The prior density for is denoted , with corresponding posterior density , where denotes the observed value of . Suppose that computation of the likelihood is intractable, so that likelihood-free inference approaches are needed to approximate the posterior distribution. In this case, we can consider summary statistics , with , and writing for the sampling density of , we use likelihood-free inference methods to approximate .\n\nThe posterior density is the conditional density of given in the joint Bayesian model for specified by . Since regression is conditional density estimation, we can fit regression models to samples , from in order to estimate for any . The responses are , and the features are . The regression predictive density given , denoted , is an estimate of .\n\nThere are many flexible regression approaches that have been applied to computation of likelihood-free inferences, such as quantile regression forests\n\n(Meinshausen, 2006; Raynal et al., 2018), copula methods (Li et al., 2017; Fan et al., 2013; Klein et al., 2019), neural approaches of various kinds (Papamakarios and Murray, 2016; Papamakarios et al., 2019) and orthogonal series methods (Izbicki and Lee, 2017; Izbicki et al., 2019) among others. In our later applications to the detection of conflicting information in summary statistics we will be concerned with the effects of conflict on inference for scalar functions of the parameter, and so only univariate regression models are needed for estimating one-dimensional marginal posterior distributions. To save notation we will use the notation both for the model parameter as well as a one-dimensional function of interest of it, where the meaning intended will be clear from the context.\n\nIn checking for summary statistic conflicts, we will partition as and we ask if the information about in conflicts with that in . We write . Our conflict diagnostic will compare an estimate of to an estimate of . If the change in the estimated posterior distribution is large, this may indicate that the summary statistics carrying conflicting information about the parameter . We must define what large means, and this is an issue of calibration of the diagnostics.\n\nTo overcome the computational difficulties of estimating the posterior distributions, we will first consider a likelihood-free regression method with features to compute . Then based on this same regression, the method of Zintgraf et al. (2017) described in Section 3 will be used to approximate by deletion and multiple imputation of . This can be done without refitting the regression. This last point is important, because sometimes fitting very flexible regression models can be computationally burdensome. For example, in the application of Section 5.2, we consider a training sample of observations, where we fit a quantile regression forest in which algorithm fitting parameters are tuned by cross-validation. Applying the method of Zintgraf et al. (2017) for approximating the posterior density given , using the fitted regression with features , is much less computationally demanding than refitting the regression with features to approximate the subset posterior density directly. Since we may wish to consider many different choices of and for diagnostic purposes, this is another reason to avoid the approach of refitting the regression model with different choices of the features.\n\nAlthough the main idea of our method is to compare estimates of and , making this precise will involve the development of some further background. We describe the method of Zintgraf et al. (2017) next, and then in Section 4 we formalize our diagnostics and consider connections to the existing literature on Bayesian model checking.\n\n## 3 Interpretable machine learning using imputation\n\nWe describe a method developed in Zintgraf et al. (2017)\n\nfor visualizing classifications made by a deep neural network. Their approach builds on earlier work of\n\nRobnik-\u0160ikonja and Kononenko (2008)\n\n. The method deletes part of a feature vector, and then replaces the deleted part with an imputation based on the other features. The change in the observed class probability is then examined to measure of how important the deleted features were to the classification made. To avoid repetition, the discussion below will be concerned with a general regression model where the response variable can be continuous or discrete, although\n\nZintgraf et al. (2017) deals only with the case where the response is a discrete class label. It is the case of regression models with a continuous response that is relevant to our discussion of likelihood-free inference.\n\nSuppose that , are response and feature vector pairs in some training set of observations. The feature vectors are -dimensional, written as . We assume the responses are scalar valued, although extension to multivariate responses is possible. Write and so that is an -vector and is an matrix. We consider Bayesian inference in this regression model with a prior density for , and likelihood . Note the different notation here to Section 2, where we considered a likelihood-free inference problem with data and parameter . Here and are the responses and features in the regression, and in likelihood-free regression the features will be simulated summary statistics, whereas the responses are simulated values of the parameters , hence the different notation. More precisely, in the likelihood-free problems of interest to us, and in the notation of Section 2, and , .\n\nThe posterior density of in the regression model is\n\n p(\u03b8|Y,X) \u221dp(\u03b8)p(Y|\u03b8,X).\n\nFor some feature vector , and corresponding value of interest for the response , we can compute the predictive density of given as\n\n p(y\u2217|x\u2217,Y,X) =\u222bp(y\u2217|\u03b8,x\u2217)p(\u03b8|Y,X)d\u03b8,\n\nwhere is the likelihood term for and it is assumed that is conditionally independent of given and .\n\nSuppose that some subector of is not observed, say the th component . Assume that the features are modelled as independent and identically distributed from a density , where the parameters are disjoint from , and that and are independent in the prior. We write for with deleted. Then under the above assumptions,\n\n p(y\u2217|x\u2217\u2212i,X,Y) =\u222bp(y\u2217|x\u2217,Y,X)p(x\u2217i|x\u2217\u2212i,X)dx\u2217i, (1)\n\nwhere\n\n p(x\u2217i|x\u2217\u2212i,X) =\u222bp(x\u2217i|x\u2217\u2212i,\u03bb)p(\u03bb|X)d\u03bb.\n\nEquation (1) says that to get we can average over the distribution of where is imputed from . In the discussion above only deletion of the th component of has been considered, but the generalization to removing arbitrary subsets of is immediate. In the likelihood-free problems discussed later, the expression (1) will give us a way of estimating the posterior distribution of based on summary statistic subsets using a regression fitted using the full set of summary statistics and a convenient imputation model. We will partition the summary statistic as , and then with and where is the observed value of , the formula (1) will give us a way of estimating the posterior distributon based on the regression predictive distribution using features .\n\nIn practice we might approximate as for some point estimate of . For example, we might assume a multivariate normal model for (in which case is the mean and covariance matrix of the normal model) and plug in the sample mean and covariance matrix as the point estimate. This is the approach considered in Zintgraf et al. (2017). Robnik-\u0160ikonja and Kononenko (2008) assumed the features to be independent in their model. Zintgraf et al. (2017) note that more sophisticated imputation methods can be used. We can also approximate by for some point estimate of .\n\nIn the case of a classification problem where the response is a class label, we can follow Zintgraf et al. (2017) and Robnik-\u0160ikonja and Kononenko (2008) and measure how much class probabilities have changed upon deletion and imputation of using an evidence measure, called weight of evidence:\n\n WE(y\u2217|x\u2217) =log2{p(y\u2217|x\u2217,Y,X)1\u2212p(y\u2217|x\u2217,Y,X)}\u2212log2{p(y\u2217|x\u2217\u2212i,Y,X)1\u2212p(y\u2217|x\u2217\u2212i,Y,X)}. (2)\n\nis positive (negative) if observing rather than imputing it from makes the class more (less) probable. Zintgraf et al. (2017) generally consider the observed class for . Measures of evidence suitable for the regression context are considered further in the next section.\n\nZintgraf et al. (2017) consider problems in image classification where the feature vector is a vector of intensities of pixels in an image. Because of the smoothness of images, if only one pixel is deleted, then it can be imputed very accurately from its neighbours. If this is the case, is not useful for measuring the importance of a pixel to the classification. Zintgraf et al. (2017) suggest to measure pixel importance by deleting all image patches of a certain size, and then average weight of evidence measures for patches that contain a certain pixel. They plot images of the averaged weight of evidence measure as a way of visualizing the importance of different parts of an image for a classification made by the network. They also consider deletion and imputation for latent quantities in deep neural network models.\n\nAn appropriate imputation method will vary according to the problem at hand, and there is no single method that will be appropriate for all problems. In our later examples for computing likelihood-free inferences we consider three different imputation methods. The first uses linear regression in a situation where the features are approximately linearly related, and we use the implementation in the\n\nmice package in R (van Buuren and Groothuis-Oudshoorn, 2011)\n\n. The second is based on random forests, as implemented in the\n\nmissRanger package (Mayer, 2019). Our final example considers time series data, and in the application where we consider the raw series as the feature vector, we use the methods in the imputeTS package (Moritz and Bartz-Beielstein, 2017). Further details are given in Section 5.\n\n## 4 The diagnostic method\n\nIn the notation of Section 2, the method of Zintgraf et al. (2017) will allow us to estimate the posterior density , from a regression using the full set of summary statistics as the features. This is described in more detail in Section 4.2 below. We can then compare estimates of and . If the difference between these two posterior distributions is large, then it indicates that different values of the parameter are providing a good fit to the data in the likelihood terms and , indicating a possible model failure. The weight of evidence measure of Zintgraf et al. (2017) doesn\u2019t apply directly as a way of numerically describing the difference in the posterior distributions and in the likelihood-free application. Here we use measures of discrepancy considered in the prior-data conflict checking literature (Nott et al., 2020) based on the concept of relative belief (Evans, 2015) instead of weight of evidence. We place our diagnostics within the framework of Bayesian model checking, and this suggests a method for calibrating the diagnostics. The discussion of prior-data conflict checking is relevant here, because the comparison of to can be thought of as a prior-to-posterior comparison in the situation where has already been observed, and then is the prior for further updating by the likelilhood term . A more detailed explanation of this is given below.\n\n### 4.1 Prior-data conflict checking\n\nPrior-data conflicts occur if there are values of the model parameter that receive likelihood support, but the prior does not put any weight on them (Evans and Moshonov, 2006; Presanis et al., 2013). In other words, prior-data conflict occurs when the prior puts all its mass out in the tails of the likelihood. Nott et al. (2020) consider some methods for checking for prior-data conflict based on prior-to-posterior divergences. In the present setting of a posterior density for summary statistics and with prior , the checks of Nott et al. (2020) would check for conflict between and using a prior-to-posterior -divergence (R\u00e9nyi, 1961) taking the form\n\n R\u03b1(S) (3)\n\nwhere . These divergences are related to relative belief functions (Evans, 2015) measuring evidence in terms of the prior-to-posterior change. Consider a function of . We define the relative belief function for as\n\n RB(\u03c8|d) =p(\u03c8|d)p(\u03c8)=p(d|\u03c8)p(d), (4)\n\nwhere is the posterior density for given , is the prior density, is the marginal likelihood given , and is the prior predictive density at . For a given value of , if , this means there is evidence in favour of , whereas if there is evidence against. See Evans (2015) for a deeper discussion of reasons why relative belief is an attractive measure of evidence, and for a systematic approach to inference based on it.\n\nAs , (3\n\n) gives the prior-to-posterior Kullback-Leibler divergence (which is the posterior expectation of\n\n), and letting gives the maximum value of the log relative belief, . So the statistic (3) is a measure of the overall size of a relative belief function, and a measure of how much our beliefs have changed from prior to posterior. Nott et al. (2020) suggest to compare the value of to the distribution of , where is the prior predictive density for ,\n\n p(S) =\u222bp(S|\u03b7)p(\u03b7)d\u03b7,\n\nby using the tail probability\n\n pS =P(R\u03b1(S)\u2265R\u03b1(Sobs)). (5)\n\nThe tail probability (5) is the probability that the overall size of the relative belief function RB is large compared to what is expected for data following the prior predictive density . So a small value for the tail probability (5) suggest the prior and likelihood contain conflicting information, as the change from prior to posterior is larger than expected. See Evans and Moshonov (2006) and Nott et al. (2020) for further discussion of prior-data conflict checking, and why the check in Nott et al. (2020) satisfies certain logical requirements for such a check.\n\n### 4.2 Definition of the diagnostics\n\nIn the present work, we have a summary statistic partitioned as , and it is conflict between and that interests us. This is related to prior-data conflict checking in the following way. Suppose that we have the posterior density . We can regard as a prior density to be updated by the likelihood term to get the posterior density . That is, . The density usefully reflects information in about , if we have checked both the model for and for prior-data conflict between and in conventional ways. If updating by the information in gives a posterior density that is surprisingly far from , this indicates that and bring conflicting information about . The appropriate reference distribution for the check is\n\n p(SB|SA) =\u222bp(SB|SA,\u03b7)p(\u03b7|SA)d\u03b7,\n\nsince we are conditioning on in the prior that reflects knowledge of before updating for .\n\nSuppose that the regression model used for the likelihood-free inference gives an approximate posterior density for summary statistic value . The change in the approximate posterior when deleting from can be examined using a mulitple imputation procedure, using the method of Zintgraf et al. (2017). We produce imputations , of and writing and following (1) we approximate by\n\n \u02dcp(\u03b7|SA,obs) =1MM\u2211i=1\u02dcp(\u03b7|S(i)).\n\nThe change in the approximate posterior density from to can be summarized by the maximum log relative belief\n\n R\u221e(SB,obs|SA,obs) =sup\u03b7log\u02dcp(\u03b7|Sobs)\u02dcp(\u03b7|SA,obs). (6)\n\nOur discussion of the prior-data conflict checks of Nott et al. (2020) suggests that an appropriate reference distribution for calibrating a Bayesian model check using (6) would compute the tail probability\n\n p =P(R\u221e(SB|SA,obs)\u2265R\u221e(SB,% obs|SA,obs)), (7)\n\nwhere . The imputations in the multiple imputation procedure approximate draws from , and we suggest drawing a fresh set of imputations , , separate from those used in computing , and to approximate (7) by\n\n \u02dcp =1M\u2217M\u2217\u2211i=1I(R\u221e(S\u2217B(i)|SA,obs)\u2265R\u221e(SB,obs|SA,obs)), (8)\n\nwhere is the indicator function which is when event occurs and zero otherwise. Our suggested checks use the statistic (6), calibrated using the estimated tail probability (8).\n\n### 4.3 The logic of Bayesian model checking\n\nEvans and Moshonov (2006) discuss a strategy for model checking based on a decomposition of the joint Bayesian model , generalizing an earlier approach due to Box (1980). Different terms in the decomposition should be used for different purposes such as inference and checking of different model components. We do not discuss their approach in detail, but an important principle is that for checking model components we should check the sampling model first, and only afterwards check for prior-data conflict. The reason is that if the model for the data is inadequate, sound inferences cannot result no matter what the prior is.\n\nIn our analysis, the posterior distribution for is\n\n p(\u03b7|Sobs) \u221dp(\u03b7)p(Sobs|\u03b7). (9)\n\nOur diagnostics consider sequential Bayesian updating in two stages,\n\n p(\u03b7|SA,obs) \u221dp(\u03b7)p(SA,obs|\u03b7), (10)\n\nand\n\n p(\u03b7|Sobs) \u221dp(\u03b7|SA,obs)p(SB,obs|SA,obs%\u00a0,\u03b7). (11)\n\nIn (10), we can check the sampling model and then check for conflict between and , and if these checks are passed, then usefully reflects information about in . We could then proceed to check the components in (11). Checking in (10) and then in (11) is not the same as checking in (9). The reason is that there can be values of providing a good fit to the data for and values of providing a good fit to the data in , but these need not be the same parameter values.\n\nFormally, we could imagine an expansion of the original model from\n\n p(S|\u03b7) =p(SA|\u03b7)p(SB|SA,\u03b7), (12)\n\nto\n\n p(S|\u03b71,\u03b72) =p(SA|\u03b71)p(SB|SA,\u03b72), (13)\n\nso that the original parameter is now allowed to vary between the two likelihood terms, with the original model corresponding to . If a good fit to the data can only be obtained with , one would expect that our diagnostics would detect this, as the likelihood terms are peaked in different regions of the parameter space, and this will become evident in the sequential updating of the posterior for the different summary statistic subsets.\n\nThe inherent asymmetry in and in the decomposition (12) has consequences for interpretation of the diagnostics. To explain this, consider once more the toy Poisson model in the introduction. Consider first and . Since is sufficient, we have , and our diagnostics would not detect any conflict. However, conventional model checking of the likelihood term would detect that the model fits poorly in this case. On the other hand, if and , then the term depends on since is non-sufficient, and is very different to . In this case, our diagnostics do indeed reveal the conflict as we show later in Section 5.1. The idea of a conflict between summary statistics is being formalized here in terms of conflict between the likelihood terms and and this is not symmetric in and . There is nothing wrong with this, but the interpretation of the diagnostics needs to be properly understood.\n\n### 4.4 Other work on model criticism for likelihood-free inference\n\nWe discuss now related work on Bayesian model criticism for likelihood-free inference, which is an active area of current research. Theoretical examinations of ABC methods under model misspecification have been given recently by Ridgway (2017) and Frazier et al. (2020b). The latter authors contrast the behaviour of rejection ABC and regression adjusted ABC methods (Beaumont et al., 2002; Blum and Fran\u00e7ois, 2010; Li and Fearnhead, 2018) in the case of incompatible summary statistics, where the observed summary statistics can\u2019t be matched by the model for any parameter. Regression adjustment methods can behave in undesirable ways under incompatibility, and the authors suggest a modified regression adjustment for this case. They develop misspecification diagnostics based on algorithm acceptance probabilities, and comparing rejection and regression-adjusted ABC inferences.\n\nRatmann et al. (2009) considered model criticism based on a reinterpretation of the algorithmic tolerance parameter in ABC. They consider a projection of data onto the ABC error, and use a certain predictive density for this error for model criticism. Ratmann et al. (2011) gives a succinct discussion of the fundamentals of the approach and computational aspects of implementation. In synthetic likelihood approaches to likelihood-free inference (Wood, 2010; Price et al., 2018) recent work of Frazier and Drovandi (2019) has considered some model expansions that are analogous to the method of Ratmann et al. (2011) for the synthetic likelihood. Their method makes Bayesian synthetic likelihood methods less sensitive to assumptions, and the posterior distribution of the expansion parameters can also be insightful about the nature of any misspecification. The work of Wilkinson (2013), although not focusing on model criticism, is also related to Ratmann et al. (2011). Wilkinson (2013) shows how the ABC tolerance can be thought of as relating to an additive \u201cmodel error\u201d, and that ABC algorithms give exact results under this interpretation. Thomas et al. (2020) discuss Bayesian optimization approaches to learning high-dimensional posterior distributions in the ABC setting in the context of the coherent loss-based Bayesian inference framework of Bissiri et al. (2016). Their work is focused on robustness to assumptions and computation in high-dimensions, rather than on methods for diagnosing model misspecification. Recent work of Frazier et al. (2020a) considers a robust ABC approach related to the model expansion synthetic likelihood method of Frazier and Drovandi (2019). This method can also be applied in conjunction with regression adjustment, and the regression adjustment approach can have better behaviour in the case of misspecification.\n\nAlso relevant to our work is some of the literature on summary statistic choice. In particuclar, Joyce and Marjoram (2008) have considered an approach to this problem which examines changes in an estimated posterior density upon addition of a new summary statistic. This is a useful method for a difficult problem, but their method is not used as a diagnostic for model misspecification, and in fact can sometimes perform poorly in exactly this situation.\n\nIn a sense, model criticism for Bayesian likelihood-free inference is conceptually no different to Bayesian model criticism with a tractable likelihood. However, issues of computation and summary statistic choice sometimes justify the use of different methods. For general discussions of principles of Bayesian model checking see Gelman et al. (1996), Bayarri and Castellanos (2007) and Evans (2015).\n\n## 5 Examples\n\n### 5.1 Poisson model\n\nWe return to the toy motivating example given in the introduction on inference for a Poisson mean, where data are observed. For these data the sample mean is and the sample variance is . In the Poisson model, and are both point estimates of the Poisson mean . The estimates bring conflicting information about the parameter, because simultaneously observing and is unlikely for any value of . Figure 1 in the introduction showed ABC estimates of the posterior density for different summary statistic choices, for the prior described in Section 1. Recall that the rejection ABC algorithm performs poorly for the summary statistic , because of the difficulty of matching the observed values, and this may indicate a poorly fitting model.\n\nWe apply the diagnostic method of Section 4 for this example, to show how it can alert the user to the conflicting information in the summaries. The summary statisitcs and are approximately linearly related to each other, since they both estimate , and so we use linear regression for imputation using the R package mice (van Buuren and Groothuis-Oudshoorn, 2011). The mice function from this package is used to generate multiple imputations with the Bayesian linear regression method and default settings for other tuning parameters. For the regression likelihood-free inference, we are using the quantile regression forests approach (Meinshausen, 2006) adapted to the ABC setting by Raynal et al. (2018) and available in the R package abcrf. For the random forests regression we use simulations from the prior, and we tune three parameters of the random forests algorithm (\u2018m.try\u2019, \u2018min.node.size\u2019 and \u2018sample.fraction\u2019) using the tuneRanger package (Probst et al., 2019). Figure 2 shows the true posterior density, and some random forests estimates of it. There are three estimates obtained from the fitted random forests regression with the full set of features . The first is based on the observed summary statistic for . The second uses the same fitted regression but replaces the observed summary statistics with , where denotes an imputed value for from the observed . With imputation the estimate shown is an average over imputed values. The third uses where is an imputed value for based on the observed . Also shown are density estimates where the regression is fitted using only features , and where the regression is fitted only using features .\n\nWe make four observations. First, using the full summary statistic with quantile regression forests results in an accurate estimate of the true posterior density, in contrast to the ABC algorithm described in the introduction. The reason for this is the variable selection capability of the quantile regression forest approach, which results in the summary statistic being ignored as it is not informative given the minimal sufficient statistic . This is what is expected for our diagnostic, following the discussion of Section 4.3. Our second observation is that imputing from results in very little change to the estimated posterior density. Again this is because the random forest regression fit ignores , and so replacing its observed value with a very different imputation is unimportant. Our third observation is that imputing from does result in a posterior density with very different inferential implications. Finally, fitting the quantile regression forest with features and then deleting and imputing one of the features for the observed data gives a similar posterior density estimate to that obtained by fitting the quantile regression with only the feature that was not deleted. This is desirable, because if we examine deletion and imputation for many subsets of features it may be computationally intensive to refit regression models repeatedly, but the imputation process is less computationally burdensome.\n\nFinally, Figure 3 illustrates our suggested calibration of for the choices , and , and . The vertical lines in the graphs are the observed statistic values, and the histograms shows reference distribution values for the statistics for imputations of from . The estimated tail probability (8) corresponds to the proportion of reference distribution values above the observed value. The change in the posterior density when is imputed from is surprisingly large (bottom panel).\n\nWhat would we do in this and similar examples once a conflict is found? In this example it is natural to change the model so that the mean and variance need not be the same (using a negative binomial model rather than Poisson, for instance). Alternatively, if the problem is such that the current model is \u201cgood enough\u201d in the sense that the fitted model reproducing aspects of the data we care about in the application at hand, we might change the summary statistics so that the conflict is removed while retaining the important information.\n\n### 5.2 Stereological extremes\n\nThe next example was discussed in Bortot et al. (2007) and examines an ellpitical model for diameters of inclusions in a block of steel. The size of the largest inclusion is thought to be an important quantity related to the steel strength. The ellpitical model, which has an intractable likelihood, extends an earlier spherical model considered in Anderson and Coles (2002). We do not give full details of the model but refer to Bortot et al. (2007) for a more detailed description.\n\nThere are 3 parameters in the model. The first is the intensity of the homogeneous Poisson point process of the inclusion locations. There are also two parameters in a model for the inclusion diameters. This model is a generalized Pareto distribution with scale parameter and shape , for diameters larger than a threshold which is taken as m. Writing , the prior density for is uniform on . The observed data consists of inclusion diameters observed from a single planar slice. The summary statistic used consists of and the quantiles of diameters at levels . Here there may be some interest in whether the simple Pareto model can fit well for the observations in the lower and upper tail simultaneously. Quantile-based summary statistics for ABC were also considered in Erhardt and Sisson (2016). It is expected that the Pareto model will fit the upper quantiles well, but using only the most extreme quantiles might result in a loss of information. Capturing the behaviour of the diameters in the upper tail is most important for the application here, given the relationship between the largest inclusions and steel strength.\n\nWe apply our diagnostic method in the following way. First, we used quantile regression forests to estimate the marginal posterior densities for each parameter , , separately, and using the full set of summary statistics, which we denote by . We can write , where denotes the vector of lower quantiles at levels and denotes the vector of upper quantiles at levels . In fitting the random forests regressions we used simulations of parameters and summary statistics from the prior, and the random forest tuning parameters were chosen using the tuneRanger package in R. We apply our diagnostic by deleting and imputing and respectively to see if there is conflicting information in the lower and upper quantiles about the parameters. The imputation is done using the R package missRanger, which uses a random forests approach (Mayer, 2019). We use the missRanger function in this package with and 20 trees with other tuning parameters set at the default values. Figure 4 shows how the estimated marginal posterior densities change for the various parameters upon deletion and imputation of and .\n\nWe make two observations. First, when the upper quantiles are imputed from the lower ones, the estimated marginal posterior densities change substantially for and , the parameters in the inclusion model. This does suggest that the Pareto model is not able to simultaneously fit the lower and upper quantiles well. Given the importance in this application of capturing the behaviour of the largest diameters, we might remove the lower quantiles from the vector of summary statistics to obtain a model that is fit for purpose. Secondly, and unlike our first example, the results of deletion and imputation do not match very well with the estimated posterior densities obtained by refitting the regression for parameter subsets directly. However, the estimates based on deletion and imputation are sufficiently good for the diagnostic purpose of revealing the conflict, and the computational burden of imputation is much less than refitting, given that our regression training set contains observations, and that algorithm parameters need to be tuned by cross-validation.\n\nFigure 5 shows our suggested calibration of for the choices , and , and . The vertical lines in the graphs are the observed statistic values, and the histograms shows reference distribution values for the statistics for imputations of from . When is imputed from (bottom row), the change in the estimated posterior density is surprising for and .\n\n### 5.3 Ricker model with threshold-autoregressive auxiliary model\n\nHere we consider a Ricker model (Ricker, 1954), a simple model for the dynamics of animal population sizes in ecology. Likelihood-free inference will be considered using summary statistics which are point estimates from an auxiliary model with tractable likelihood.\n\nThe auxiliary model is a two-component self-exiciting threshold autoregression (SETAR) model (Tong, 2011), in which the two auto-regressive components describe dynamic behaviour of the process at high and low levels respectively. Maximum likelihood estimates of the SETAR model parameters provide the summary statistics. The use of an auxiliary models with tractable likelihood is a common way to obtain summary statistics for likelihood-free inference - see Drovandi et al. (2015) for a unified discussion of such approaches. We focus on whether there is conflict between the summary statistics for the two autoregressive components in our auxiliary model. Our checks can be insightful about the ways in which the Ricker model fails to fit well at high and low levels.\n\nLet , be a series of unobserved population sizes, and suppose we observe values , where is a sampling parameter. The series has some initial value and one-step conditional distributions are defined by\n\n Nt+1 =rNtexp(\u2212Nt+et+1),\n\nwhere is a growth parameter and is an independent environmental noise series. We write for the parameters, and the prior density for is uniform on the range . The prior was chosen to achieve a reasonable scale and variation based on prior predictive simulations. The Ricker model can exhibit chaotic behaviour when the environmental noise variance is small. In this case, it can be challenging to fit the model using methods which perform state estimation to approximate the likelihood. Wood (2010) and Fasiolo et al. (2016) discuss further the motivations for using likelihood-free methods for time series models with chaotic behaviour. Model misspecification could be another reason for conditioning only on data summaries that we care about \u2013 the model for the full data may be considered as a device for implicitly defining a model for summary statistics, and it may be that we only care about good model specification for certain summary statistics important in the application.\n\nFor a time series , , the SETAR model used to obtain summary statistics takes the form\n\n Xt ={a0+a1Xt\u22121+a2Xt\u22122+\u03f5t,\u03f5t\u223cN(0,\u03c12)if\u00a0Xt\u22121\n\nIndependence is assumed at different times for the noise sequence . The parameter is a threshold parameter, and the dynamics of the process switches between two autoregressive components of order 2 depending on whether the threshold is exceeded. To obtain our summary statistics, we fit this model to the observed data, and fix based on the observed data fit. With this fixed the SETAR model is then fitted to any simulated data series to obtain maximum likelihood estimates of the SETAR model parameters, which are the summary statistics denoted by . We write , where and are maximum likelihood estimates for the autoregressive component parameters for low and high levels respectively. The SETAR models are fitted using the TAR package (Zhang and Nieto, 2017) in R. In simulating data from the model there were some cases where there were no values of the series above the threshold . Since the number of such cases was small, we simply discarded these simulations.\n\nThe observed data are a series of blowfly counts described in Nicholson (1954). Nicholson\u2019s experiments examined the effect of different feeding restrictions on blowfly population dynamics. We use the series for the adult food limitation condition shown in Figure 3 of Nicholson (1954). The Ricker model fits the blowfly data poorly, but the example is instructive for illustrating methodology for model checking. A much better model is described in Wood (2010), based on a related model considered in Gurney et al. (1980). In the model of Wood (2010), the population size is a sum of a recruitment and survival process, with the recruitment process related to previous population size at some time lag. This model is able to reproduce the strong periodicity and other complex features of the data, which the simple Ricker model does not do.\n\nWe compute ABC posterior estimates for each parameter using quantile regression forests, once again tuning algorithm parameters by cross-validation using the tuneRanger package. The quantile regression forests are fitted based on values from the prior with corresponding TAR summary statistics. We consider fitting the random forests regression using summaries , only and only. For the fit with summary statistics we consider the posterior density estimated using the observed , as well as values of where is imputed from , and where is imputed from . The imputation is done using the R package missRanger (Mayer, 2019) using the missRanger function with and 20 trees with other tuning parameters set at the default values. The results are shown in Figure 6.\n\nWe make two observations. First, the posterior density for is very different when only is used compared to either only or . This suggests that the dynamics at high and low levels of the series are inconsistent with a single fixed value of the growth parameter . Second, the posterior densities estimated using quantile regression forests with features only, are estimated quite well by the corresponding estimates using features and deletion and imputation. For the posterior densities estimated using only, they are also estimated quite well for , but not the other parameters, using features and deletion and imputation of .\n\nFigure 7 shows our suggested calibration of for the choices , and , . The vertical lines in the graphs are the observed statistic values, and the histograms shows reference distribution values for the statistics for imputations of from . When is imputed from (bottom row), the change in the estimated posterior density for is surprising.\n\n### 5.4 Ricker model without summary statistics: convolutional neural networks\n\nWe now consider using the whole time series as the feature vector in the Ricker model, and use a convolutional neural network as the regression method. Convolutional networks are not described in detail here; the reader is referred to Polson and Sokolov (2017) and Fan et al. (2019) for introductory discussions suitable for statisticians. Dinev and Gutmann (2018) considered the use of convolutional networks for automated summary statistic choice for likelihood-free inference for time series and showed that a single architecture can provide good performance in a range of problems. In fitting the convolutional network we use a squared error loss, and after obtaining point estimates for the network parameters and response variance we use a plug-in normal predictive distribution.\n\nWriting, as before, for both the full parameter , as well as some scalar function of interest (where the meaning intended is clear from the context), we estimate the marginal posterior density for from samples , . We used below. The regression model is\n\n \u03b7(i) =fw(d(i))+\u03f5(i),\n\nfor errors , where is a convolutional neural network with weights . Figure 8 shows the architecture used, which is based on the architecture shown in Figure 6 (a) of Dinev and Gutmann (2018).\n\nTraining of the network was done using the Keras API for Python, using the Adam optimizer with default settings. The model was trained for 50 epochs with a batch size of 64. After estimating\n\nas , the estimated posterior density for data is .\n\nWe wish to develop some diagnostics useful for measuring the influence of the observation at time on inference. A method is developed here similar to that of Zintgraf et al. (2017) for measuring the influence of a pixel in image classification. Deletion of \u201cwindows\u201d of the raw series containing can be considered (i.e. are the values of the series in a window of width , say, containing , and is the remainder of the series) and then we consider averages of the statistics over all windows containing . In this example we will consider windows of size , and window values are imputed from one neighbouring value to the left and right of the window. At the boundary points where only one neighbouring value is available we use this. The method is described more precisely in the Appendix, as well as our approach to the multiple imputation. When computing the maximum log relative belief statistic (6), we do not truncate the normal predictive densities for the regression model to the support of the parameter space, but we do compute the supremum over this support.\n\nFor the parameter , Figure 9 shows a plot of the raw series values with points with calibration probability for our diagnostic less than indicated by vertical lines (top panel), and a plot of the values themsleves indicated by coloured bands (bottom panel). Some of the smallest values in the series around four of the local minima are influential for the estimation of . Similar plots for the other two parameters did not show any points where the calibration probabilities are very small, except for one point near the boundary for ; however, in that case the failure of the imputation method to handle boundary cases well may be an issue. Compared to our previous analysis, the approach using convolutional networks examines misfit for temporally localized parts of the series. Poor fitting regions seem to particularly affect the environmental noise variance parameter that describes variation unexplained by the model dynamics.\n\n## 6 Discussion\n\nWe have discussed a method for detecting the existence of conficting summary statistics using regression approaches to likelihood-free inference. The approach uses a recent idea from the interpretable machine learning literature, based on deletion and imputation of part of a feature vector to judge the importance of subsets of features for the prediction. In likelihood-free regression approximations, where the regression predictive distribution is the estimated posterior distribution, the method estimates the posterior distribution conditioning only on a subset of features, and compares this with the full posterior distribution. The deletion and imputation process is less computationally burdensome than fitting a flexible regression model for different feature subsets directly. The approach can be related to prior-data conflict checking methods examining the consistency of different sources of information, and in this interpretation the posterior distribution based on a subset of the features is considered as the prior, which is updated by the likelihood term for the remaining features. Based on this connection, a way to calibrate the diagnostics is suggested.\n\nA concern expressed in the work of Zintgraf et al. (2017) was possible sensitivity of their procedure to the imputation method used. That is a concern in our applications also, although we used a number of different imputation methods in the examples and did not find this sensitivity to be a problem for reasonable choices. The diagnostics described are computed using regression approaches to likelihood-free inference, but they may be useful even if another likelihood-free inference approach is employed for inferential purposes, or in the case where the likelihood is tractable. We believe that insightful methods for model criticism are very important, since they can result in meaningful model expansions and refinements, and ultimately more appropriate inferences and decisions.\n\n## Acknowledgements\n\nMichael Evans was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.\n\n## Appendix\n\n### Details of diagnostic for the example of Section 5.4\n\nWe describe how we implement our diagnostic for the example of Section 5.4. Roughly speaking, all windows of width are considered including a time , and then we average over where consists of the series values in and is the remaining values.\n\nTo make the method precise we need some further notation. Let denote a time series of length . For some subset of the times, , we write and . Let be a fixed time. Let denote the set of all windows of width containing of the form for some . For each suppose that is some time series of length , and write . Write for the value of where for all where is the observed series. Let denote the value of where and i.e. the observation for in are generated from the conditional prior predictive given the observed value for the remainder of the series. The draws are independent for different . Let\n\n Rt,k(dt,k.) =1nt,knt,k\u2211j=1R\u221e(dt,kj(Ct,kj)|dt,kj(\u2212Ct,kj)).\n\nWe base our diagnostic on , calibrated by\n\n pt =P(Rt,k(dt,k,\u2217.)\u2265Rt,k(dt,kobs)), (14)\n\nand estimate (14) by\n\n \u02dcpt =1M\u2217M\u2217\u2211i=1I(Rt,k(dt,k,i.)\u2265Rt,k(dt,kobs)), (15)\n\nwhere , are approximations of draws of based on imputation, i.e. we have imputed from independently for each and .\n\n### Details of the imputation method for the example of Section 5.4\n\nFigure 10 illustrates the idea behind the window-based imputation we use in the example of Section 5.4. We need to impute values of the series for a window of size which has been deleted (indicated by the blue region in the figure). A larger window around the one of width is considered (red patch in the figure). To impute, we first obtain a mean imputation using the functions in the imputeTS package (Moritz and Bartz-Beielstein, 2017). 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Murray (2019) Sequential neural likelihood: fast likelihood-free inference with autoregressive flows. 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Centreville – città della Contea di Bibb, Alabama
Centreville – census-designated place della Contea di Fairfax, Virginia
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Centreville – capoluogo della Contea di Queen Anne, Maryland
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Pagine correlate
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{
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\section{Introduction}
Estimating the motion of soft tissues undergoing deformation is a major topic in medical imaging research. Magnetic resonance~(MR) tagging~\cite{axel1989heart, axel1989mr} has a wide range of applications in diagnosing and characterizing coronary artery disease~\cite{mcveigh1998imaging, edvardsen2006regional}, cardiac imaging~\cite{kolipaka2005relationship, ibrahim2011myocardial}, speech and swallowing research~\cite{parthasarathy2007measuring, xing2019atlas, gomez2020analysis}, and brain motion in traumatic injuries~\cite{knutsen2014improved}. MR tagging temporarily magnetizes tissue with a spatially modulated periodic pattern, creating transient tags in the image sequence that move with the tissue, thus capturing motion information. However, MR tagging has not been widely used in clinical settings~\cite{budinger1998cardiac} due to the long post-processing time and the problem of tag fading caused by T1 relaxation.
The harmonic phase (HARP) method~\cite{osman1999cardiac,osman2000imaging,osman2000visualizing} addresses these issues by computing phase images from sinusoidally tagged MR images using bandpass filters in the Fourier domain.
Based on the fact that the harmonic phases of material points do not change with motion, HARP tracking uses harmonic phase images as proxies in the image registration framework to avoid the violation of brightness consistency caused by tag fading. However, interpolating phase values during registration can be challenging, as it requires local phase unwrapping~\cite{PVIRA}. Also, the unwrapping operation is not differentiable, making it difficult to leverage in an end-to-end learning framework. Global phase unwrapping, used as a preprocessing step, is one possible solution to this problem, but it has been found to be extremely difficult and error-prone~\cite{jenkinson2003fast}. In this paper, we propose a sinusoidal transformation for harmonic phases that eliminates the need for phase interpolation or phase unwrapping, while still being resistant to imaging artifacts and tag fading. Given this transformed input, we designed an unsupervised multi-channel image registration framework for a set of 3D tagged images with different tag orientations.
In this study, we focus on estimating tongue motion. According to the American Cancer Society, approximately 48,000 people in the US are diagnosed with oral or oropharyngeal cancer annually, and 33\% of these cases affect the tongue~\cite{ACS2016}. Understanding the motion differences between healthy subjects and those who have undergone a glossectomy can help inform surgical decisions and assist in speech and swallowing remediation. Compared to extensively-studied cardiac motion, tongue motion has four unique properties that make motion estimation challenging: 1)~the tongue moves quickly relative to the temporal resolution of the scan during speech; 2)~the motion is aperiodic and highly variable among subjects; 3)~the tongue is highly deformable during speech due to its interdigitated muscle architecture~\cite{abd1955part}; and 4)~the air gap present in the oral cavity can significantly affect the quality of imaging, causing severe artifacts. To address these issues, we developed an unsupervised deep learning model that utilizes phase information of tagged MR images~(MRIs) to estimate the motion field. Our model has shown superior performance on healthy subject data and has also demonstrated good generalization to patients who have had a glossectomy.
Incompressibility is another crucial factor to consider when analyzing biological movements. For example, research has shown that the volume change of the myocardium during a cardiac cycle is less than 4\%~\cite{yin1996compressibility}, and the volume change of the tongue during speech and swallowing is even smaller~\cite{gilbert2007anatomical}. Therefore, it is necessary to assume that muscle motion is incompressible in order to accurately represent the physical tissue properties~\cite{kier1985tongues}. In this paper, we propose a determinant-based learning objective that allows the network to learn to estimate incompressible flow fields. To the best of our knowledge, this is the first work that learns to estimate incompressible motion fields within a deep learning-based image registration framework.
\subtitle{Contributions}
1)~We propose a sinusoidal transformation for harmonic phases, which is resistant to noise, artifacts, and tag fading, and can be easily incorporated into the end-to-end training of modern deep learning-based registration frameworks.
2)~We propose a determinant-based objective for learning 3D incompressible flow that better represents the motion of human biological tissue.
3)~With the aforementioned two features, we propose a novel unsupervised deep learning-based method to directly estimate 3D dense incompressible motion field on tagged MRI. Our approach is robust to tag fading, large motion, and can generalize well to pathological data.
\section{Background \& Related Work}
\subtitle{Tagging MRI-based 3D motion estimation} Tracking 3D motion is generally necessary when estimating the motion of biological structures. In the past, traditional 2D MR tagging motion estimation methods have been extended to 3D~\cite{ryf2002myocardial, abd2007three, spottiswoode20083d}. However, these methods require the acquisition of a large number of closely spaced image slices, making them impractical for routine clinical use due to the large amount of time required. Other approaches estimate 3D motion directly from sparse imaging geometries, such as using finite element or finite difference methods~\cite{o1995three}, tag line tracking based on 2D images~\cite{denney1995reconstruction}, or spline interpolation~\cite{denney1995reconstruction, huang1999spatio}. These methods typically require a 3D tissue segmentation, which can be time-consuming and may require human intervention or automated segmentation algorithms.
PVIRA~\cite{PVIRA} proposed to interpolate tag images to form a finer grid for later tracking and also uses HARP magnitude images to eliminate the need for a segmentation model. However, PVIRA uses phase images for registration, requiring local phase unwrapping during interpolation, which can be error-prone and is non-differentiable. In contrast, we propose a novel sinusoidal transformation for 3D harmonic phase images, thus avoiding the need for phase unwrapping and allowing for differentiable interpolation techniques such as trilinear interpolation. By incorporating this transformation into a learning-based registration framework, we can achieve end-to-end training and improved accuracy. More recently, \cite{ye2021deeptag} proposed a deep learning-based registration method for tracking cardiac tagged images. However, it only tackles 2D motion and does not account for tag-fading or the incompressibility of the tissue during heartbeats. In contrast, our approach is based on phase information and can directly estimate a dense 3D incompressible motion field.
\subtitle{Deep learning-based image registration}
Iterative optimization approaches~\cite{ANTs, diffeoDemons, ilogdemons2011} have been successful in achieving good accuracy in intensity-based deformable image registration. However, these methods can be slow and require manual tuning for each new image pair. Alternatively, deep learning-based approaches can directly take a pair of moving and fixed images as input and output the corresponding estimated deformations, resulting in faster inference speeds and comparable accuracy to iterative methods~\cite{balakrishnan2018unsupervised,voxelmorph2019,mok2020fast,qiu2021learning,im2grid2022, Transmorph2022, LKUnet2022}. Such registration frameworks learn the function $g_{\theta}(F, M) = \bm{\phi}$ which gives the transformation $\bm{\phi}$ that is used to align the fixed $F$ and moving image $M$. The function $g$ is parametrized by learnable parameters $\theta$.
The parameters are learned by optimizing the generalized objective:
\begin{equation}
\hat{\theta} = \argmin_{\theta} \mathcal{L}_\mathrm{sim}(F, M \circ g_{\theta}(F, M)) + \lambda \mathcal{L}_\mathrm{smooth}(g_{\theta}(F, M))\,.
\end{equation}
The first term, $\mathcal{L}_\mathrm{sim}$, encourages image similarity between the fixed and warped moving image. The second term, $\mathcal{L}_\mathrm{smooth}$, imposes a smoothness constraint on the transformation. The parameter $\lambda$ determines the trade-off between these two terms. However, these approaches are limited by their reliance on only two scalar images---one fixed and one moving---as input. In contrast, our method allows for the input of three pairs of tagged images with different tag orientations, referred to as multi-channel registration. Additionally, these approaches are unable to preserve the incompressibility of the motion field, whereas our approach estimates an incompressible flow field whose quality is comparable to the iterative methods~\cite{ilogdemons2011, PVIRA, NewStartPoint2023}, while being much faster.
\subtitle{Incompressiblity}
Incompressible flow fields, also known as divergence-free vector fields or
volume-preserving transformations, have been a longstanding research topic in fluid dynamics~\cite{majda2002vorticity, ma2005geometric, aris2012vectors} and image registration~\cite{song1991computation, gorce1997estimation}. In this paper, we focus on their application to biological image registration. Previously, there have been two main types of approaches: iterative approaches~\cite{mansi2009physically,ilogdemons2011,PVIRA, NewStartPoint2023} and determinant-based approaches~\cite{rappoport1995volume,rohlfing2003volume, haber2004numerical, bistoquet2008myocardial}.
Iterative approaches incorporate incompressibility into diffeomorphic demons~\cite{diffeoDemons} when updating the stationary velocity fields iteratively, making them computationally expensive. Determinant-based approaches focus on constraining the deformation field with a penalty on the Jacobian determinant of the deformation. This assumes that tissue can be deformed locally, but the volume (local and total) remains approximately constant.
In the past, the Jacobian determinant constraint has been applied to achieve volume preservation during interactive deformation of volumetric models~\cite{rappoport1995volume}.
It has also been used as an incompressibility regularization term to constrain coordinate transformation during B-spline-based nonrigid image registration~\cite{rohlfing2003volume}. However, this constraint is non-linear and requires ad-hoc numerical schemes that are computationally demanding~\cite{haber2004numerical, ilogdemons2011}. Recent work~\cite{mok2020fast} enforces orientation consistency of deformation field using determinant constraint for diffeomorphism while leaving incompressilibility unsolved. In contrast, we introduce a novel Jacobian determinant-based learning objective into the unsupervised deep learning-based registration framework and show its effectiveness in preserving volume and achieving a diffeomorphism. Furthermore, our learned model takes less than a second to process a single pair of frames, compared to tens of minutes required by previous works.
\section{Method}
\begin{figure}[!tb]
\floatconts
{fig:pipeline}
{\caption{Top: HARP processing pipeline. Bottom: HARP phases of fixed and moving images are taken as input. They are first transformed by sinousoidal transformation and sent into UNet-like multi-channel registration network. }\vspace{-1em}}
{\includegraphics[width= 0.9\linewidth]{figures/pipeline.pdf}\vspace{-1em}}
\end{figure}
\subtitle{HARP processing}
The harmonic phase~(HARP) algorithm is a well-established method for processing and analyzing tagged MRIs~\cite{osman2000imaging}.
Specifically, HARP filtering involves extracting the first spectral peak in the Fourier domain of a tagged image slice to obtain a complex-valued image, where the phase part~(HARP phase) contains motion information and the magnitude part~(HARP magnitude) contains anatomical information. Since tag images are typically acquired with lower through-plane resolution, they are interpolated onto a finer grid before HARP processing~\cite{PVIRA}. \figureref{fig:pipeline} shows the 3D tagged image processing using interpolation and HARP. Our method applies HARP filtering to the three interpolated tag volumes \ensuremath{I_{\mathrm{Sh}}}\xspace, \ensuremath{I_{\mathrm{Sv}}}\xspace, and \ensuremath{I_{\mathrm{Av}}}\xspace. For example, for the vertically-tagged axial volume $\ensuremath{I_{\mathrm{Av}}}\xspace(\bm{x})$, the complex image $J_\mathrm{Av}(\bm{x})$ after HARP filtering is computed as follows:
\begin{equation}
J_\mathrm{Av}(\bm{x})=\ensuremath{D_{\mathrm{Av}}}\xspace(\bm{x}) e^{j \ensuremath{\Psi_{\mathrm{Av}}}\xspace(\bm{x})}\,,
\label{eq:compleximage}
\end{equation}
where \ensuremath{D_{\mathrm{Av}}}\xspace is the HARP magnitude volume and \ensuremath{\Psi_{\mathrm{Av}}}\xspace is the HARP phase volume. The same notation applies for the horizaonally- and veritcally-tagged sagital volumes, yielding \ensuremath{D_{\mathrm{Sh}}}\xspace, \ensuremath{\Psi_{\mathrm{Sh}}}\xspace, \ensuremath{D_{\mathrm{Sv}}}\xspace, and \ensuremath{\Psi_{\mathrm{Sv}}}\xspace. We average over the three maginitude images to obatain \ensuremath{I_{\mathrm{Mag}}}\xspace.
\subtitle{Sinousoidal transform}
Phase-based registration is recognized as more robust than intensity-based registration for dealing with tag fading, geometric distortions between frames, and noise~\cite{fleet1993stability, hemmendorff2002phase}. Interpolating phase values requires local phase unwrapping when the phase difference between two points exceeds $\pi$~\cite{PVIRA}. However, phase unwrapping is non-differentiable, which is a problem for deep learning-based registration methods, whose training typically rely on backpropagation.
To address this, we propose a simple sinusoidal transformation for phase images. Specifically, given a phase image $\Psi$, we apply element-wise $\sin$ and $\cos$ operations,
\begin{equation}
I^{\sin}(\bm{x}) = \sin(\Psi (\bm{x})) \quad \text{ and } \quad I^{\cos}(\bm{x}) = \cos(\Psi (\bm{x})),
\end{equation}
to obtain two corresponding images $(I^{\sin}, I^{\cos})$.
Thus a phase value is uniquely associated with a $(\sin, \cos)$ pair and vice versa, i.e., one-one mapping. This transformation allows for smooth interpolation while still retaining the robustness of phase-based registration to tag fading, distortions between frames, and noise. Additionally, the flat (low-contrast) regions and steep (high-contrast) region in $\sin$ and $\cos$ are compensated for by each other, as demonstrated in \figureref{fig:pipeline}.
An alternative way to view this sinusoidal transformation is by writing the complex image in~\equationref{eq:compleximage} as $J(\bm{x})= D(\bm{x}) (\cos(\Psi(\bm{x})) + j \sin(\Psi(\bm{x})))$, where the subscript is omitted. Thus, $(I^{\cos}, I^{\sin})$ can be seen as the real and imaginary parts of the complex image $J(\bm{x})/D(\bm{x})$.
\subtitle{Multi-channel registration}
Harmonic phase is a material property that can be used to solve the aperture problem in optical flow by tracking the three harmonic phase values that come from three linearly independent tag directions. Instead of tracking phase values directly, however, because of the one-to-one nature of the sinusoidal transformation, we can track the patterns in the sinusoidally transformed image pairs. Our task differs from existing registration networks~\cite{voxelmorph2019, Transmorph2022, im2grid2022} which only take a single pair of fixed and moving images as input; here, must match \textit{multiple} fixed and moving sinusoidal images at the same time. To do this, we used the following mean squared error~(MSE) as our similarity loss during training:
\begin{equation}
\mathcal{L}_\mathrm{sim} = \sum_{k\in \{\mathrm{Av}, \mathrm{Sh}, \mathrm{Sv} \}} \hspace*{1ex} \sum_{l\in \{\sin,\cos\}} \mathrm{MSE}(F_k^l, M_k^l\circ \bm{\phi})\,,
\end{equation}
where
\begin{equation}
\bm{\phi} = g_\theta \left( \left\{ F_k^l, M_k^l \mid k\in \{\mathrm{Av},\mathrm{Sh},\mathrm{Sv}\}, l\in \{\sin, \cos\} \right\} \right)\,.
\end{equation}
\subtitle{Incompressible constraint} Volume preservation, also known as incompressibility, is an important feature for image registration in moving biological tissues. Accordingly, we introduce the following Jacobian determinant-based learning objective on the transformation field to encourage incompressiblity:
\begin{equation}
\mathcal{L}_\mathrm{incompress} = \sum_{\bm{x}} \ensuremath{I_{\mathrm{Mag}}}\xspace (\bm{x}) \left| \log \max \left( \left |J_\phi(\bm{x}) \right| ,\epsilon \right) \right| - \sum_{\bm{x}} \min \left( \left| J_\phi(\bm{x}) \right| , 0 \right)\,,
\label{eq:incompress}
\end{equation}
where $\epsilon$ is a small positive number and \ensuremath{I_{\mathrm{Mag}}}\xspace is the HARP magnitude image with a range of [0,1]. \ensuremath{I_{\mathrm{Mag}}}\xspace serves as a soft mask for tissues such as the tongue. The first term penalizes the deviation of the Jacobian determinant $\left| J_\phi(\bm{x}) \right|$ from unity and is spatially weighted by \ensuremath{I_{\mathrm{Mag}}}\xspace.
We introduced a second term in \equationref{eq:incompress} both to prevent the solution where all determinants are negative and to encourage a diffeomorphism by directly penalizing negative determinants. The proposed loss encourages $\bm{\phi}$ to be incompressible in tissue regions and diffeormophic everywhere including in air gaps.
While the L1 and L2 penalties $|\left| J_\phi(\bm{x}) \right| - 1|_{\{1, 2\}}$ are also viable, they were found to be less effective than \equationref{eq:incompress}.
\subtitle{Overall training objective} We encourage the spatial smoothness of the displacement $\bm{u}$, with the smoothness loss $\mathcal{L}_\mathrm{smooth} = \sum_{\bm{x}} \| \nabla \bm{u}(\bm{x}) \|^2$. Thus the overall loss for training is
$\mathcal{L}_\mathrm{total} = \mathcal{L}_\mathrm{sim} + \lambda \mathcal{L}_\mathrm{smooth} + \beta \mathcal{L}_\mathrm{incompress},$
where $\lambda$ and $\beta$ are hyper-parameters.
\section{Experiments}
\subtitle{Materials} The present study includes a dataset of 25 unique (subject-phrase) pairs, consisting of 8 healthy controls~(HCs) and 2 post-partial glossectomy patients with tongue flaps. To capture tongue movement during speech, the participants were asked to say one or more phrases---``a thing'', ``a souk'', or ``ashell''---while tagged MRIs were acquired. The recorded phrases had a duration of 1 second, with 26 time frames captured during this period. The in-plane resolution of the MR images is 1.875 $\times$ 1.875 mm, and the slice thickness is 6 mm. The tagged MR images were collected using the CSPAMM pulse sequence in both sagittal (both vertical and horizontal tags) and axial (vertical tags only) orientations.
The HC data was split into training, validation, and test datasets in a ratio of 0.6:0.2:0.2; patient data was reserved for testing.
The images are manually cropped to include the tongue region and then zero-padded to $64 \times 64 \times 64$.
\subtitle{Network architecture} As our goal is to explore the value of the proposed sinousoidal transformation and incompressible objective in a generic setting, we used the well-established 3D U-Net~\cite{Unet} architecture with a convolutional kernel of size ($5\times5\times5$) to increase the effective receptive field~\cite{LKUnet2022}.
To accommodate our multi-channel setting, we set the input channel of the first convolutional kernel to 12 to accept 6-channels from each of the fixed and moving sinusoidal images---$\sin$ and $\cos$ for each of the three acquired images. A scaling and squaring layer~\cite{dalca2018unsupervised} is used as the final layer to encourage our models to be diffeomorphic. To test the scalibility of our model, we trained a larger model, termed ``Ours-L'', by doubling the number of intermediate feature channels.
\subtitle{Training details} During training, fixed and moving image pairs are randomly selected from a speech sequence. We augment each pair of images with random center-crops during training. No overfitting is observed. The best loss weights (hyper-parameters) are determined by grid search for each model to ensure fair comparision. We set $\lambda=0.01$ and $\beta=0.4$ for the models denoted as ``Ours'' and ``Ours-L''. We set $\lambda = 0.08$ for the ``Ours w/o inc.'' model where the $\mathcal{L}_\mathrm{incompress}$ is not applied. In all experiments, we used the Adam optimizer with a batch size of one and a fixed learning rate of $1 \times 10^{-4}$ throughout training.
\section{Results}
\begin{table}[!tb]
\floatconts
{tab:main}%
{\caption{Quantitative measurement of performance on registration accuracy (w/ RMSE), incompressiblity (w/ Det\_AUC), diffeomorphims (w/ NegDet), and speed (w/~Time).
The p-values of Wilcoxon signed-rank tests between ``Ours" and others are reported.} \vspace{-1.5em}}%
{\resizebox{0.95\textwidth}{!}{%
\begin{tabular}{lcccccccc}
\toprule
&
\multicolumn{3}{c}{\textbf{Registration Acc: RMSE $\downarrow$}} &
\multicolumn{3}{c}{\textbf{Incompressibility: Det\_AUC $\uparrow$}} &
\multicolumn{1}{c}{\textbf{NegDet} (\%) $\downarrow$} &
\multirow{2}{*}{\begin{tabular}[c]{@{}c@{}}\textbf{Time} $\downarrow$ \\ (s/pair) \end{tabular}} \\
\cmidrule(rl){2-4} \cmidrule(rl){5-7} \cmidrule(rl){8-8}
& mean $\pm$ std & median & $p$ & mean $\pm$ std & median & $p$ & mean $\pm$ std & \\ \cmidrule(rl){2-4} \cmidrule(rl){5-7} \cmidrule(rl){8-8} \cmidrule(rl){9-9}
PVIRA & 0.153 $\pm$ 0.053& 0.160 & \textless{}0.001 & 0.936 $\pm$ 0.031& 0.935 & \textless{}0.001 & 0.000 $\pm$ 0.005 & 49 \\
Ours w/o inc. & 0.122 $\pm$ 0.041& 0.126 & \textless{}0.001 & 0.862 $\pm$ 0.077 & 0.870 & \textless{}0.001 & 0.019 $\pm$ 0.039 & \textless{}0.1 \\
Ours & 0.132 $\pm$ 0.045 & 0.137 & -- & \textbf{0.950 $\pm$ 0.038} & \textbf{0.956} & -- & \textbf{0.000 $\pm$ 0.000} & \textless{}0.1 \\
Ours-L & \textbf{0.122 $\pm$ 0.038} & \textbf{0.126} & \textless{}0.001 & 0.950 $\pm$ 0.039 & 0.956 & \textless{}0.001& 0.000 $\pm$ 0.001 & \textless{}0.1 \\ \bottomrule
\end{tabular}%
}}
\end{table}
\begin{figure}[!tb]
\floatconts
{fig:quali}
{\caption{\textbf{(A)}~An example of a fixed and moving frame pair is shown, with only the sin pattern displayed (the cos pattern is omitted). The contour of the tongue region is annotated in the fixed image with a red dotted line. \textbf{(B-D)}~Results of three different methods are shown, including 3D motion field, the warped moving images, and a sagittal and an axial slice of the 3D Jacobian determinant map.}\vspace{-1em}}
{\includegraphics[width=0.90\linewidth]{figures/quali.pdf}\vspace{-1em}}
\end{figure}
\subtitle{Registration accuracy} It is often difficult to obtain the true dense motion field for evaluating the accuracy of registration algorithms. However, we can use the harmonic phase as a ground truth, as it is a property of tissue that moves with the tissue. The sinusoidal transformation is a one-to-one mapping between phase and sinusoidal pattern, so we use the root mean squared error~(RMSE) between the sinusoidal-transformed fixed and moved images as a measure of registration accuracy. A more accurate motion field should better match the sinusoidal patterns of the fixed and moved images, resulting in a smaller RMSE.
\subtitle{Incompressility} A perfect incompressible flow field has a $\left| J_\phi(\bm{x}) \right|$ of $1$ everywhere. To assess incompressibility, we compute the histogram of determinant errors (\emph{i.e.} $\left| \left| J_\phi(\bm{x}) \right| - 1\right|$) and weight it by \ensuremath{I_{\mathrm{Mag}}}\xspace. We then calculate the area under the cumulative distribution function~(CDF) curve~(AUC) as a scalar metric. A higher AUC indicates a more incompressible motion field.
As shown in \tableref{tab:main}, The proposed method (labeled ``Ours") significantly outperforms PVIRA in terms of both registration accuracy and incompressibility. Without the proposed incompressibility constraint ($\mathcal{L}_\mathrm{incompress}$), ``Ours w/o inc." model fails to preserve incompressibility and is non-diffeomorphic in some instances. However, it still performs well in terms of registration accuracy, indicating a general trade-off between these two factors. Interestingly, our larger model (``Ours-L") achieves the best registration accuracy of all the models while also maintaining nearly the same ability to estimate incompressible flow as the best model (``Ours"). \figureref{fig:quali} shows an example when the subject initiates the phrase ``a thing" from a neutral position, the tongue moves back and downward. The example shows our model accurately registers tags while maintaining incompressibility of the flow fields.
\begin{figure}[!tb]
\begin{tabular}{cc cc}
\includegraphics[width = 0.22\linewidth]{figures/RMSE_Gap.pdf} &
\includegraphics[width = 0.22\linewidth]{figures/Det_Gap.pdf} &
\includegraphics[width = 0.22\linewidth]{figures/for_patient/R_MSE_patient.pdf} &
\includegraphics[width = 0.22\linewidth]{figures/for_patient/R_Det_AUC_patient.pdf} \\
\textbf{(a)} & \textbf{(b)} & \textbf{(c)} & \textbf{(d)}\\
\end{tabular}
\caption{Shown in \textbf{(a)} and \textbf{(b)}~are the performance of the various methods against large motion. While~\textbf{(c)} and \textbf{(d)}~show performance on the pathological cases.}\vspace{-1em}
\label{fig:timegap}
\label{fig:patient}
\end{figure}
\subtitle{Degradation with large time gaps} We also evaluated the methods on pairs of frames with different time gaps, which are assumed to be proportional to the magnitude of motion (within a short time window during speech, e.g., 8-frame window). As shown in \figureref{fig:timegap}, our model degrades less severely as the motion becomes larger. Additionally, since the effect of tag-fading accumulates with larger time gaps, these results also demonstrate the robustness of our models to tag-fading.
\subtitle{Generalizability to pathological subjects}
Our model also demonstrates better performance on patients who have undergone a glossectomy, as shown in \figureref{fig:patient}. We note that our models were only trained on data from HCs and were then directly evaluated on patient data without any fine-tuning. This demonstrates the generalizability of our models, despite their being trained on a different population.
\section{Conclusion}
We proposed a sinusoidal transformation and determinant-based objective for unsupervised estimation of dense 3D incompressible motion fields from tagged MRI. The method is robust to tag fading and large motion, and can generalize well to pathological data. We believe that the success of our preliminary tongue motion study indicates the potential of our proposed techniques for cardiac and brain motion tracking with tagged MRI.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,084
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from __future__ import unicode_literals
import frappe
from frappe import _
import frappe.sessions
from frappe.utils import cstr
import mimetypes, json
from werkzeug.wrappers import Response
from werkzeug.routing import Map, Rule, NotFound
from frappe.website.context import get_context
from frappe.website.utils import get_home_page, can_cache, delete_page_cache
from frappe.website.router import clear_sitemap
from frappe.translate import guess_language
class PageNotFoundError(Exception): pass
def render(path, http_status_code=None):
"""render html page"""
path = resolve_path(path.strip("/ "))
try:
data = render_page_by_language(path)
except frappe.DoesNotExistError, e:
doctype, name = get_doctype_from_path(path)
if doctype and name:
path = "print"
frappe.local.form_dict.doctype = doctype
frappe.local.form_dict.name = name
elif doctype:
path = "list"
frappe.local.form_dict.doctype = doctype
else:
path = "404"
http_status_code = e.http_status_code
try:
data = render_page(path)
except frappe.PermissionError, e:
data, http_status_code = render_403(e, path)
except frappe.PermissionError, e:
data, http_status_code = render_403(e, path)
except frappe.Redirect, e:
return build_response(path, "", 301, {
"Location": frappe.flags.redirect_location,
"Cache-Control": "no-store, no-cache, must-revalidate"
})
except Exception:
path = "error"
data = render_page(path)
http_status_code = 500
data = add_csrf_token(data)
return build_response(path, data, http_status_code or 200)
def build_response(path, data, http_status_code, headers=None):
# build response
response = Response()
response.data = set_content_type(response, data, path)
response.status_code = http_status_code
response.headers[b"X-Page-Name"] = path.encode("utf-8")
response.headers[b"X-From-Cache"] = frappe.local.response.from_cache or False
if headers:
for key, val in headers.iteritems():
response.headers[bytes(key)] = val.encode("utf-8")
return response
def render_page_by_language(path):
translated_languages = frappe.get_hooks("translated_languages_for_website")
user_lang = guess_language(translated_languages)
if translated_languages and user_lang in translated_languages:
try:
if path and path != "index":
lang_path = '{0}/{1}'.format(user_lang, path)
else:
lang_path = user_lang # index
return render_page(lang_path)
except frappe.DoesNotExistError:
return render_page(path)
else:
return render_page(path)
def render_page(path):
"""get page html"""
out = None
if can_cache():
# return rendered page
page_cache = frappe.cache().hget("website_page", path)
if page_cache and frappe.local.lang in page_cache:
out = page_cache[frappe.local.lang]
if out:
frappe.local.response.from_cache = True
return out
return build(path)
def build(path):
if not frappe.db:
frappe.connect()
try:
return build_page(path)
except frappe.DoesNotExistError:
hooks = frappe.get_hooks()
if hooks.website_catch_all:
path = hooks.website_catch_all[0]
return build_page(path)
else:
raise
def build_page(path):
if not getattr(frappe.local, "path", None):
frappe.local.path = path
context = get_context(path)
html = frappe.get_template(context.template).render(context)
# html = frappe.get_template(context.base_template_path).render(context)
if can_cache(context.no_cache):
page_cache = frappe.cache().hget("website_page", path) or {}
page_cache[frappe.local.lang] = html
frappe.cache().hset("website_page", path, page_cache)
return html
def resolve_path(path):
if not path:
path = "index"
if path.endswith('.html'):
path = path[:-5]
if path == "index":
path = get_home_page()
frappe.local.path = path
if path != "index":
path = resolve_from_map(path)
return path
def resolve_from_map(path):
m = Map([Rule(r["from_route"], endpoint=r["to_route"], defaults=r.get("defaults"))
for r in frappe.get_hooks("website_route_rules")])
urls = m.bind_to_environ(frappe.local.request.environ)
try:
endpoint, args = urls.match("/" + path)
path = endpoint
if args:
# don't cache when there's a query string!
frappe.local.no_cache = 1
frappe.local.form_dict.update(args)
except NotFound:
pass
return path
def set_content_type(response, data, path):
if isinstance(data, dict):
response.headers[b"Content-Type"] = b"application/json; charset: utf-8"
data = json.dumps(data)
return data
response.headers[b"Content-Type"] = b"text/html; charset: utf-8"
if "." in path:
content_type, encoding = mimetypes.guess_type(path)
if not content_type:
content_type = "text/html; charset: utf-8"
response.headers[b"Content-Type"] = content_type.encode("utf-8")
return data
def clear_cache(path=None):
frappe.cache().delete_value("website_generator_routes")
delete_page_cache(path)
if not path:
clear_sitemap()
frappe.clear_cache("Guest")
frappe.cache().delete_value("_website_pages")
frappe.cache().delete_value("home_page")
for method in frappe.get_hooks("website_clear_cache"):
frappe.get_attr(method)(path)
def render_403(e, pathname):
path = "message"
frappe.local.message = """<p><strong>{error}</strong></p>
<p>
<a href="/login?redirect-to=/{pathname}" class="btn btn-primary">{login}</a>
</p>""".format(error=cstr(e.message), login=_("Login"), pathname=frappe.local.path)
frappe.local.message_title = _("Not Permitted")
return render_page(path), e.http_status_code
def get_doctype_from_path(path):
doctypes = frappe.db.sql_list("select name from tabDocType")
parts = path.split("/")
doctype = parts[0]
name = parts[1] if len(parts) > 1 else None
if doctype in doctypes:
return doctype, name
# try scrubbed
doctype = doctype.replace("_", " ").title()
if doctype in doctypes:
return doctype, name
return None, None
def add_csrf_token(data):
return data.replace("<!-- csrf_token -->", '<script>frappe.csrf_token = "{0}";</script>'.format(
frappe.local.session.data.csrf_token))
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,466
|
\section{Introduction}
In nuclear physics, {\it ab initio} methods aim to solve the nuclear
many-body problem starting from Hamiltonians with two- and
three-nucleon forces using controlled
approximations~\cite{dickhoff2004,navratil2009,lee2009,barrett2013,roth2012,dytrych2013,hagen2014,carlson2015,hergert2016}. Most
of these methods employ finite model spaces, and this makes it
necessary to account for finite-size corrections or to extrapolate the
results to infinite model spaces. While light nuclei with large
separation energies require little or no extrapolations, finite-size
effects are non-negligible in weakly bound nuclei or heavy nuclei.
Various empirical extrapolation schemes
\cite{horoi1999,zhan2004,hagen2007b,forssen2008,bogner2008} have been
used. More recently, rigorous extrapolation formulas were derived
based on an understanding of the infrared and ultraviolet cutoffs of
the harmonic oscillator
basis~\cite{furnstahl2012,coon2012,more2013,furnstahl2014,konig2014,wendt2015,odell2016,forssen2018}.
These extrapolation formulas are akin to L{\"u}schers
formula~\cite{luscher1985} derived for the lattice and its
extension~\cite{konig2017} to many-body systems. Unlike the lattice,
however, the harmonic oscillator basis mixes ultraviolet and infrared
cutoffs, and this complicates extrapolations. Very recently, Negoita
and coworkers~\cite{negoita2018a,negoita2018} employed artificial
neural networks for extrapolations. They trained a network on NCSM
results obtained in various model spaces, i.e. for various oscillator
spacings $\hbar\omega$ and different numbers $N_{\rm max}\hbar\omega$
of maximum excitation energies. In practical calculations, $N_{\rm
max}\approx 10 \ldots 20$ in light nuclei. The neural network then
predicted extrapolations in very large model spaces of size $N_{\rm
max}\sim 100$. Impressively, the neural network also predicted that
the ground-state energies and radii cease to depend on the oscillator
spacing as $N_{\rm max}$ increases. Negoita and coworkers employed
about 100 neural networks, each differed by the initial set of
parameters (weights) from which the training started. The resulting
distributions for observables occasionally exhibited a multi-mode
structure stemming from multiple distinct solutions the neural
networks arrived at. In this work, we want to address this challenge
and focus on the network robustness and avoidance of multiple
solutions.
In recent years, artificial neural networks have been used for various
extrapolations in nuclear
physics~\cite{clark2001,athanassopoulos2004,costiris2009,akkoyun2013,utama2016,utama2016b,utama2017,utama2018,neufcourt2018},
and for the solution of the quantum many-body
system~\cite{carleo2017}. Artificial neural networks use sets of
nonlinear functions to describe the complex relationships between
input and output variables. The universality of using artificial
neural networks to solve extrapolation problems is largely guaranteed,
because no particular analytical functions are needed. Artificial
neural networks are controlled by two hyperparameters, i.e. the number
of layers and the number of neurons for each layer.
There are still two major challenges when introducing neural networks
in extrapolations of results from {\it ab initio}
computations. Firstly, unlike other applications in which large
amounts of training data can be acquired, the inputs provided by the
{\it ab initio} calculations are limited to small data sets. The
statistics is clearly not enough to support the network training
without overfitting. Secondly, randomness, caused by the nature of
basic network algorithms, is an intrinsic quality of the neural
network that conflicts with the high-precision requirement for
extrapolations.
In this work, we use an artificial neural network and extrapolate
observables computed with the NCSM and CC methods. Besides standard
techniques such as regularization, we use interpolation of data to
mitigate the overfitting problem and also take into account the
correlations in the resulting data set. The random initialization of
the network parameters provides us with a ``forest'' of
artificial neural networks. This allows us to gain insights
into uncertainties of the extrapolated observables,
under the precondition that the distribution of extrapolation results
has a single peak.
We note here that the extrapolation problem we are concerned with is
special in the sense that a well defined asymptotic value exists for
the observable of interest (i.e. an energy or a radius), that there is
a simple pattern in the learning data, and that the learning data is
already close to this asymptotic value. We will see below that this
makes an artificial neural network a useful tool for this kind of
extrapolation. Needless to say, for a general problem there is no tool
to extrapolate: we cannot extrapolate from available data to next
week's stock market value or next month's weather. We refer the reader
to the literature for attempts to use deep learning in
extrapolations~\cite{martius2016}, and for a counter
example~\cite{haley1992}.
This paper is organized as follows. In the next Section we introduce
the theoretical framework and artificial neural networks and present a
detailed account of how we construct, train, and use neural
networks. We then present and discuss the extrapolation results for
$^4$He, $^6$Li, and $^{16}$O. Finally, we summarize our work.
\section{Theoretical Framework}
\subsection{Artificial Neural Network Architecture}
An artificial neural network is a computing system that consists of a
number of interconnected blocks which process the input information
and yield an output signal. Modeled loosely after the human brain,
the neural network is typically organized by similar blocks called
``layers,'' and each layer contains a certain number of parallel
``neurons.'' The numbers of layers and neurons define the depth and
the width of the neural network, respectively.
\begin{figure}
\includegraphics[width=0.47\textwidth]{NN_schematic_diagram.pdf}
\caption{(Color online) Schematic structure of a typical feed-forward neural network. }
\label{fig:NN_schematic_diagram}
\end{figure}
Figure~\ref{fig:NN_schematic_diagram} shows the schematic structure of a
simple feed-forward neural network. The algorithm basically consists of two
parts. First, the input signal $x$ is propagated to the output layer
$y$ by a series of transformations. The whole network can be seen as a
complex function between the input and output variables. In the simple case
with one hidden layer, the function can be written as follow,
\begin{eqnarray}
z_{j} = \displaystyle\sum_{i}x_{i} w_{ij}+b_{j},
\end{eqnarray}
with $\sigma$ as the activation function,
\begin{eqnarray}
x'_{j}= \sigma(z_{j})
\end{eqnarray}
\begin{eqnarray}
y_{k}= \displaystyle\sum_{j}x'_{j} w'_{jk}+b'_{k}.
\end{eqnarray}
Here, $x_{i}$ are the input variables, and $y_{k}$ are the output
variables. The weights $w~(w')$ and bias $b~(b')$ are free parameters
of the neural network. There exist a few choices one can make for the
activation function $\sigma$, such as the sigmoid, tanh and
Rectified~Linear~units (ReLu). These are non-linear functions which
enable the neural network to capture complex non-linear relationships
between variables. For the extrapolation we follow
Ref.~\cite{negoita2018} and use a smooth activation function that only
acts on the hidden layer.
Back-propagation is the second part of the
algorithm~\cite{rumelhart1986}. This is the central mechanism that
allows neural network methods to ``learn.'' The error signals, often
referred to as the ``loss,'' which measure the deviation between the
predicted output $y_{\rm{pre}}$ and the training target
$y_{\rm{true}}$, are propagated backwards to all the parameters of the
network and allow the optimizer to update the network status
accordingly. Note that, in practice, the neural network always
processes the data in batches, which makes the input (output) signals
$x~(y)$ matrices and the network functions become matrix operations.
In order to construct the artificial neural network aiming to solve
the extrapolation problem, we first need to determine its topological
structure. There are a lot of variants for neural networks, such as
Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM) and
Convolutional Neural Network (CNN), which are designed for various
assignments. One should choose the appropriate type of network
according to the organizational structure of the dataset and the goal
that one wants to achieve. In the case of extrapolation, the data for
training is assigned to a structure consisting of three members,
namely $\hbar \omega$, $N_{\rm{max}}$, and the corresponding target
observables, i.e. the ground-state energy and the point-proton
radius. On the other hand, the main purpose of the neural network is
to provide reasonable predictions for the observables at any values of
$\hbar \omega$ and $N_{\rm{max}}$. In this paper we use the
feed-forward neural network, which takes the $\hbar \omega$ and
$N_{\rm{max}}$ as two inputs $(x)$ and the target observables as
output $(y_{\rm{true}})$. One could as well apply the RNN structure
to achieve the same goal. The only difference between the two choices
is that the data structure need to be reorganized in terms of
sequential observable values with increasing $N_{\rm{max}}$ under the
same $\hbar \omega$.
Once the basic structure is decided, the next task is to control the
complexity of the network. The network's ability of describing complex
features is determined by the numbers of the hidden layers and neurons
in each layer. In other words, the depth and the width of the neural
network control the upper limit of the neural network
description. Ideally, in order to lower the loss of the training
dataset, adding more layers and neurons is always helpful to incease
its accuracy. However, as the neural network becomes more complex it
becomes harder to train. Given the same amount of training data, a
deeper and wider network requires more time to get converged results,
and one risks overfitting of the network's parameters. In extreme
cases, for instance, when the network is so complex that it has much
more parameters than the number of input data, it can easily get 100\%
of accuracy on the training set, but still perform poorly on testing
samples. Instead of learning the pattern, the network simply memorizes
the training data and exhibits no predictive power.
Even though there is no exact answer for how to configure the numbers
of layers and neurons in the neural network, there are still some
guiding principles to follow. For a start, we consider a network with
one hidden layer. Based on the universal approximation
theorem~\cite{cybenko1989,funahashi1989,hornik1991} any continuous
function can be realized by a network with one hidden layer. Of
course, a deep neural network (with multiple hidden layers) will have
certain advantages over the shallow one (with few hidden layers). For
example, the deep neural network can reach the same accuracy of a
shallow one with much fewer
parameters~\cite{bengio2009,seide2011,mhaskar2016}. However, in order
to prevent problems such as vanishing gradients and overfitting, the
architecture of the deep neural network needs careful construction
including, but not limited to: initialization of the network
parameters~\cite{glorot2010}, design of the activation
function~\cite{glorot2011}, using the proper
optimizer~\cite{kingma2014}, and improving the training
procedure~\cite{bengio2007}. For our task of extrapolation, a deep
neural network would be an overkill. As for the numbers of neurons,
there are several empirical rules~\cite{stathakis2009} and techniques,
such as pruning~\cite{heaton2008} that can be applied. In the present
work, we start with a simple structure and then increase the numbers
of neurons and layers until we arrive at a sufficiently small loss for
the training dataset. For the results shown below, we arrived at
neural networks with a single hidden layer, consisting of eight and 16
nodes for the extrapolation of energies and radii, respectively.
Figure ~\ref{fig:cluster_compare} shows some of the data we used in
extrapolations of the ground-state energy of $^4$He. The black points,
taken from Ref.~\cite{forssen2018}, denote results from NCSM
computations based on the NNLO$_{\rm opt}$
potential~\cite{ekstrom2013}. The ground-state energies are shown as a
function of the oscillator frequency and labeled by the number $N_{\rm
max}$ of employed oscillator excitations.
\begin{figure}[b]
\includegraphics[width=0.43\textwidth]{cluster_compare.pdf}
\caption{(Color online) Ground-state energies from NCSM computations
of $^4$He based on the NNLO$_{\rm opt}$ potential (black data
points). The green full line and the red dashed line show two
different neural network solutions for learning the ground-state
energy of $^4$He in finite model spaces. }
\label{fig:cluster_compare}
\end{figure}
Figure ~\ref{fig:cluster_compare} also shows that the data exhibits a simple pattern, namely U-shaped
curves that get wider and move closer together as $N_{\rm max}$
increases (See also Fig.~\ref{fig:different_Nmax_observables_O16} for
another example.) To capture this behavior with an artificial neural
network, we choose a sigmoid as the activation function,
i.e. $\sigma(x)=(1+e^{-x})^{-1}$. It is then clear that asymptotic
values of large $N_{\rm max}$ either map to zero or to one in the
activation function, and this explains why -- by design -- an
asymptotically flat function results in the extrapolation. Indeed,
using a ReLu function as the activation function
(i.e. $\sigma(x)=\max{(0,x)}$) leads to noisy extrapolation results.
\subsection{Data Interpolation and Correlated Loss}
Despite the fact that we can easily design a neural network that gives
satisfactory accuracy on training data, a good performance on making
predictions is not guaranteed for the extrapolation problem. More
often than not the loss of the testing data will be much larger than
the loss of the training data, which is a clear sign of
overfitting. Overfitting is a major issue for neural network
applications, which is usually caused by the conflict between having
insufficient information from a limited dataset, and the networks
flexibility to approximate complex non-linear functions. This is
exactly the case for the {\it ab initio} extrapolation task at hand.
The {\it ab initio} calculations are restricted to a not-too-large
value of $N_{\rm{max}}$, and for a given $N_{\rm max}$ only a few
oscillator spacings $\hbar\omega$ are available. In the case of
$^4$He, for instance, we only have 144 data points from NCSM
calculations, and this is is inadequate for training even a very
simple neural network, thus overfitting seems inevitable.
There are a few strategies that can be introduced to avoid overfitting
in neural networks, including regularizations~\cite{zou2005},
dropout~\cite{srivastava2014}, and early
stopping~\cite{prechelt1998}. Such methods can be used together or
separately to increase the network robustness and reduce
generalization errors. The price to pay is that one will have to deal
with more hyperparameters and determine the best combination of
them. Besides these methods, one of the best ways to reduce
overfitting is to enlarge the data set. In our case, however, the
commonly used practice of data augmentation~\cite{tanner1987} and
addition of random noise to the data set will not be helpful, because
extrapolation is a quantitative problem that requires high accuracy
and input data with a clear physical foundation.
To enlarge the data set, we note that the {\it ab initio} calculations
for a given $N_{\rm{max}}$ should give a continuous smooth curve for
the target observable values as a function of $\hbar\omega$. The
limited input data is merely restricted by the computation cost but
not by the method itself. Thus, performing interpolation on existing
data is an economical way to obtain more information. In this work,
we employ a quadratic spline for interpolation in $\hbar\omega$ at
fixed $N_{\rm max}$. This procedure increases the robustness of the
neural network even with the basic single-hidden-layer architecture
and avoids overfitting.
As a large portion of the training data is generated by interpolation,
the standard ``$\chi^2$'' loss function (valid for independent data)
might not be appropriate. As the generation of $n$ points via
interpolation yields $n$ correlated samples, we introduce the
correlated loss function
\begin{eqnarray}
\label{losscorr}
L = \displaystyle\sum_{i=1}^{n}\displaystyle\sum_{j=1}^{n} W_{ij}R_{i}R_{j} .
\end{eqnarray}
Here $W_{ij}$ are the elements of a correlation matrix, and $R_{i}$
$(R_{j})$ are the residuals of the $y_{\rm{pre}}$ and the target
$y_{\rm{true}}$. In this work, we will either consider the absence of
correlations (i.e. $W_{ij}=\delta_{ij}$) or include correlations as
described in what follows. The elements $W_{ij}$ form a block matrix,
because only points interpolated at fixed $N_{\rm max}$ are correlated
by the spline. For fixed $N_{\rm{max}}$ the block matrix is taken to
be tridiagonal with all non-zero matrix elements equal to one. This
indicates that the correlation is only between neighboring data
points. We note that the loss function~(\ref{losscorr}) is usually not
a built-in function for much of the mainstream neural network
development environments. Thus, we employ a customized loss function,
and the position $i$ or $j$ of each data point is needed as an
additional input for the network to generate the correlation matrix
with elements $W_{ij}$.
Training a neural network starts with a random initialization of the
network parameters (weights and biases). During training the loss
function is minimized using the training data set as input. It is
clear that the random starting points will lead to different trained
networks, because optimizers can generally not find the global minimum
of the loss function. The existence of many local minima with an
acceptable loss will thus lead to different network predictions.
Inspired by the random forest algorithm \cite{breiman2001}, in which
the decision forest always gives better performance than a single
decision tree, we introduce multiple neural networks with the same
structure but with different initialized parameters to address the
uncertainty problem. The outputs of all the networks are being
integrated in order to obtain a range of predictions and uncertainty
estimates. This approach is going to help us to reveal some insights
into neural networks, and guide us in selecting favorable neural
network solution.
Figure~\ref{fig:multi-NN_distribution} demonstrates the impact of
including correlations into the loss function. The left panels shows
the predictions of 100 neural networks for the ground-state energy of
$^4$He. The input data consists of NCSM data for model spaces with a
maximum value of $N_{\rm max}$ as indicated, and the correlation
matrix $W$ of Eq.~(\ref{losscorr}) is taken to be diagonal, i.e. no
correlations are included. The displayed ground-state energies are the
neural network predictions for $N_{\rm max}=100$, and there is
virtually no $hw$-dependence. The shown distribution function results
from Kernel Density Estimations (KDE), i.e. by replacing the
delta-function corresponding to each individual data point with a
Gaussian. The distribution becomes narrower as the input data includes
increasing values of $N_{\rm max}$. We note that the distributions are
bi-modal.
\begin{figure}[htb]
\includegraphics[width=0.52\textwidth]{multi-NN_distribution_bare_vs_corr.pdf}
\caption{(Color online) Distributions of multiple neural network
trained with different max$(N_{\rm{max}})$ datasets for
ground-state energy of $^4$He using $\chi^2$ loss function (left
panel) and correlated loss (right panel). }
\label{fig:multi-NN_distribution}
\end{figure}
The inclusion of correlations, shown in the right panel of
Fig.~\ref{fig:multi-NN_distribution}, somewhat reduces the importance
of the smaller peak. The main peaks, which include most of the network
results, exhibit a smaller average loss and therefore are believed to
be the better solution. Their central values are likely the to be the best
predictions for these networks. However, for uncorrelated and
correlated loss functions, the second peak does not appear by accident
and can not be neglected. Its persistence against different optimizers
and hyperparameter adjustments shows that it is a stable local minimum
and not too narrow. From this point of view, both peaks can be treated
as the solutions of the multiple neural networks. As the maximum
$N_{\rm{max}}$ of the input data is increased, the two peaks are
getting closer to each other but remain distinguishable. Thus, a
significant uncertainty remains.
\subsection{Multiple Neural Network and Data Preprocessing}
We want to understand the bi-modal structure of the distribution
functions. For this purpose, we focus on the correlated loss function.
Figure~\ref{fig:multi_NN} presents results from 100 neural networks
for the correlated loss versus the ${^4}$He ground-state energy
$E_{\rm{g.s.}}$. Each cross in Fig.~\ref{fig:multi_NN} represents one
fully trained neural network and has already reached convergence
(i.e. the loss shift is within a required accuracy). As before, the
shown distribution function results from KDE. Each individual data
point (crosses) and contour lines are also shown. The top and right
panels show the integrated distributions for the ground-state energy
and the loss, respectively.
\begin{figure}
\includegraphics[width=0.45\textwidth]{multi_NN.pdf}
\caption{(Color online) Multiple neural network predictions for extrapolating
ground-state energy of $^4$He with NCSM calculated dataset
max$(N_{\rm{max}})=20$ as input. Kernel density estimations for
$E_{\rm{g.s.}}$ and loss are also given along side. The
calculation contains 100 independent random initialized neural network. }
\label{fig:multi_NN}
\end{figure}
We understand the double-peak structure as follows. The cluster of
networks under the dominant peak predict a U-shape for the curves
$E_{\rm g.s.}(\hbar\omega,N_{\rm max})$ at fixed $N_{\rm
max}$. However they deviate in ``higher-order'' terms that define
the precise shape. The smaller cluster of networks under the small
peak predict curves $E_{\rm g.s.}(\hbar\omega,N_{\rm max})$ that
increase monotonically as a function of $\hbar\omega$. They have a
higher loss. This interpretation is based on the results shown in
Fig.~\ref{fig:cluster_compare}. Here, the black squares are the input
data of ground-state energies for given $\hbar\omega$ and $N_{\rm
max}$. The green full lines show predictions from the first cluster
of networks under the dominant peak of Fig.~\ref{fig:multi_NN}. In
contrast, the red dashed lines are predictions from the second cluster
of networks under the smaller peak in Fig.~\ref{fig:multi_NN}. It is
evident that the networks of cluster 1 learned the pattern of all data
while those of cluster 2 failed to predict the trend of the data
points at smaller $\hbar\omega$. How did the neural networks of
cluster 2 make this mistake?
Inspection showed that the imbalanced dataset is the root of the
problem. Our dataset includes many points at relatively large
$\hbar\omega$ values (as we used such ultraviolet converged points for
infrared extrapolations in Ref.~\cite{forssen2018}), and the
corresponding ground-state energies are also much above the
variational minimum and the infinite-space result. In contrast, the
data set contains a smaller number of data points at relatively small
values of $\hbar\omega$, and the corresponding ground-state energies
are much closer to the infinite-space result. Thus, the failure to
correctly learn about these ``minority'' data points yields a
relatively small increase of the loss function. With random
parameters initialization, once the network reaches a local minimum,
the imbalanced dataset will, to a large extent, prevent the optimizer
from pulling the network out of it. Furthermore, with the imbalanced
training data, the effort of emphasizing the minority data directly
conflicts with the idea of reducing overfitting. Some of the common
neural network strategies, such as adding a regularization term, will
make things worse. In contrast, removing data points at too large
values of $\hbar\omega$ from the training data set, or a stronger
weighting of data closer to the variational minimum (at fixed $N_{\rm
max}$) in the loss function, reduces the number of trained networks
that would fall into cluster 2.
\begin{figure}
\includegraphics[width=0.52\textwidth]{multi-NN_distribution_corr_vs_balance.pdf}
\caption{(Color online) Distributions of multiple neural network for
ground-state energy of $^4$He, with the origin datasets (left
panel) and with the preprocessed datasets (right panel).}
\label{fig:multi-NN_distribution2}
\end{figure}
In the {\it ab initio} calculation, when the $\hbar \omega$ of the
harmonic oscillator basis is too large or too small (i.e. it deviates
from the ``optimal'' value $\hbar\omega\approx {\hbar^2\Lambda/(mR)}$,
where $\Lambda$ and $R$ are the scales set by the cutoff of the
potential and the radius of the computed nucleus~\cite{hagen2010b}),
the convergence with respect to the increasing $N_{\rm{max}}$ is slow,
because the employed basis is not efficient to capture ultraviolet and
infrared aspects of the problem. The data points that we are most
interested in are close to the variational minimum at fixed
$N_{\rm{max}}$. To overcome the problem of the imbalanced dataset, we
apply Gaussian weights on the input data, using the values of the
minima for the centroids and a standard deviation of about 8.5~MeV.
The networks are trained using these weights and a correlated loss
function. Figure~\ref{fig:multi-NN_distribution2} shows the
comparison of multiple neural network results with and without sample
weights. We note that the two panels have different ranges for
$y$-axis to better display the distribution of the ground-state
energy. Training with the original datasets (left panel) yields the
bi-modal distribution. Introducing balanced datasets via Gaussian
weights (right panel) suppresses the second peak and leaves us with
one solution for the extrapolation problem. At the same time, this
improves the precision of the predicted observable and thus yields a
smaller uncertainty for the neural network extrapolation.
\begin{figure}
\includegraphics[width=0.48\textwidth]{different_Nmax_observables_He4.pdf}
\caption{(Color online) Extrapolated results for $^4$He ground-state
energy (upper panel) and point-proton radius (lower panel) with
NCSM datasets from $\rm{max}(N_{\rm{max}})=10$ to
$\rm{max}(N_{\rm{max}})=20$ employing neural network (squares) and
IR (circles) extrapolation. Error bars represent the uncertainties
of the extrapolations that are due to changes in the initial point
in the training process.}
\label{fig:different_Nmax_observables_He4}
\end{figure}
We note here that the increased weighting of points close to the
variational minima is a akin to employing a prior in Bayesian
statistics. Such techniques could also be used for a quantification of
uncertainities~\cite{schindler2009,furnstahl2014c,carlsson2016,neufcourt2018}. In
this work, we limit ourselves to uncertainty estimates.
\section{Results and discussions}
We now present the results of the neural networks' predictions for
ground-state energies and radii, and compare with other extrapolation
methods. We start with the nucleus $^4$He. The networks are trained
separately for the ground-state energy and radius. The datasets are
generated by NCSM calculations using the NNLO$_{\rm{opt}}$
nucleon-nucleon interaction. Since the four-nucleon bound state of
$^4$He is already well converged with the maximum model space that
NCSM calculation can reach, it is a good case to perform a benchmark
and study the performance of the neural network extrapolations. The
networks are trained with different datasets which contain the NCSM
results from $N_{\rm{max}}=4$ to the given
$\rm{max}(N_{\rm{max}})$. For $^4$He, six datasets with
$\rm{max}(N_{\rm{max}})=10$ to $\rm{max}(N_{\rm{max}})=20$ are given,
providing the neural network with a sequence of mounting
information. The extrapolation result for the single neural network is
given by the prediction of $N_{\rm{max}}=100$ when the observable
value is virtually constant in the interval $10~\rm{MeV}< \hbar\omega
< 60~\rm{MeV}$. With each dataset, the multiple neural network
(containing 100 networks) is trained with randomly initialized network
values. The distribution of the multiple neural network results is
then fitted by the Gaussian function. Finally, the recommended values
of the multiple neural networks are set to be the mean value $\mu$ and
the uncertainties are defined as the standard deviation $\sigma$ of
the Gaussian.
Figure~\ref{fig:different_Nmax_observables_He4} shows the predictions
and corresponding uncertainties for the neural network approach
compared with the values obtained from the infrared (IR)
extrapolations of Ref.~\cite{forssen2018}. The error bars reflect the
variations that are due to changes in the initial point in the
training process. As we can see, the uncertainty of the neural network
predictions decreases with increasing $\rm{max}(N_{\rm{max}})$. This
indicates that the network is learning the pattern as the data set is
enlarged. The neural networks reach convergence after
$\rm{max}(N_{\rm{max}})=16$ and their predictions agree with the IR
extrapolations for both the ground-state energy and point-proton
radius. We note that the two extrapolation methods exhibit different
behaviors while reaching identical converged values.
\begin{figure}[hbt]
\includegraphics[width=0.48\textwidth]{different_Nmax_observables_Li6.pdf}
\caption{(Color online) Extrapolated results for $^6$Li ground-state
energy (upper panel) and point-proton radius (lower panel) with
NCSM datasets from $\rm{max}(N_{\rm{max}})=12$ to
$\rm{max}(N_{\rm{max}})=22$ employing neural network (squares) and
IR (circles) extrapolation. Error bars represent the uncertainties
of the extrapolations that are due to changes in the initial point
in the training process. }
\label{fig:different_Nmax_observables_Li6}
\end{figure}
$^6$Li is a more challenging task for both $ab~initio$ calculations
and extrapolations. This is a weakly bound nucleus where a weakly
bound deuteron orbits the $^4$He core. Thus, the radius is relatively
large, and the calculated observables converge slowly as the model
space increases. This nucleus is a good challenge for extrapolation
methods. The results for neural network extrapolations are shown in
Figure~\ref{fig:different_Nmax_observables_Li6}. For the ground-state
energy, the neural network gives $E_{\rm{g.s.}}=-30.743\pm 0.061
~\rm{MeV}$ with the largest dataset $\rm{max}(N_{\rm{max}})=22$ and
the results start to converge when $\rm{max}(N_{\rm{max}})$ reaches
16. As a long-range operator the radius converges even slower than the
energy, which makes it more difficult for the extrapolation method to
obtain a reliable prediction. With the largest dataset, the neural
network extrapolated result is $r_{\rm{p}}=2.471\pm 0.028 ~\rm{fm}$
and the predictions start to converge at $\rm{max}(N_{\rm{max}})=20$.
The error bars reflect the variations that are due to changes in the
initial point in the training process.
So far, we have only studied the uncertainties from the random
starting point when training the network. To study the robustness of
the trained neural networks, we proceed as follows. Once a network is
trained, i.e. once its weights and biases $w$ are determined, we take
a random vector (with components drawn at random from a Gaussian
distribution with zero mean) $\Delta w$ in the space of weights and
biases and adjust its length such that the loss function fulfills
$L(w+\Delta w) = c L(w)$, with $c=2$ or $c=10$. These values are
motivated as follows. For a chi-square distribution with uncorrelated
degrees of freedom, $c=2$ would map out the region of one standard
deviation. However, our networks are not that simple and network
parameters are correlated. For this reason we also consider the case
$c=10$. We note that this approach yields uncertainty estimates but
not quantified uncertainties. We then use the new network parameters
$w+\Delta w$ to predict the observable of interest. Taking 100 random
vectors $\Delta w$ for each single network, we compute the variance in
the observable of interest, and also record the maximum deviation. The
results are shown in Tables~\ref{tab:tabnew1} and \ref{tab:tabnew2}
for $c=2$ and $c=10$, respectively. We see that the network is
approximately parabolic at its optimal training point (as variances
and maximal deviations increase by about a factor $\sqrt{5}$ as we go
from $c=2$ to $c=10$. For energies and radii, the networks are
robust. For $c=2$ and $c=10$, the network parameters $|\Delta w|/|w|$
change by about one per mill and one percent, respectively. Allowing
for a twofold increase of the loss function, the uncertainty from the
training of the network does not exceed the uncertainties from the
random initial starting points. However, allowing weights and biases
to change such that the loss function is increased by a factor of ten,
yields larger uncertainties. In this case, the maximum uncertainties
from the neural network (when added to the errorbars shown in
Fig.~\ref{fig:different_Nmax_observables_Li6}), would lead the
errorbars from the neural network extrapolation to overlap with those
from the IR extrapolation. We note finally that the single-layer
neural networks we employ are not resilient with regard to
dropout. Removing a single node after training of the network on
average changes the predictions for energies and radii by almost 20\%.
\begin{table}
\caption{
\label{tab:tabnew1}
Uncertainty analysis of NN extrapolated results for $^6$Li with
weights $w+\Delta w$. The random vector $\Delta w$ of weights and
biases is adjusted to double the loss function, i.e. $L(w+\Delta w) =
2 L(w)$. The quantities $\sigma _{E_{\text{g.s.}}}$ and $\sigma _{r}$
are the standard deviation of the new predictions for ground-state
energy (in MeV) and point-proton radius (in fm),
respectively. $\text{max}(\Delta E_{\text{g.s.}})$ (in MeV) and
$\text{max}(\Delta r)$ (in fm) show the maximal deviation between the
new predictions and the origin results. $|\Delta w| / |w|$ are the
ratio between norms of the weights deviation and the origin weights.
}
\begin{ruledtabular}
\begin{tabular}{l cccccc p{cm}}
&&& \multicolumn{2}{c}{max($N_\text{{max}}$)} &&\\
\cline{2-7}
& 12 &14 & 16 & 18 &20&22\\
\colrule
$\sigma _{E_{\text{g.s.}}}$ & 0.013 & 0.010 & 0.009 & 0.008 & 0.009 & 0.006 \\
$\text{max}(\Delta E_{\text{g.s.}})$ & 0.068 & 0.049 & 0.037 & 0.031 & 0.032 & 0.024 \\
$|\Delta w| / |w|$ & 0.0009 & 0.0008 & 0.0008 & 0.0008 & 0.0008 & 0.0008 \\
\hline
$\sigma _{r}$ & 0.0034 & 0.0038 & 0.0042 & 0.0049 & 0.0054 & 0.0061 \\
$\text{max}(\Delta r)$ & 0.0152 & 0.0176 & 0.0200 & 0.0212 & 0.0233 & 0.0269 \\
$|\Delta w| / |w|$ & 0.0050 & 0.0043 & 0.0037 & 0.0042 & 0.0043 & 0.0030\\
\end{tabular}
\end{ruledtabular}
\end{table}
\begin{table}
\caption{
\label{tab:tabnew2}
Same as as Table~\ref{tab:tabnew1} but for random vectors $\Delta w$
of weights and biases that yield a tenfold increase of the loss
function.}
\begin{ruledtabular}
\begin{tabular}{l cccccc p{cm}}
&&& \multicolumn{2}{c}{max($N_\text{{max}}$)} &&\\
\cline{2-7}
& 12 &14 & 16 & 18 &20&22\\
\colrule
$\sigma _{E_{\text{g.s.}}}$ & 0.037 & 0.025 & 0.023 & 0.020 & 0.035 & 0.016 \\
$\text{max}(\Delta E_{\text{g.s.}})$ & 0.183 & 0.121 & 0.098 & 0.084 & 0.153 & 0.066 \\
$|\Delta w| / |w|$ & 0.0025 & 0.0023 & 0.0021 & 0.0021 & 0.0023 & 0.0021 \\
\hline
$\sigma _{r}$ & 0.0093 & 0.0093 & 0.0115 & 0.0139 & 0.0154 & 0.0165\\
$\text{max}(\Delta r)$ & 0.0415 & 0.0393 & 0.0525 & 0.0635 & 0.0684 & 0.0723\\
$|\Delta w| / |w|$ & 0.0122 & 0.0096 & 0.0105 & 0.0105 & 0.0114 & 0.0090\\
\end{tabular}
\end{ruledtabular}
\end{table}
To illustrate the universality of neural network extrapolation, we
apply the multiple neural network approach on the ground-state energy
of $^{16}$O, computed with the coupled-cluster
method~\cite{forssen2018}. The upper panel of
Fig.~\ref{fig:different_Nmax_observables_O16} shows the neural network
performance with the largest datasets
[$\rm{max}(N_{\rm{max}})=12$]. As we can see in the lower panel of the
figure, the neural network extrapolation results start to converge at
$\rm{max}(N_{\rm{max}})=8$. Note that, by then, the neural network is
trained with only three sets of $N_{\rm{max}}$ data and still be able
to capture the correct pattern. This is due to the quick convergence
of the coupled-cluster method itself and the relatively flat curve
around the minimum of the energy as a function of $\hbar \omega$,
which are both favorable for the neural network extrapolation
approach.
\begin{figure}[t]
\includegraphics[width=0.45\textwidth]{different_Nmax_observables_O16.pdf}
\caption{(Color online) neural network predictions (upper panel) based on the
CCSD(T) dataset with $\rm{max}(N_{\rm{max}})=12$ and multiple neural network
extrapolated results (lower panel) with datasets form
$\rm{max}(N_{\rm{max}})=6$ to $\rm{max}(N_{\rm{max}})=12$.}
\label{fig:different_Nmax_observables_O16}
\end{figure}
\section{Summary}
In this paper, we presented a neural network extrapolation method to
estimate the ground-state energies and point-proton radii from NCSM
and the coupled-cluster calculations. To counter the overfitting
problem which is caused by the limited set of $ab~initio$ results, we
enlarged the data set by interpolating between different data points,
and used a loss function that accounts for the correlations between
the data points. Because of the random nature of the neural network
algorithm, we employed multiple neural network approach to obtain
recommended results and uncertainties of the extrapolations. We
applied balanced sample weights as data preprocessing to eliminate the
influences of the persistent local minima, and to obtain a more
pronounced single solution for the multiple neural network
predictions.
We presented neural-network-extrapolated energies and radii of
$^{4}$He, $^{6}$Li for NCSM and compared them with IR extrapolated
results from Ref.~\cite{forssen2018}. The neural network
extrapolations gave reliable predictions for both observables with
reasonable uncertainties. The extrapolations for the ground-state
energy of $^{16}$O from coupled-cluster calculations also yielded
accurate results. The strong pattern learning ability of the neural
network allowed us to apply the same network architecture for NCSM and
CC extrapolation without employing any particular functions. In
conclusion, the neural networks studied in this work are useful tools
for extrapolating results from \emph{ab initio} calculations performed
in finite model-spaces.
\begin{acknowledgments}
We thank Andreas Ekstr{\"o}m, Christian Forss{\'e}n, Dick Furnstahl
and Stefan Wild for very useful and stimulating
discussions. Weiguang Jiang acknowledges support as an FRIB-CSC
Fellow. This material is based upon work supported in part by the
U.S. Department of Energy, Office of Science, Office of Nuclear
Physics, under Award Numbers DE-FG02-96ER40963 and DE-SC0018223. Oak
Ridge National Laboratory is managed by UT-Battelle for the
U.S. Department of Energy under Contract No. DE-AC05-00OR22725.
\end{acknowledgments}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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{"url":"http:\/\/mebassett.blogspot.com\/2012\/08\/","text":"## Sunday, August 19, 2012\n\n### Progress (or lack thereof) on NCG de Rham Cohomology of Finite Field Extensions\n\nI've been working on calculations of the aforementioned entity, in particular, I want $H^0$, id est, the kernel of the exterior derivative, to be $\\mathbb{F}_p$ when I pass to the limit leading to the algebraic closure.\n\nI'm going to make that more precise, but first let me clear up some notation: since $H^0$ does not capture the isomorphism class of field extensions, and since the differential calculi of a field $K$ are in one-to-one correspondence with the monic irreducible polynomials in $K[x]$, we shall write $H^0(m(\\mu), K)$ to mean the 0th cohomology of the field extension $K[\\mu] (m(\\mu))$, or simply $H^0(m(\\mu))$ when the field is understood. Also, I shall write $\\langle m(x) \\rangle_K$ to mean the $K$-span of the set $\\{ m(x)^n : n\\in \\mathbb{N}\\} = \\{ f(m(x)) : f\\in K[x]\\}$.\n\nMore precisely, we know that the algebraic closure of $\\mathbb{F}_2$ is the colimit of fields $\\mathbb{F}_{2^k}$, $n\\in\\mathbb{N}$, with field morphisms $\\varphi_{kj} : \\mathbb{F}_{2^k} \\rightarrow \\mathbb{F}_{2^j}$ whenever $k$ divides $j$. It is hoped that $H^0$ is a contravariant functor, yielding a morphism $H^0 (\\varphi_{kj}) : H^0(m_j(\\mu)) \\rightarrow H^0(m_k(\\mu))$ for monic irreducible polynomials $m_j(\\mu)$ and $m_k(\\mu)$ of degrees $j$ and $k$, respectively. This will give us a projective system and thus a projective limit:\n\n$\\displaystyle H^0(\\varinjlim_{k\\in\\mathbb{N}} m_k(\\mu) ) = \\varprojlim_{k\\in\\mathbb{N}} H^0(m_k(\\mu))$\n\nSo our goal is to answer two questions:\n\n1. What conditions are needed on the polynomials $m_k(x)$, $k\\in\\mathbb{N}$ so that $H^0(\\varphi_{jk})$ is well defined?\n2. When it is defined, when does the above limit equal $\\mathbb{F}_2$?\n(I'm starting to think the first question is vacuous, but I didn't until recently.)\n\n### 1. Calculating $H^0(m_k(\\mu), \\mathbb{F}_2)$\n\nSo first I tried to calculate the 0th cohomology for the simplest case: $H^0(\\mu^2 + \\mu + 1)$. Finding the cohomology amounts to finding which polynomials satisfy $f(x +\\mu) = f(x)$. After staring at the equation for awhile, it's pretty easy to see that if $f(x) \\in H^0$, then $\\text{deg} f = 2^k$ for some $k$.\n\nAfter some effort (and help), I was able to prove that $H^0(\\mu^2 + \\mu + 1) = \\langle x^4 - x \\rangle_{\\mathbb{F}_2}$. The proof went like this:\n\n1. Find the smallest polynomial $f(x)$ in $H^0$, in this case, $f(x)=x^4 - x$.\n2. Let $g(x) \\in H^0$, prove that $\\text{deg} f$ divides $\\text{deg} g$. (This requires some effort - I've only done it in specific cases by exhaustion).\n3. Hence $\\text{deg} \\, g = r \\, \\text{deg}\\, f$. Then $g(x) - f(x)^r$ has degree divisible by $\\text{deg}f$, so it's also in $H^0$, and it's also of smaller degree, so continuing in this fashion we have to end back at $f(x)$, and we're done.\n\nNOTE: I don't know that there is always only one polynomial of smallest degree in $H^0$, but I've not yet found a case where this isn't true, either.\n\nIt's not hard to prove that $x^{p^k} - x$ is always in $H^0(m_k(\\mu), \\mathbb{F}_p)$. However, $H^0$ can contain a lot more than just $x^{2^k} - x$. But since this is a particularly nice polynomial (its splitting field is $\\mathbb{F}_{p^k}$) and $\\varprojlim \\langle x^{p^k} - x \\rangle_{\\mathbb{F}_p}$ looks like it's just $\\mathbb{F}_p$ (I think, I really have no idea how to calculate that limit, I've not thought about it much yet), one might desire to choose polynomials for the algebraic closure such that $H^0(m_k(\\mu)) = \\langle x^{p^k} - x\\rangle$ .\n\nNote that in this case ($k$ divides $j$, so $j = kq$), we have:\n\n$\\displaystyle x^{p^j} - x = - \\sum_{i=0}^{q-1} \\left( x^{p^{j - k(i+1)}} -x^{p^{j - ik}} \\right) = - \\sum_{i=0}^{q-1} (x^{p^k} - x)^{p^{k(q-i)}}$\n\nSo that $H^0(\\varphi_{kj})$ is simply the identity on $H^0(m_j(\\mu))$ embedding it into $H^0(m_k(\\mu))$\n\nSo, as a guess, we're going to try to find a specific set of polynomials such that $H^0(m_k(\\mu)) = \\langle x^{p^k} - x\\rangle$. Also as a guess, our first candidates are...\n\n### 2. Conway's polynomials and fields\n\nConway polynomials of degree $k$ for $\\mathbb{F}_p$ are the least monic irreducible polynomial in $\\mathbb{F}_p[x]$ under a specific lexicographical ordering. To the best of my knowledge, their primarily use is to provide a consistent standard for the arithmetic of $\\mathbb{F}_{p^k}$ for portability across different computer algebra systems. Since these are the standard convention'' for Galois Fields, we try them first.\n\nSadly, they let us down. The Conway polynomial of degree 4 for $\\mathbb{F}_2$ is $\\mu^4 + \\mu + 1$. Using a computer algebra system (sage), I found that $H^0( \\mu^4 + \\mu + 1) = \\langle x^8 + x^4 + x^2 + x^1 \\rangle_{\\mathbb{F}_2}$.\n\nIn addition to those polynomials, John Conway has also described the algebraic closure of $\\mathbb{F}_2$ as a subfield of $\\text{On}_2$, the set of all ordinals with a field structure imposed by his nim-arithmetic''. The description of this field, from his On Numbers and Games'' does not treat $\\overline{\\mathbb{F}_2}$ as a direct limit over various simple extensions. Instead, he shows that the quadratic closure'' of $\\mathbb{F}_2$ lies in $\\text{On}_2$, and then extends the quadratic closure to a cubic closure, also in $\\text{On}_2$, et cetera.\n\nThis means that for us to use his description, we first have calculate things like the minimal polynomial for $\\omega$ and $\\omega^\\omega$ (where $\\omega$ is the least infinite ordinal) over $\\mathbb{F}_2$, these calculations are quite difficult (I haven't been able to do a single one), in fact, it's quite a bit of work just figuring out which ordinal corresponds to which $\\mathbb{F}_{2^k}$.\n\nBut fortunately for us, the quadratic closure only relies on finite ordinals, namely $2^k$. With some help from the internet, we have polynomials $m_{2^k}(\\mu)$ describing Conway's quadratic closure. They are given by the recursive relations $m_{2^k}(\\mu) = m_{2^{k-1}} ( \\mu^2 + \\mu)$ with $m_2(\\mu) = \\mu^2 + \\mu + 1$, obviously.\n\nSo $m_4(\\mu)$ corresponds to the Conway polynomial (this is not the case in general), and we've already used Sage to show that this polynomial doesn't have the cohomology we're looking for.\n\n### 3. So what next?\n\nWell, for one, we could just define the polynomials $m_k(\\mu)$ to be such that $H^0 = \\langle x^{2^k} -x \\rangle$. But is this choice unique?\n\nTurns out no: again using Sage, I have that both $H^0(1 + \\mu + \\mu^2 + \\mu^3 + \\mu^4)$ and $H^0(1+\\mu^3+\\mu^4)$ are $\\langle x^{16} -x \\rangle$.\n\nSo let's revisit the requirement on $H^0$. I was probably being a dunce insisting on it in the first place. After all, if $H^0$ really is a functor (as it should be, though I've not tried to prove it, or even defined the categories), then the projective system is always well-defined, and we really just need to calculate the limit.\n\nIn fact, what we really want is that the chain of polynomial subalgebras $H^0(m_k(x))$ becomes coarser as $k$ tends towards larger integers (thus $m_k(x)$ tends towards larger degrees), and that we have sane maps between $H^0(m_j(x))$ and $H^0(m_k(x))$ whenever $k$ divides $j$.\n\nIf my assumption that $H^0$ is always spanned'' by a single polynomial is correct, and if my sketch of a proof of $H^0 = \\langle f(x) \\rangle$ always works, then we might be able to find said map. Say that $H^0(m_k(x)) = \\langle \\tilde{m}_k(x) \\rangle$. We know that $x^{2^k} - x \\in H^0(m_k(x))$, so that $\\langle x^{2^k} - x \\rangle \\subset \\langle \\tilde{m}_k(x) \\rangle$, we also know that $\\langle x^{2^j} - x \\rangle \\subset \\langle x^{2^k} -x \\rangle$ as, from before:\n\n$\\displaystyle x^{p^j} - x = - \\sum_{i=0}^{q-1} (x^{p^k} - x)^{p^{k(q-i)}}$\n\nSince $x^{2^j} -x \\in H^0(m_j(x))$, we know that $f(m_j(x)) = x^{2^j} - x$ for some polynomial $f \\in \\mathbb{F}_2[x]$. Let $g(x) \\in H^0(m_j(x))$, then\n\n$\\displaystyle g(x) = \\tilde{m}_j(x)^s + g_{s-1} \\cdot \\tilde{m}_j(x)^{s-1} + \\ldots + g_0$\n\nby definition. Define a map from $H^0(m_j(x)) \\rightarrow H^0(m_k(x))$ by\n\n$\\displaystyle g(x) \\mapsto f(\\tilde{m}_j(x))^s + g_{s-1} \\cdot f(\\tilde{m}_j(x))^{s-1} + \\ldots + g_0$\n\nAssuming that makes sense, and I haven't made an other stupid errors (a big if!), then I guess that leaves the following for a TODO to show that $H^0$ goes to $\\mathbb{F}_2$ for any algebraic closure.:\n\n1. Check that $H^0$ is indeed spanned'' by a single polynomial, id est, that $H^0(m(x)) = \\langle f(x) \\rangle$ for all $m$.\n2. Define the categories for which $H^0$ is a functor, check that the above map works (or find a new one?)\n3. Prove that the subalgebras $H^0$ become coarser, as stated above. (Intuitively, it makes sense that they do, but I haven't thought about a proof yet. Also, if they do become coarser, then it seems obvious'' that the limit goes is $\\mathbb{F}_2$, as those are the only elements left in an series of smaller and smaller subalgebras.","date":"2017-05-26 16:51:26","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9483564496040344, \"perplexity\": 176.20666453614615}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-22\/segments\/1495463608669.50\/warc\/CC-MAIN-20170526163521-20170526183521-00414.warc.gz\"}"}
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Buhari sacks amnesty coordinator – Royal Times of Nigeria.
President Muhammadu Buhari on Tuesday sacked his Special Adviser on Niger Delta and Coordinator of the Presidential Amnesty Programme, Brig.-Gen. Paul Boroh (retd.).
This was confirmed in a statement by his Special Adviser on Media and Publicity, Femi Adesina.
Adesina said Prof. Charles Dokubo has been named as his replacement.
Buhari also directed the National Security Adviser, Babagana Monguno, to carry out a full investigation into the activities of the Amnesty Programme from 2015 to date.
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A Mermaid Melody Pichi Pichi Pitch (マーメイドメロディーぴちぴちピッチ) sódzso manga- és animesorozat, amit Yokote Michiko (横手 美智子) írt és Hanamori Pink (花森 ぴんく) rajzolt.
A sorozat címe szabad fordításban 'Hableány Melódiá'-t jelent, de több változatával is lehet találkozni. Könnyen rá lehet jönni, hogy ezt az animében szereplő sellőkről kapta.
Történet
Pitch
Nanami Luchia, az Észak-Csendes-óceán sellő hercegnője, a szárazra úszik, hogy visszaszerezze gyöngyét, amit még hétévesen egy fiúnak adott, hogy megmentse életét. Nővérével, pingvinjével és egy jósnővel a Pearle Piari nevezetű szállodában laknak, amit mellesleg ők is irányítanak. Csak később derül ki, hogy minden oldalról fenyegetés övezi nem csak őket, hanem a többi sellőt is. Egymás után bukkannak fel vízi démonok, aki a 'Dark Lovers', azaz a 'Sötét Szeretők' néven tevékenykednek Gaito – akinek az a célja, hogy ő uralja mind a hét tengert – keze alatt. Eközben Luchia emberi életében is fordulatok követnek fordulatokat: beleszeret Doumoto Kaitóba, a suli legmenőbb srácába, aki mellesleg viszonozza is érzelmeit; összebarátkozik Hosho Hanonnal és Toin Linával, a Dél- és Észak-Atlanti-óceán hercegnőivel; és persze birkózik az iskolai feladatokkal, ami persze nem a legkönnyebb egy sellő számára. Eddig minden rendben van, nem? Hiszen mindig elűzik a démonokat csodálatos hangjukkal és énekükkel, s néha még közönségük is akad. Egyetlen baj maradt csupán: egy sellő és egy ember között tilos szerelmi kapcsolat. Ugyanis, ha a hableányok felfedik igazi kilétüket, buborékká válnak. Viszont, ha fordítva történik, nincs semmi gond. És hogy teljesítik-e a lányok küldetésüket, az kiderül, ha megnézed az animét.
Pure
A második széria az előző részből megismert Nanami Luchia és Doumoto Kaito könnyes búcsújával veszi kezdetét, mivel a fiú Hawaiira utazik. A sellők királyságaikban most béke honol, ám egyik pillanatról a másikra újabb ellenség bukkan fel. Mikeru, a főgonosz a három világot akarja egyesíteni. Újra feltűnik a Black Beauty Sisters és még pár ellenfél. Közben Sarah örökösét, Seirát is fel kell éleszteni a gyöngyből, amit Luchiának adott. Úgy tűnik, minden rendben van, de egyszer szörnyű hírt kapnak: Kaito a tengerbe veszett a szörfversenyen! Hamarosan azonban kiderül, él, de nem emlékszik egyik sellőre sem. De elég ennyi a tartalomból, mert ha megnézed megtudod.^^
Szereplők
Sellők
Nanami Luchia (七海 るちあ)
Az anime kis főhőse. Ő az Észak-Csendes-óceán hercegnője. Nagyon kedves, aranyos és könnyen zavarba jön. Imád énekelni és ő vezeti a három fős csapatot: mindig ő beszél Aqua Reginával, ő kezdi az új dalokat és szinte mindig ő van a középpontban. Szoros barátságot ápol Hanonnal és Linával, sosem hagyják cserben egymást. Luchia birtokolja a rózsaszín gyöngyöt (Pink Pearle Mermaid). Fülig szerelmes Kaitóba, és ez szerencsére kölcsönös is. Karakterdalai: Koi wa Nandarou?/Splash Dream/Mother Symphony
Hosho Hanon (宝生 波音)
A Dél-Atlanti-óceán hercegnője. Nagyon élénk és vidám, viszont néha hamar kijön a sodrából. Nagyon könnyen szerelmes lesz, ahhoz képest, hogy eleinte nem nézte jó szemmel Luchia és Kaito kapcsolatát. Ő a kék (aqua) gyöngy birtokosa (Mizuiro Pearle Mermaid). A Pitch-ben teljesen odavan a zongorista Mitsuki Tarou-ért, de miután az a Pure-ban elmegy Németországba, Hanon találkozik Nagisával és fellobban a igaz szerelem. Karakterdalai: Ever Blue/Mizuiro no Senritsu
Toin Lina (洞院 リナ)
Az Észak-Atlanti-óceán sellőhercegnője. Kiegyensúlyozott, nyugodt, mindig higgadt személyiség jellemzi. Nehezen bízik meg bárkiben, de akivel összebarátkozik, azt szívébe fogadja. Komoly, de ugyanakkor vidám is tud lenni, főleg, hogy imádja a plazma tv-t. A hangja mély Luchiáéhoz és Hanonéhoz képest, de így is szép kórust alkotnak. Lina a zöld gyöngyöt birtokolja (Green Pearle Mermaid). A Pitch-ben egykeként ismerhetjük meg, de a Pure-ban beleszeret Masahiróba. Karakterdalai: Star Jewel/Piece of Love
Karen (かれん)
Az elején nem túl kedves a lányokhoz, főleg Linához, mert őt hibáztatja, hogy Noelle-t elkapták Gaitóék. Mikor aztán kiderül az ellenkezője, sokkal barátságosabb és segít Luchiáéknak felkeresni az ellenséget. Coco, ő és Noelle – aki a nővére/ikertestvére is – elválaszthatatlan barátok. Ő a Dél-Jeges-tenger hercegnője. Karen birtokolja a lila gyöngyöt (Purple Pearle Mermaid). Karakterdala: Aurora no Kaze ni Notte
Noelle (ノエル)
Noelle az Észak-Jeges-tenger hercegnője. Vidám lány, de csendes és kicsit zárkózott. Gaito és csapata elrabolta őt, ezért a Pitch-ben alig-alig szerepel. Ő Karen ikertestvére és Coco legjobb barátnője, de Linával is mindig megtalálják a közös hangot. Noelle az aiiro gyöngy birtokosa (Aiiro Pearle Mermaid).
Coco (ココ)
Pasizós, bulizós lány, imád mindenféle hasonló dolgot (napozás, koktélozás). Őt is elkapták Gaitóék, ezért a Pitch-nek csak a végén szerepel. Nagyon jó barátnők Neolle-lel és Karennel, és mindannyian nagyon jól röplabdáznak. Ő a Dél-Csendes-óceán hercegnője. Coco a sárga gyöngyöt birtokolja (Yellow Pearle Mermaid).
Sara (沙羅)
Az Indiai-óceán hercegnője. Első szerelme Mitsuki-sensei volt, de ő elhagyta, s ezután beállt a gonosz oldalra. Palotáját lerombolták. A végén a haja visszaváltozott eredeti színére és ő is a többiekkel együtt győzte le Gaitót, de végül mégis mellette maradt a Panthalassában. A Pitch-ben ő a narancssárga gyöngy birtokosa (Orange Pearle Mermaid). Karakterdala: Return to the Sea
Seira (星羅)
Sarah gyöngyéből született, de ennek ellenére nem a lánya vagy testvére, csak az örököse. Kicsit pimasz és szereti bosszantani a többieket. Nagyon vidám és gyerekes. Az Indiai-óceán második hercegnője. Seira birtokolja a narancssárga gyöngyöt a Pure-ban (Orange Pearle Mermaid II). Karakterdalai: Beautiful Wish/Birth of Love
Epizódlista
A Mermaid Melody epizódjainak listája
Seiyuu
Zenék
Mivel a sellők dalaikkal űzik el az ellenségeket, sokat énekelnek.
Openingek
Taiyou no Rakuen ~Promised Land~ by Kobe Miyuki /Pitch/
Rainbow Notes by Kobe Miyuki /Pitch/
Before the Moment by Kitamura Eri /Pure/
Endingek
Daiji na Takarabako by Nakata Asumi /Pitch/
Sekai de Ichiban Hayaku Asa ga kuru Basho by Nakata Asumi, Terakado Hitomi & Asano Mayumi /Pitch/
Ai no Ondo °C by Nakata Asumi, Terakado Hitomi & Asano Mayumi /Pure/
Sellők dalai
Legend of Mermaid by Nakata Asumi, Terakado Hitomi, Asano Mayumi, Kogure Ema, Nagata Ryoko, Arai Satomi, Ueda Kana & Kitamura Eri
Koi wa Nandarou? by Nakata Asumi
Ever Blue by Terakado Hitomi
Star Jewel by Asano Mayumi
Super Love Songs! by Nakata Asumi, Terakado Hitomi & Asano Mayumi
Yume no Sono Saki He by Nakata Asumi, Terakado Hitomi & Asano Mayumi
KIZUNA by Nakata Asumi, Terakado Hitomi & Asano Mayumi
Splash Dream by Nakata Asumi
KODOU ~Perfect Harmony~ by Nakata Asumi, Terakado Hitomi, Asano Mayumi, Kogure Ema, Nagata Ryoko, Arai Satomi & Ueda Kana
Aurora no Kaze ni Notte by Kogure Ema
Return to the Sea by Ueda Kana
Beautiful Wish by Kitamura Eri
Mizuiro no Senritsu by Terakado Hitomi
Mother Symphony by Nakata Asumi
Piece of Love by Asano Mayumi
Birth of Love by Kitamura Eri
Nanatsu no Umi no Monogatari ~Pearls of Mermaid~ by Nakata Asumi, Terakado Hitomi & Asano Mayumi
Kibou no Kaneoto ~Love goes on~ by Nakata Asumi, Terakado Hitomi, Asano Mayumi, Kogure Ema, Nagata Ryoko, Arai Satomi, Kitamura Eri & Yamakado Kumi
Ellenségek dalai
Kuro no Kyousoukyoku ~concerto~ by Tsuchiya Miki & Shitaya Noriko
Yami no Baroque by Tsuchiya Miki & Shitaya Noriko
Ankoku no Tsubasa by Kobayashi Sanae
Hana to Chou no Serenade by Kojima Megumi
Star Mero Mero Heart by Kurata Masayo
Tsubasa wo Daite by Minagawa Junko
Ashita ga Mienakute by Shintani Ryoko
Mangák
Animék
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{"url":"http:\/\/mathhelpforum.com\/math-software\/227133-matlab-defining-function-various-constants-print.html","text":"# Matlab; Defining a Function with various constants\n\n\u2022 Mar 24th 2014, 02:43 PM\nMatlab; Defining a Function with various constants\nSo when I create a function with arbitrary constants, for instance $f(x)=\\frac{a}{x}-\\frac{b}{x^2}$, how can I make multiple plots of this function using different values for the parameters 'a' and 'b' without having to make a separate file for each pair of (a,b).... My function file looks like this,\n\nfunction Veff = V(x)\na = 1\nb = 1\nVeff = a*x.^(-1) - b*x.^(-2)\n\nI also have another file that creates the plot when I run it, although the code I'm using for the x and y labels does not seem to be working. The graph shows up without the labels.\n\nylabel('Effective Potential');\ny = V(x);\nplot(x,y)\n\u2022 Mar 27th 2014, 07:20 AM\nzzephod\nRe: Matlab; Defining a Function with various constants\nQuote:\n\nSo when I create a function with arbitrary constants, for instance $f(x)=\\frac{a}{x}-\\frac{b}{x^2}$, how can I make multiple plots of this function using different values for the parameters 'a' and 'b' without having to make a separate file for each pair of (a,b).... My function file looks like this,\n\nfunction Veff = V(x)\na = 1\nb = 1\nVeff = a*x.^(-1) - b*x.^(-2)\n\ndefine a and b at the console or in the outer script, then\n\nCode:\n\nfunction Veff = V(x) \u00a0 global a \u00a0 global b \u00a0 Veff = a*x.^(-1) - b*x.^(-2);\n\n.\n\u2022 Mar 27th 2014, 07:36 AM\nzzephod\nRe: Matlab; Defining a Function with various constants\nQuote:","date":"2017-12-11 14:00:59","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 2, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6681259274482727, \"perplexity\": 1807.4169817094514}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-51\/segments\/1512948513512.31\/warc\/CC-MAIN-20171211125234-20171211145234-00145.warc.gz\"}"}
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Żelazków (do 1954 gmina Zborów) – gmina wiejska w Polsce położona w województwie wielkopolskim, w powiecie kaliskim. W latach 1975–1998 gmina administracyjnie należała do województwa kaliskiego.
Siedziba gminy to Żelazków.
Według danych z 31 grudnia 2016 gminę zamieszkiwało 9421 osób. Natomiast według danych z 31 grudnia 2019 roku gminę zamieszkiwało 9546 osób.
Struktura powierzchni
W 2005 obszar gminy Żelazków wynosił 113,57 km² (ob. 113,67 km²), w tym:
użytki rolne: 94,92 km²:
grunty orne: 86,37 km²,
sady: 1,53 km²,
łąki: 5,77 km²,
pastwiska: 1,25 km²,
lasy: 8,92 km²,
pozostałe grunty (w tym nieużytki): 9,73 km².
Demografia
Dane z 31 grudnia 2016:
Piramida wieku mieszkańców gminy Żelazków w 2014 roku.
Sołectwa
Anielin, Czartki, Dębe, Florentyna, Garzew, Goliszew, Helenów, Ilno, Janków, Kokanin, Kolonia Kokanin, Kolonia Skarszewek, Borków Nowy, Pólko, Russów, Skarszew, Skarszewek, Borków Stary, Szosa Turecka, Tykadłów, Wojciechówka, Zborów, Złotniki Małe, Złotniki Wielkie, Żelazków.
Pozostałe miejscowości
Biernatki, Chrusty, Góry Zborowskie, Góry Złotnickie, Koronka, Michałów, Niedźwiady, Russówek, Strugi, Witoldów.
Sąsiednie gminy
Blizanów, Ceków-Kolonia, Kalisz, Mycielin, Opatówek, Stawiszyn
Przypisy
|
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Dr. Crisp is a family practitioner practicing in Columbia, SC. He was educated at Medical University of South Carolina College of Medicine in 2007.
Dr. Dixon is a family practitioner practicing in Prosperity, SC. He was educated at University of Virginia School of Medicine in 1987.
Dr. Schmidt is a family practitioner practicing in Evans, GA. He was educated at University of North Carolina at Chapel Hill School of Medicine in 1995.
Dr. Smith is a family practitioner practicing in Columbia, SC. He was educated at Medical University of South Carolina College of Medicine in 1982.
Dr. Mckay is a family practitioner practicing in Irmo, SC. He was educated at Wayne State University School of Medicine in 1996.
Dr. Beaver is a family practitioner practicing in Columbia, SC. He was educated at University of South Carolina School of Medicine in 1986.
Dr. Korman is a family practitioner practicing in Lexington, SC. He was educated at Medical University of South Carolina College of Medicine in 2000.
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Q: How to convert Bytes object to _io.BytesIO python? I am making a simple flask API for uploading an image and do some progresses then store it in the data base as binary, then i want to download it by using send_file() function but, when i am passing an image like a bytes it gives me an error:
return send_file(BytesIO.read(image.data), attachment_filename='f.jpg', as_attachment=True) TypeError: descriptor
'read' requires a '_io.BytesIO' object but received a 'bytes'
and My code for upload an image as follow:
@app.route('/upload', methods=['POST'])
def upload():
images = request.files.getlist('uploadImages')
n = 0
for image in images:
fileName = image.filename.split('.')[0]
fileFormat = image.filename.split('.')[1]
imageRead = image.read()
img = BytesIO(imageRead)
with graph.as_default():
caption = generate_caption_from_file(img)
newImage = imageDescription(name=fileName, format=fileFormat, description=caption,
data=imageRead)
db.session.add(newImage)
db.session.commit()
n = n + 1
return str(n) + ' Image has been saved successfully'
And my code for downloading an image:
@app.route('/download/<int:id>')
def download(id):
image = imageDescription.query.get_or_404(id)
return send_file(BytesIO.read(image.data), attachment_filename='f.jpg', as_attachment=True)
any one can help please???
A: It seems you are confused io.BytesIO. Let's look at some examples of using BytesIO.
>>> from io import BytesIO
>>> inp_b = BytesIO(b'Hello World', )
>>> inp_b
<_io.BytesIO object at 0x7ff2a71ecb30>
>>> inp.read() # read the bytes stream for first time
b'Hello World'
>>> inp.read() # now it is positioned at the end so doesn't give anything.
b''
>>> inp.seek(0) # position it back to begin
>>> BytesIO.read(inp) # This is same as above and prints bytes stream
b'Hello World'
>>> inp.seek(0)
>>> inp.read(4) # Just read upto four bytes of stream.
>>> b'Hell'
This should give you an idea of how read on BytesIO works. I think what you need to do is this.
return send_file(
BytesIO(image.data),
mimetype='image/jpg',
as_attachment=True,
attachment_filename='f.jpg'
)
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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{"url":"http:\/\/math.stackexchange.com\/questions\/312348\/recursive-combinatorics-with-numbers-and-operators?answertab=active","text":"# Recursive combinatorics with numbers and operators\n\nI have the following question that I have difficulty to grasp: A string from 0,1,+,-,*,\/\n\nThere are 2 rules: 1) string must start and end with a number. 2) string must not have two operators one after another.\n\nThe lecturer answer is f(n)=2f(n-1)+8f(n-2), while f(n) is the number of possible strings of length n, answering on said rules.\n\nWhile 2f(n-1) is clear 8f(n-2) is not, as it creates possible duplications.\n\nAny idea?\n\nThanks.\n\n-\nThis question doesn't seem complete. What is $f$ supposed to be? The number of possible strings of length $n$? \u2013\u00a0 Ben Millwood Feb 23 '13 at 21:49\nThanks for your remark, clarified. \u2013\u00a0 SyBer Feb 24 '13 at 8:54\n\nOK, consider a valid sequence. It is either:\n\n\u2022 Just a 0\n\u2022 Just a 1\n\u2022 A valid sequence, followed by 0 or 1\n\u2022 A valid sequence, followed by an operator $+$, $-$, $*$, $\/$, and one of 0 or 1\n\nPulling the different alternatives together: $$f(n + 2) = 2 f(n + 1) + 8 f(n) \\quad f(0) = 1, f(1) = 2$$ Can even solve explicitly: Define $F(z) = \\sum_{n \\ge 0} f(n) z^n$, using properties of ordinary generating functions: $$\\frac{F(z) - f(0) - f(1) z}{z^2} = 2 \\frac{F(z) - f(0)}{z} + 8 F(z)$$ I.e.: $$F(z) = \\frac{1}{1 - 2 z - z^2}$$ By partial fractions this splits into two geometric series, unfortunately somewhat messy: $$F(z) = \\frac{1}{2^{3\/2} (1 + \\sqrt{2})} \\cdot \\frac{1}{1 + z(1 + \\sqrt{2})^{-1})} - \\frac{1}{2^{3\/2} (1 - \\sqrt{2})} \\cdot \\frac{1}{1 - z(1 + \\sqrt{2})^{-1})}$$ From here: $$f(n) = \\frac{1}{2^{3\/2} (1 + \\sqrt{2})} (\\sqrt{2} - 1)^{-n} - \\frac{1}{2^{3\/2} (1 - \\sqrt{2})} (\\sqrt{2} + 1)^{-n}$$ (I hope I didn't mistype what Maxima gave)\n\n-\nThanks for the effort, though joriki answer did the click for me. \u2013\u00a0 SyBer Feb 26 '13 at 12:14\nQuestion, why we don't take into account the case of: A valid sequence, followed by one of 0 or 1, and one of 0 or 1 \u2013\u00a0 SyBer Mar 2 '13 at 20:21\n@SyBer, it is included: There are 2 ways of adding a digit (0, 1), and that increases the length by 1; there are 8 ways of adding an operator and a digit (+, +, *, \/ with 0, 1), the length increases by 2. \u2013\u00a0 vonbrand Mar 2 '13 at 20:24\nThat's exactly my question (probably of whole recurrence idea) - if it included in (n-1), it will be included in following (n-i)? I.e. the only option to take a case with different situation? What about cases where the situation would be the same (i.e. string of only digits with no limitations)? Thanks for any clarification on this. \u2013\u00a0 SyBer Mar 4 '13 at 12:39\n@SyBer, in this case all valid sequences end in 0 or 1. To extend some sequence of length $k$, y append a 0 or 1 (2 possibilities) giving a sequence of length $k + 1$, or an operator and a 0 or 1 (8 possibilities in all) and length $k + 2$. Now turn the argument around: How can a valid sequence of length $n$ be made? From the above, in 2 ways from a valid sequence of length $n - 1$, and in 8 ways from a valid sequence of length $n - 2$. \u2013\u00a0 vonbrand Mar 4 '13 at 13:20\nA string of length $n$ can end either in a digit or in an operator. If it ends in a digit, it is the concatenation of any string of length $n-1$, of which there are $f(n-1)$, with any digit, of which there are $2$, which accounts for $2f(n-1)$. If it ends in an operator, it is the concatenation of any string of length $n-2$, of which there are $f(n-2)$, with any digit, of which there are $2$, and any operator, of which there are $4$, which accounts for $4\\cdot2\\cdot f(n-2)=8f(n-2)$.\n@SyBer: I don't understand what you mean by referring to that as a \"case\". I distinguished two exhaustive and mutually exclusive cases, strings ending in a digit and strings ending in an operator, and I counted the two cases and added the results. If by your notation you're referring to an arbitrary string of length $n-2$ followed by two digits, those are being counted correctly in the first case, the strings ending in a digit, of which there are $2f(n-1)$. It's also true that there are $4f(n-2)$ strings ending in two digits, but that's irrelevant to the case distinction I made. \u2013\u00a0 joriki Mar 2 '13 at 22:00\n@SyBer: Using \"cases\" amounts to taking the set $S$ you are counting and writing it as a disjoint union of subsets of $S$. The union of the subsets being $S$ means that you have covered every possibility once, while the subsets being disjoint means you haven't double counted anything. In joriki's case, he decomposed the set $S$ of valid strings into two subsets: (1) those that end with a digit; and (2) those that end with an operator. It is clear (I hope) that this the set of all valid strings is the disjoint union of these two subsets. So it would be incorrect to (continued below) ... \u2013\u00a0 Michael Joyce Mar 4 '13 at 12:56","date":"2014-03-10 12:36:27","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.786927342414856, \"perplexity\": 392.8441300671193}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-10\/segments\/1394010779425\/warc\/CC-MAIN-20140305091259-00033-ip-10-183-142-35.ec2.internal.warc.gz\"}"}
| null | null |
{"url":"http:\/\/lists.racket-lang.org\/dev\/archive\/2011-November\/008352.html","text":"[racket-dev] generating tex with a different component order from Scribble\n\n From: Matthew Flatt (mflatt at cs.utah.edu) Date: Sat Nov 26 11:16:03 EST 2011 Previous message: [racket-dev] generating tex with a different component order from Scribble Next message: [racket-dev] Missing pregexp syntax in Racket Messages sorted by: [date] [thread] [subject] [author]\n\nAt Fri, 25 Nov 2011 18:53:11 -0500, Sam Tobin-Hochstadt wrote:\n> Given that I have an existing paper in Scribble, which I need to get\n> into this format, which of the following would be\n> easiest\/prettiest\/most useful for the future?\n>\n> - writing a new renderer\n> - generalizing the existing latex renderer\n> - hacking prefix.tex (although I don't see how this would work)\n\nProbably the last option, followed by the second as needed.\n\n> I think the most expedient thing is to add an option so that\n> render-one method in latex-render.rkt doesn't include scribble-tex (or\n> includes a replacement that you specify).\n\nReplacing \"scribble.tex\" outright isn't likely to work. In a sense,\neverything in that file is part of the renderer, since it defines\nmacros that the renderer relies on directly. It might be useful to have\nsome option or protocol to let \"scribble.tex\" be included at a\ndifferent time or explicitly included by the prefix.\n\n> I don't know what the right general purpose fix would be, but it would\n> be nice if that fix also had the property that scribble only puts\n> \\include{}s when we know that they are going to be needed (so we can\n> deal with people who choose not to install texlive and still expect\n> scribble to work (but get skull-related errors)).\n\nI've changed the Latex renderer to include the \"skull\" package only if\nneeded. The \"wasysym\" and \"textcomp\" packages could be handled the same\nway, I think, but I haven't heard that those are causing trouble.\n\n Posted on the dev mailing list. Previous message: [racket-dev] generating tex with a different component order from Scribble Next message: [racket-dev] Missing pregexp syntax in Racket Messages sorted by: [date] [thread] [subject] [author]","date":"2015-10-04 11:13:44","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9048678874969482, \"perplexity\": 7828.2744513623475}, \"config\": {\"markdown_headings\": false, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-40\/segments\/1443736673439.5\/warc\/CC-MAIN-20151001215753-00066-ip-10-137-6-227.ec2.internal.warc.gz\"}"}
| null | null |
Cnaeus Domitius Ahenobarbus (? – Utica, Kr. e. 81) római politikus, hadvezér, az előkelő, plebeius származású Domitia gens Ahenobarbus-ágához tartozott. Édesapja, szintén Cnaeus, Kr. e. 96-ban consul volt.
Életéről nem sokat tudunk. Felesége Cornelia volt, Lucius Cornelius Cinna lánya, ami nyilvánvalóvá teszi, hogy Marius és Sulla polgárháborújában az előbbi oldalán állt. Amikor Kr. e. 82-ben Sulla magához ragadta a teljhatalmat, Ahenobarbust proscribálták, és számos hasonló helyzetű arisztokratával együtt Afrikába menekült. Hiarbas numidiai király segítségével sereget gyűjtött, ám Utica mellett az ifjú Cnaeus Pompeius megsemmisítő győzelmet mért rá. Egyes források szerint a táborának lerohanásakor halt meg, mások szerint Pompeius parancsolta meg kivégzését a csata után.
Források
Dictionary of Greek and Roman Biography and Mythology. Szerk.: William Smith (1870)
Domitius Ahenobarbus Cnaeus 81
Domitius Ahenobarbus Cnaeus 81
|
{
"redpajama_set_name": "RedPajamaWikipedia"
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| 5,924
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Q: Laravel 5 - Load views blade file from storage folder Is it possible to load views from storage folder instead from resources\views?
A: Yes, you have a couple of choices.
1. Add another path to your view config file
Open up config/view.php and add your new path to the paths array:
'paths' => [
storage_path(),
realpath(base_path('resources/views')),
],
Laravel will return whichever view that matches first, so be sure to sort the paths accordingly.
2. Add a view namespace
Open up app/Providers/AppServiceProvider.php and add your new view namespace:
public function boot()
{
$this->loadViewsFrom(storage_path(), 'custom_name');
}
With this you can access the views with a prefix like custom_name:
return view('custom_name::home');
A: Yes it is possible.
Just config your view.php file like this
<?php
return
['paths' => [realpath(base_path('storage/views')),],
'compiled' => realpath(storage_path('framework/views')),
];
?>
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,812
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\section{Introduction}\label{intro}
The constituent laws of friction are well known in the context of classical mechanics,
with Amontons-Coulomb's (AC) law, which states that the static friction force is proportional to
the applied normal load and independent of the apparent contact surface, and that the kinetic
friction is independent of the sliding velocity \cite{persson}. This law has proved to be
correct in many applications. However, thanks to advances in technologies, with the possibility to
perform high precision measurements and to design micro-structured interfaces, its validity range
was tested and some violations were observed in experiments, e.g. \cite{exp1}\cite{exp2}.
Indeed, despite the apparent simplicity of the macroscopic laws, it is not easy to identify the
origin of friction in terms of elementary forces and to identify which microscopic degrees of
freedom are involved.
For these reasons, in recent years many models have been proposed \cite{rev}, additionally incorporating
the concepts of elasticity of materials, in order to explain the macroscopic friction properties
observed in experiments and to link them to the forces acting on the elementary components of the
system. Although many results have been achieved, it turns out that there is no universal model
suitable for all considered different materials and length scales. The reason is that the
macroscopic behaviour, captured in first approximation by the AC friction law,
is the result of many microscopic interactions acting at different scales.
As pointed out in the series of works by Nosonovsky and Bhushan \cite{nos1}\cite{nos2},
friction is intrinsically a multiscale problem: the dominating effects change through the
different length scales, and they span from molecular adhesion forces to surface roughness contact
forces. Hence, there are many possible theoretical and numerical approaches, depending on the
system and the length scales involved (see ref. \cite{rev} for an exhaustive overview).
The situation is much more complicated if the surfaces are designed with patterned
or hierarchical architectures, as occurs in many examples in Nature: the
hierarchical structure of the gecko paw has attracted much interest
\cite{gecko_nature}-\cite{gecko_gorb}, and research has focused on manufacturing artificial
materials reproducing its peculiar properties of adhesion and friction. In general, the purpose of
research in bio-inspired materials is to improve the overall properties (e.g. mechanical) by
mimicking Nature and exploiting mainly structural arrangements rather than specific chemical or
physical properties. In this context, nano and biotribology is an active research field, both
experimental and theoretical \cite{nanotrib1}-\cite{snake}.
Since hierarchical structures in Nature present such peculiar properties, it is
also interesting to investigate their role in the context of tribology, trying to understand, for
example, how structured surfaces influence the friction coefficients. This can be done by
means of numerical simulations based on ad-hoc simplified models, from which useful information can
be retrieved in order to understand the general phenomenology. From a theoretic and
numerical point of view, much remains to be done. For this reason, we propose a simple model, i.e.
the spring-block model in one dimension, in order to explore how macroscopic friction properties
depend on a complex surface geometry.
The paper is organized as follows: in section \ref{sec_mod}, we present the model in details and
we discuss results for non structured surfaces, that are useful to understand the basic
behaviour of the system. In section \ref{sec_patt}, we present results for various types of
patterned surfaces. In section \ref{conc}, we discuss them and provide the conclusions and
future developments of this work.
\newpage
\section{The Model}\label{sec_mod}
\begin{figure}[h!]
\begin{center}
\includegraphics[scale=0.19]{model_spring_block.png}
\caption{\footnotesize Schematic of the spring-block model with the notation used in the text.}
\label{figmodel}
\end{center}
\end{figure}
As stated in the introduction, the purpose of this work is to investigate the variation of
friction coefficients in the presence of structured surfaces, also taking into account material
elasticity. With this in mind, we start from a one dimensional spring-block model.
This model was first introduced in 1967 by Burridge and Knopoff \cite{burr} in the study of the
elastic deformation of tectonic plates. Despite its simplicity, the model is still used not only in
this field \cite{equake1}-\cite{equake3}, but also to investigate some aspects of dry friction on
elastic surfaces, e.g. the static to dynamic friction transition
\cite{braun}-\cite{urb}, stick-slip behaviour \cite{capoz1}-\cite{sche} and the role of regular
patterning \cite{capoz3}.
The model is illustrated in figure \ref{figmodel}: an elastic body, sliding along a rigid surface,
is discretized in a chain of blocks of mass $m$ connected by springs of stiffness $K_{int}$,
attached to a slider moving at constant velocity $v$ by means of springs of stiffness $K_{s}$ to
take into account shear deformation. The surface of the sliding plane is considered as a first
approximation homogeneous and infinitely rigid.
Friction between the blocks and the surface can be introduced in many ways: for example in
\cite{braun} it is modeled through springs that can attach and detach during
motion. However, in our study we will use a classical AC friction force between blocks and
surface through microscopic friction coefficients, as it is done, for example, in \cite{trom}. In
this way it is possible to directly introduce a pressure load as in the figure. Hence, on
each block the acting forces are:
\begin{enumerate}[(i)]
\item The shear elastic force due to the slider uniform motion, $F_s = K_s (vt+l_i-x_i)$,
where $x_i$ is the position of the block $i$ and $l_i$ is its rest position.
\item The internal elastic restoring force between blocks $F_{int} = K_{int}
(x_{i+1}+x_{i-1}-2x_i)$.
\item The normal force $F_n$, which is the total normal force divided for the number of blocks in
contact with the surface.
\item A viscous force $F_{damp} = -m \gamma \dot{x_i}$ to account for damping effects, with
$\gamma$ chosen in the underdamped regime.
\item The AC friction force $F_{fr}$: if the block $i$ is at rest, the friction force is equal
and opposite to the resulting moving force, up to the threshold $F_{fr} = {\mu_s}_i \; {F_n}$.
When this limit is exceeded, a constant dynamic friction force opposes the motion, i.e. $F_{fr} =
{\mu_d}_i \; F_n$.
The microscopic friction coefficients of each block, namely ${\mu_s}_i$ and
${\mu_d}_i$, are assigned through a Gaussian statistical dispersion to account for the random
roughness of the surface. Thus, the probability distribution for the static coefficient is $
p({\mu_s}_i) = (\sqrt{2\pi}\sigma_{s})^{-1} \exp{[-({\mu_s}_i-(\mu_s)_m)^2/(2\sigma_{s}^2)]} $,
where $(\mu_s)_m$ denotes the mean microscopic static coefficient and $\sigma_s$ is its standard
deviation. The same distribution is adopted for the dynamic coefficient ( substituting subscript
$d$ to $s$). The macroscopic friction coefficients, obtained through the sum of
all the friction forces on the blocks, will be denoted as $(\mu_s)_M$ and $(\mu_d)_M$.
\end{enumerate}
Hence, we have a system of equations for the block motion that can be solved numerically with
a fourth-order Runge-Kutta algorithm. Since the friction coefficients of the blocks
are randomly extracted at each run, the final result of any observable consists on an
average of various repetitions of the simulation. Usually, we assume an elementary integration time
step of $h=10^{-4}$ ms and we repeat the simulation about twenty times.
In order to relate the model to a realistic situation, we fix the macroscopic quantities, i.e. the
global shear modulus $G=5$ MPa, the Young's modulus $E=15$ MPa, the mass density $\rho=1.2$
g/cm$^3$ (typical values for a rubber-like material with Poisson ratio $\nu=0.5$), the total length
$L_x$, the transversal dimensions of the blocks $l_y$, $l_z$ and the number of blocks $N$. These
quantities are then related to the stiffnesses $K_{int} = E\cdot (N-1) l_{z} l_{y}/L_{x} $ and $K_s
= G\cdot l_{y}L_{x}/ (l_{z} N)$, the length of the blocks $l_x=L_x/N$, and their mass $m=\rho
l_xl_yl_z$. The default values of the parameters are specified in table \ref{par_table}. An example
of the simulated friction force time evolution of the system with these values is
shown in figure \ref{fig1}.
\vspace{20pt}
\begin{table}[h]
\begin{center}
\begin{tabular}{lr}
\hline
parameter & default value \\
\hline
shear modulus G & 5 MPa \\
elastic modulus E & 15 MPa \\
density $\rho$ & 1.2 g/cm$^3$ \\
total load pressure $P_{load}$ & 1 MPa \\
damping $\gamma$ & 10 ms$^{-1}$ \\
slider velocity $v$ & 0.05 cm/s \\
length $l_y$ & 1 cm \\
length $l_z$ & 0.1 cm \\
micro. static coeff. $(\mu_s)_m$ & 1.0 (1) \\
micro. dynamic coeff. $(\mu_d)_m$ & 0.50 (1) \\
\hline
\end{tabular}
\caption{\footnotesize Values of the default parameters of the model. For the microscopic friction
coefficients we denote in round brackets the standard deviation of their Gaussian dispersion. The
total length $L_x$ and the number $N$ of blocks will be specified for each considered case.}
\label{par_table}
\end{center}
\end{table}
\subsection{Smooth surfaces}\label{sec_smooth}
Before introducing surface patterning, as a preliminary study we show some results
with the system in the standard situation of all blocks in contact. First, we show how
the macroscopic friction coefficients depend on microscopic ones and
longitudinal dimensions. As seen in figure \ref{fig_s1}, with $l_x$ fixed, the
friction coefficients decrease with the number of blocks $N$ and, consequently, the overall length
$L_x = N l_x$. This effect is analogous to that seen in fracture mechanics, in which the global
strength decreases with increasing element size, due to the increased statistics
\cite{fbm1}\cite{fbm2}. Indeed, a reduction in width of the distribution of the microscopic $\mu_s$
leads, as expected, to an increase in the global static friction coefficient. This statistical
argument is a possible mechanism for the breakdown of AC law, observed for example in
\cite{exp1}.
The macroscopic dynamic coefficient, instead, is largely unaffected by the number of blocks, as
shown in figure \ref{fig_s1}, and in any case its variation is less than $10\%$. We observe
also that it is greater than the average microscopic coefficient. This is to be expected, since
during the motion some blocks are at rest and, hence, the total friction force in the sliding
phase has also some contributions from the static friction force (see also section \ref{an_calc}).
On the other hand, by varying $l_x$ with fixed $N$, the values of the stiffnesses $K_{s}$
and $K_{int}$ are changed and, hence, the relative weight of the elastic forces. Depending on
which one prevails, the system displays two different qualitative regimes: if
$K_{int} > K_s$, the internal forces dominates so that, when a block begins to move after its
static friction threshold has been exceeded, the rupture propagates to its neighbor and a
macroscopic sliding event occurs shortly after. In this case, the total friction force in the
dynamic phase exhibits an irregular stick-slip behaviour, as shown, for example, in figure
\ref{fig1}. Instead, if $K_{int} \lesssim K_s$, the internal forces are less influential, so that
the macroscopic rupture occurs only when the static friction threshold of a sufficient number of
blocks has been exceeded.
In a real material, the distance $l_x$ can be related to the characteristic length between
asperities on the rough surface of the sliding material. Hence, the regime with a shorter $l_x$,
implying a larger $K_{int}$, can be interpreted as a material whose asperities are close packed and
slide together, while in the other limit they move independently. In the following, we will
consider the regime $K_{int} > K_s$, which is more representative for the rubber-like parameters we
have chosen with realistic length scales.
The plot of the resulting macroscopic friction coefficients as a function of the stiffnesses is
shown in figure \ref{fig_s2}: the static friction coefficients is constant in the region
$K_{int} > K_s$ and it starts to increase when the stiffnesses become comparable. This is to be
expected, since by reducing the force between blocks only the force due to shear
deformation remains. The dynamic friction coefficients slightly increase by reducing
$K_{int}$ in both the regimes for the same reason of the static coefficients: the total
force is reduced during the sliding phase and, hence, the fraction of resting blocks is
increased.
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.4]{Fig1.png}
\caption{\footnotesize Plot of the total friction force normalized with the total normal load as a
function of time with the default set of parameters and $L_x=4.0$ cm and $N=200$. We can observe
the typical AC force behaviour with a linear phase up to the detachment threshold followed
by a dynamic phase with an irregular stick-slip behaviour due to the randomness of the microscopic
friction coefficients. From this plot we can extract for example the static friction coefficient
from the first load peak and the dynamic one from the average over the dynamic phase. The plot also
shows the variation in time of the number of detached blocks.}
\label{fig1}
\end{center}
\begin{center}
\includegraphics[scale=0.4]{Fig_s1.png}
\caption{\footnotesize Macroscopic static (a) and dynamic (b) friction coefficients using the
default set of model parameters as a function of material discretization $N$. The block length is
fixed at $l_x=L_x/N = 0.02$ cm, so that the ratio $K_{int}/K_s$ is also fixed. The dynamic
coefficient is practically constant while the static coefficient slightly decreases. Two sets of
values for the local coefficients are considered, as indicated in the legend, with the standard
deviation of their Gaussian dispersion reported in round brackets. A wider statistical
dispersion reduces the global static friction coefficient.
}
\label{fig_s1}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.4]{Fig_s2.png}
\caption{\footnotesize Macroscopic static (a) and dynamic (b) friction coefficients using the
default set of parameters as a function of $K_{int}/K_{s}$ obtained by varying $l_x$ for set values
of $N$. The dynamic coefficients increase by reducing $K_{int}$. The static coefficients instead
are constant for $K_{int} > K_{s}$, and they decrease for larger $N$, as in figure \ref{fig_s1}.
The static coefficients begin to increase only when the stiffnesses are comparable.}
\label{fig_s2}
\end{center}
\end{figure}
\subsection{Dynamic friction coefficient}\label{an_calc}
In this section, we calculate analytically the dynamic friction coefficient in the limit of
$K_{int}=0$. This is useful as a further test of the program and to highlight some interesting
properties of the macroscopic friction coefficient. In this limit, the blocks move independently,
so that the resulting friction force can be obtained by averaging the behavior of a single block.
Let us consider a single block of mass $m$, which is pulled by the slider, moving at constant
velocity $v$, with an elastic restoring force of stiffness $k$.
The AC friction force acts on the block, whose static and dynamic friction coefficient
are ${\mu_s}_i$ and ${\mu_d}_i$ respectively. In the following, we will drop the index $i$ for
simplicity.
The maximum distance $r_0$ between the block and the slider can be found by equating the
elastic force and the static force, ${\mu_s} F_n = k r_{0}$, where $F_n$ is the normal force
on the block. From this distance the block starts to move under the effect of the elastic force and
dynamic friction force, therefore we can solve the motion equation for the position $x$ of
the block:
\begin{equation}\label{eq1}
\ddot{x}(t) = - \omega^{2} \; ( x(t) - vt - r_{0} ) - {\mu_d} \frac{F_n}{m}
\end{equation}
where $\omega= \sqrt{k/m}$, and $r_{0} = {\mu_s} F_n /k$ is the
initial distance between the block and the slider. By solving the differential equation with
initial conditions $x(0)=0$, $\dot{x}(0)=0$ we obtain:
\begin{equation}\label{eq2}
x(t) = \frac{v}{\omega}\; ( \omega t-\sin{\omega t} ) +
\frac{F_n}{k} \; ({\mu_s}-{\mu_d}) \; (1-\cos{\omega t} )
\end{equation}
\begin{equation}\label{eq3}
\dot{x}(t) = v \; (1-\cos{\omega t} ) + \frac{\omega F_n}{k} \; (\mu_s-\mu_d) \; \sin{\omega t}
\end{equation}
The equation for the velocity (\ref{eq3}) can be used to find the time duration $T_d$ of the
dynamic phase. After this time the block halts and the static friction phase begins. Hence,
by setting $\dot{x}(t) =0$ and solving for $t>0$, after some manipulations using
trigonometric relations, we find:
\begin{equation}\label{eq4}
T_d = \frac{2}{\omega} \Bigg[ \pi - \arctan{\left( (\mu_s-\mu_d)\frac{\omega F_n}{k v}\right)}
\Bigg]
\end{equation}
In order to characterize the static phase, it is important to calculate the distance $\Delta
r$ between the slider and the block at the time $T_d$, because the subsequent duration $T_s$ of
the static phase will be determined by the time necessary for the slider to again reach the maximum
distance $r_{0}$. Therefore, we must calculate $\Delta r \equiv x(T_d)-v T_d-r_{0}$. After
some calculations we find:
\begin{equation}\label{eq5}
\Delta r = \frac{F_n}{k} \;(\mu_s-2 \mu_d )
\end{equation}
Hence, if $2 \mu_d = \mu_s$ the block exactly reaches the slider after every dynamic phase. If $2
\mu_d <(>) \; \mu_s$ the block stops after (before) the slider position. Hence there are two
regimes determined by the friction coefficients. From this we can calculate the distance required by
the slider to again reach the maximum distance $r_0$ and, hence, the duration time $T_s$
of the static phase:
\begin{equation}\label{eq6}
T_s = \frac{2 F_n}{k v} \;(\mu_s-\mu_d )
\end{equation}
Now we have all the ingredients to calculate the time average of the friction force, from which the
dynamic friction coefficient can be deduced. We restore the index $i$ to distinguish the
microscopic friction coefficients from the macroscopic one $(\mu_d)_M$. We write
the time average of the friction force as the sum of the two contributions from the dynamic phase
and the static one:
\begin{equation}
(\mu_d)_M \equiv \frac{< F_{fr} >}{F_n} = \frac{1}{F_n} \left( \frac{T_d}{T_{tot}} {\mu_d}_i F_n +
\frac{T_s}{T_{tot}} < F_{stat} > \right)
\end{equation}
so that:
\begin{equation}\label{eq7}
(\mu_d)_M = {\mu_d}_i + \frac{T_s}{T_{tot}} \left( \frac{ < F_{stat} >}{F_n} - {\mu_d}_i \right)
\end{equation}
where $T_{tot}=T_d+T_s$ and $F_{stat}$ is the static friction force. In the static phase the
friction force is equal to the elastic force, hence, in practice, we must calculate the time
average of the modulus of the distance between block and slider in the static phase, i.e. the
average of $k|vt + \Delta r| $ over the time necessary for the slider to go from $\Delta r$ to
$r_0$. For this
reason, we must distinguish the two regimes depending on the sign of $\Delta r$ calculated in
equation (\ref{eq5}). After some calculations we find:
\begin{align}\label{eq8}
< F_{stat} > = \left\{ \begin{array}{ll}
F_n \; {\mu_d}_i \;\; \mbox{if} \;\; 2 {\mu_d}_i \geq {\mu_s}_i \\
\\
F_n \frac{({\mu_s}_i - 2{\mu_d}_i)^{2} + {{\mu_s}_i}^2}{4 ({\mu_s}_i - {\mu_d}_i)} \;\; \mbox{if}
\;\;2 {\mu_d}_i < {\mu_s}_i
\end{array} \right.
\end{align}
Finally, by substituting equation (\ref{eq8}) into (\ref{eq7}), we obtain:
\begin{align}\label{eq9}
(\mu_d)_M = \left\{ \begin{array}{ll}
{\mu_d}_i \;\; \mbox{if} \;\;\; 2 {\mu_d}_i \geq {\mu_s}_i \\
\\
{\mu_d}_i + \frac{T_s}{T_{tot}} \frac{( {\mu_s}_i-2{\mu_d}_i )^2}{2({\mu_s}_i-{\mu_d}_i )}\;\;
\mbox{if} \;\;2 {\mu_d}_i < {\mu_s}_i
\end{array} \right.
\end{align}
showing that the limit case ${\mu_d}_i = {\mu_s}_i/2$ of the two expressions coincides. Now,
if we have $N$ non-interacting blocks, we can average the equations (\ref{eq9}) over the index $i$
in order to calculate the macroscopic friction coefficient in terms of the mean microscopic ones,
$(\mu_s)_m$ and $(\mu_d)_m$. Since the second term of equation (\ref{eq9}) contains a
complicated expression, this can be done exactly only numerically. Nevertheless, we can
deduce that, at least in the regime of negligible $K_{int}$, (i) the resulting dynamic friction
coefficient is always greater or equal to the microscopic one, and (ii) there are two regimes
discriminated by the condition $2 \;(\mu_d)_m \gtrless (\mu_s)_m$. We observe also
that in the case $2\;(\mu_d)_m \simeq (\mu_s)_m$, owing to the statistical dispersion
of the coefficients, each block could be in both the regimes, so that the final result will be
an average between the two conditions of (\ref{eq9}).
The following plot (figure \ref{fig2}) shows the behavior predicted by equation (\ref{eq9})
compared with the simulations either in ideal case $K_{int}=0$, that perfectly match with the
theory, and with blocks interactions, that diverge from the predictions only for
$(\mu_d)_m/(\mu_s)_m<0.5$. This is to be expected, since the internal forces become much more
influential if the blocks can move without a strong kinetic friction.
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.4]{Fig2.png}
\caption{\footnotesize Macroscopic dynamic friction coefficient as a function of the microscopic
one. The red curve shows the theory prediction by Eq. (\ref{eq9}). Results of the ideal case
$K_{int}=0$ are the black dots, which follow exactly the predictions. The yellow and the blue
dots show the data sets with blocks interaction, with and without the damping $\gamma$,
respectively. The data are obtained with the default system parameters, $N=200$ and $L_x=4.0$ cm.
}
\label{fig2}
\end{center}
\end{figure}
\section{Structured Surfaces} \label{sec_patt}
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.20]{model_spring_block2.png}
\caption{\footnotesize In order to evaluate the effect of surface structuring, we assume in the
spring-block model that a number of blocks is no longer in contact with the sliding plane and is
instead free to oscillate. The total pressure is maintained constant, so that the normal force on
the blocks in contact increases.}
\label{figmodel2}
\end{center}
\end{figure}
\subsection{First level patterning}\label{sec_patt1}
Next, we set to zero the friction coefficients relative to some blocks in order to simulate the
presence of structured surfaces on the sliding material (figure \ref{figmodel2}). We start with a
periodic regular succession of grooves and pawls. This pattern has already been
studied both experimentally \cite{brass}\cite{snake} and numerically with a slightly different
model \cite{capoz3}. Our aim is therefore to first obtain known results so as validate the model.
We consider a succession of $N_g$ grooves of size $L_g$ at regular distances of $L_g$, so that
only half of the surface is in contact with respect to previous simulations. The number of blocks
in each groove is $n_g = N/(2 N_g)$, and $L_g=n_g L_x/N$. The friction coefficients of these blocks
are set to zero while default values are used for the remaining ones.
Figure \ref{fig_p1} shows that, as expected, the static friction coefficient decreases with larger
grooves while the dynamic coefficient is approximately constant. In the case of small grooves, e.g.
for $n_g \leq 2$, there is no reduction, confirming the results in \cite{capoz3}, where it is found
that the static friction reduction is expected only when the grooves length is inferior to a
critical length depending on the stiffnesses of the model. The critical length can be rewritten
in terms of the adimensional ratio $N_g/N$ and, by translating it in the context of our model, we
obtain $(N_g/N)_{cr} = 2 \sqrt{K_{s}/K_{int}}$. For the data set of figure \ref{fig_p1} the
critical value is $(N_g/N)_{cr} \simeq 0.23$ and, indeed, our results display static friction
reduction for groove size whose $N_g/N$ is inferior to this.
The origin of this behaviour in the spring-block model can easily be understood by looking at the
stress distribution on the patterned surfaces (figure \ref{fig3} a): stresses at the edge of the
pawls increase with larger grooves, so that the detachment threshold is exceeded earlier and the
sliding rupture propagates starting from the edge of the pawls. The larger the grooves, the more
stress is accumulated. Thus, for a constant number of blocks in contact, i.e. constant real contact
area, the static friction coefficient decreases with larger grooves.
Next, we evaluate configurations in which the pawls and the grooves have different sizes, i.e.
the fraction of surface in contact is varied. This is equivalent to changing the normal force
applied to the blocks in contact, since the total normal force is fixed. We must denote these
single-level configurations with two symbols, the number of blocks in the grooves $n_g$ as
previously, but also the number of blocks in the pawls, namely $n_p$. When they are the same we
will report only to $n_g$, as in figure \ref{fig_p1}. All the results obtained for the macroscopic
friction coefficient are reported in table \ref{tpat0} and shown in figure \ref{fig4}.
We can observe that, for a given fraction of surface in contact, the static friction
decreases for larger grooves, as in the case ${n_p}={n_g}$. However, with different ${n_p}$ and
${n_g}$ values, static friction increases when the pawls are narrower than the grooves, i.e. when
the real contact area is smaller than one half.
This would appear to be in contrast with results observed previously relative to the relative
groove size. However, the normal load applied to the blocks must also be taken into account: if the
normal force is distributed on fewer blocks, the static friction threshold will also be greater
although the driving force is increased (figure \ref{fig3} b). Hence, static friction reduction
due to larger grooves can be balanced by reducing the real contact area, as highlighted by results
in table \ref{tpat0}.
The interplay between these two concurrent mechanisms explains the observed behaviour of the
spring-block model with single-level patterning using pawls and grooves of arbitrary size.
The dynamic friction coefficient, on the other hand, displays reduced variation in the presence of
patterning, and in practice increases only when there is a large reduction of the number of blocks
in contact.
Finally, we have also tested a configuration with randomly distributed grooves, i.e. half the
friction coefficients of randomly chosen blocks are set to zero. This turns out to be the
configuration with the smallest static friction. This can be explained by the fact that there are
grooves and pawls at different length scales, so that it is easier to trigger sequences of
ruptures, leading to a global weakening of the static friction. Thus, the simulations show that in
general a large statistical dispersion in the patterning organization is detrimental to the static
friction of a system, whilst an ordered structure is preferable in most cases.
\vspace{20pt}
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.4]{Fig_p1.png}
\caption{\footnotesize Static and dynamic friction coefficients for a periodic regular
patterned surface as a function of number of blocks in a groove $n_g$. Results are obtained
with the default set of parameters, $L_x=7.2$ cm and $N=360$, and microscopic friction coefficients
$(\mu_s)_m=1.0(1)$ and $(\mu_d)_m=0.50(1)$. The behaviour is analogous to that observed in the
literature \cite{snake}. }
\label{fig_p1}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.3]{Fig3.png}
\caption{\footnotesize Normalized stress distribution $\sigma$ as a function of the longitudinal
distance $L$ along the patterned surface, i.e. stress acting on each block normalized by the total
applied pressure. For the three considered cases, the patterning profile is illustrated with a
black line.
\newline
a) Case of regular periodic patterning for different $n_g$ values. For larger grooves, the stress
on the blocks at the pawl edges increases.
\newline
b) Three cases varying the relative length of grooves and pawls: for small pawls, despite the
larger grooves, the stress is reduced because of the increased normal load on the blocks in contact.
}
\label{fig3}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.4]{Fig4.png}
\caption{\footnotesize Plot of the static friction coefficient as a function of the size of
grooves and pawls (see table \ref{tpat0}). }
\label{fig4}
\end{center}
\end{figure}
\subsection{Hierarchical patterning} \label{sec_patt2}
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.15]{mod.png}
\caption{\footnotesize Example of the elementary structure of surfaces with two (a) and
three (b) levels of patterning. With the notation used in the text the left configuration
is denoted by $\lambda_1=1/3$, $\lambda_2=1/15$, the right one by $\lambda_1=1/3$,
$\lambda_2=1/15$, $\lambda_3=1/75$.}
\label{figmodel3}
\end{center}
\end{figure}
We now consider grooves on different size scales, arranged in 2- and 3-level hierarchical
structures, as shown in figure \ref{figmodel3}. Further configurations can be constructed with more
hierarchical levels, by adding additional patterning size scales.
The configurations are identified using the ratios between the length of the grooves at
level $i$ and the total length: $\lambda_i \equiv L_{g}^{(i)}/L_x$. For example, a hierarchical
configuration indicated with $\lambda_1=1/5$, $\lambda_2=1/15$, $\lambda_3=1/120$ has three levels
with groove sizes $L_{g}^{(1)} = L_x/5$, $L_{g}^{(2)} = L_x/15$, $L_{g}^{(3)} = L_x/120$,
respectively, from the largest to the smallest. In the spring block model this implies that the
number of blocks in each groove at level $i$ is $n_{g}^{(i)} = N \lambda_i$. For readability,
these numbers will be shown in the tables. Macroscopic friction coefficients for various
multi-level configurations are reported in the appendix \ref{appendix}. The comparison of the total
friction force as a function of the time between the case of a smooth surface, single level and
two-levels patterning is shown in figure \ref{fig5}.
In general, by adding more levels of patterning (as in figure \ref{figmodel3}) the static friction
coefficients increases with respect to the single-level configuration whose groove size is that of
the first hierarchical level (see figure \ref{fig_p2}). This effect is due to the increased normal
force on the remaining contact points, since the total normal force applied to the whole surface is
constant, but it is distributed on a smaller number of blocks. This increase of the
static friction becomes more significant the more the length scales of the levels are different.
Indeed, if the groove size of the first level is fixed, there is a progressive reduction of the
static friction as the second-level groove size increases, down to the value obtained with a single
level. These trends can be clearly observed in tables \ref{tpat1} and \ref{tpat2}. On the other
hand, if we compare a hierarchical configuration with a single-level one with the same contact area,
i.e. if we compare the results of table \ref{tpat0} and table \ref{tpat2} for the same fraction
of surface in contact and the same first level size, we observe a reduction of the static friction
(see figure \ref{fig_p3}).
Hence, a multi-structured surface produces an increase in static friction with respect to a
single-level patterning with the same first level groove size, but a decrease with respect to
that with the same real contact area. The explanation is the following: if the normal load is
fixed, a structure of nested grooves allows to distribute the longitudinal forces on more points of
contact on the surface, so that the static threshold will be exceeded earlier with respect an
equal number of points arranged without a hierarchical structure. In other words, the
hierarchical structure increases the number of points subjected to stress concentrations at the
edges of the grooves.
Hence the role of the hierarchy can be twofold: if the length scale of the grooves at some level is
fixed, by adding a further hierarchical level with a smaller length scale we can strengthen the
static friction by reducing the number of contact points. On the other hand, among the
configurations with the same fixed fraction of surface in contact, the hierarchical one has the
weakest static friction, because the longitudinal stress is distributed on more points.
Moreover, the dynamic friction coefficients do not show variations greater
than a few percent with respect the case of smooth surfaces, but they increase by
reducing the blocks in contact and, consequently, also by adding hierarchical levels.
From all of these considerations, we can also deduce that, by increasing the number of
hierarchical levels and by appropriately choosing the groove size at each level, it is possible
to fine tune the friction properties of a surface, exploiting an optimal compromise between the
extremal effects. Hierarchical structure is essential as it provides the different length scales
needed to manipulate the friction properties of the surface.
\begin{figure}[h!]
\begin{center}
\includegraphics[scale=0.4]{Fig5.png}
\caption{\footnotesize Comparison of the total friction force normalized with the total load
for increasing levels of patterning, using the default set of parameters and $L_x=7.2$ cm and
$N=360$. A reduction of the static friction force is observed with respect to the non patterned
case. However, adding a further level, the static friction increases again, and dynamic friction
displays a more evident time variation although the average is approximately the same.
}
\label{fig5}
\end{center}
\end{figure}
\begin{figure}[h!]
\begin{center}
\includegraphics[scale=0.4]{Fig_p2.png}
\caption{\footnotesize Static and dynamic friction coefficients obtained by adding
further hierarchical levels (labeled as in table \ref{tpat1}) but keeping fixed the first level
size. For each considered case the grooves profile along the surface is shown. Results are
obtained with the default set of parameters, $L_x=2.4$ cm, $N=120$ and microscopic friction
coefficients $(\mu_s)_m=1.0(1)$ and $(\mu_d)_m=0.50(1)$.
}
\label{fig_p2}
\end{center}
\end{figure}
\begin{figure}[h!]
\begin{center}
\includegraphics[scale=0.4]{Fig_p3.png}
\caption{\footnotesize Comparison of static and dynamic friction coefficients for some cases of
one- and two-level patterning with the default parameters, $L_x=7.2$ cm, $N=360$. For each
considered case the groove profile along the surface is shown. With two levels
the static friction is reduced with respect to the corresponding one-level case with same contact
area and same size of the largest grooves.
}
\label{fig_p3}
\end{center}
\end{figure}
\section{Conclusions}\label{conc}
In this paper, we have investigated how the macroscopic friction coefficients of an elastic
material are affected by a multilevel structured surface constructed with patterning at different
length scales. Our results were obtained by means of numerical simulations using a one-dimensional
spring-block model, in which friction is modeled using the classical AC friction force
with microscopic friction coefficients assigned with a Gaussian statistical distribution. System
parameters were chosen in such a way as to be as close as possible to realistic situations for
rubber-like materials sliding on a rigid homogeneous plane.
Tests were initially performed for a smooth surface: in this case the model predicts that
the friction coefficients slightly decrease with the number of asperities in contact, i.e. the
number of blocks, an effect that can be ascribed to statistical dispersion. The friction
coefficients also decrease if the asperities are close-packed (i.e. the blocks distance is
shorter), because their slipping occurs in groups and the local stress is increased .
The presence of patterning was then simulated by removing contacts (i.e. friction) at
selected locations, varying the length of the resulting pawls and grooves and the number of
hierarchical levels. The model predicts the expected behaviour for a periodic regular
patterning, correctly reproducing results from experimental studies.
We have shown that in order to understand the static friction behaviour of the system in presence
of patterning two factors must be taken into account: the length of the grooves and the
discretization of the contacts (i.e. number of blocks in contact). The longitudinal force acting on
the pawls increases with larger grooves, so that a smaller global static coefficient can be
expected. However, if the fraction of surface in contact is small, the friction threshold increases
and so does the global static friction. Single-level patterning frictional behaviour
can be understood in terms of these mechanisms.
In a multi-level patterned structure, the hierarchy of different length scales provides a solution
to reduce both the effects. If at any level of the hierarchy the grooves are so large that the
static friction is severely reduced, a further patterning level, whose typical length scales are
definitely smaller, can enhance it again, since with a reduced number of contact points the
static threshold is increased.
On the other hand, if we compare the configurations with the same fraction of surface in contact,
the hierarchical structure has the weakest static friction, since it increases the number of points
at the edges between pawls and grooves and, consequently, the fraction of surface effectively
subjected to longitudinal stress concentrations. Thus, a hierarchical structure can be used to
construct a surface with a small number of contact points but with reduced static friction.
These results indicate that exploiting hierarchical structure, global friction properties
of a surface can tuned arbitrarily acting only on the geometry, without changing
microscopic friction coefficients. To achieve this, it is essential to provide structuring at
various different length scales.
In this study, the effect of different length scales and structure has been studied for constant
material stiffnesses and local friction coefficients, but in future we aim to verify the existence
of universal scaling relations by changing the system size parameters, and to analyze the role of
the mechanical properties, e.g. for composite materials or graded frictional surfaces. Also, a
natural extension of this study is to consider two- or three-dimensionally patterned surfaces,
allowing a more realistic description of experimental situations and a larger variety of surface
texturing possibilities. These issues will be explored in future works.
\section*{Acknowledgments}
N.M.P is supported by the European Research Council (ERC StG Ideas 2011 BIHSNAM no. 279985 and ERC
PoC 2015 SILKENE no. 693670), and by the European Commission under the Graphene Flagship (WP14
'Polymer nanocomposites', no. 696656). G.C. and F.B. are supported by BIHSNAM.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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Creech Holler is a band from Murfreesboro, Tennessee (and later relocated to Nashville Tennessee). The band name "Creech Holler" is not very intuitive. At first I thought the name was composed of two last names from a fantasy book by Sharon Creech called Ruby Holler. But on the Internet, I found the right answer. "Creech" is the family name of one member. The family comes from the mountainous areas outside Kingsport, Tennessee. "Holler" has two contextual meanings. In the South, "Holler" refers to a narrow valley between mountains. "Holler" also refers to a beastly sound, guttural cry or an exclamation. "Holler" is thus open to different interpretations and that is probably also why the band chose this name. The matter has been investigated and the case is closed (at least for my part). One should not underestimate the significance of a band name. A good name must interact with the lyrics and the music. If they in turn interacts with the album cover that would really close the circle.
Creech Holler was formed in 2004 and consists of Jeff Zentner (vocals, guitar and banjo), Christian Brooks (drums) and Joey Campbell (bass). Jeff Zentner and Christian Brooks met at a concert with Black Diamond Heavies, where the former performed solo. Joey Campbell - who was already familiar to Christian Brooks – joined up later. At the time Jeff Zentner lived in Asheville, North Carolina while Christian Brooks and Joey Campbell lived in Nashville, Tennessee. It is 400 km or a 4 ½ hour drive between the cities. This circumstance made it important for the band to make use of the time together during tours and in other contexts. Their creative process normally begins with Jeff Zentner who does a solo version of the song. Subsequently, the two other members come into the process. This implies a quick songwriting process. Themes for the songs are "murder, misery, religion and death." The debut album was called "With Signs Following". The title is a direct reference to "The Church of Jesus Christ with Signs Following" which is part of the Pentecostal movement. They are also called "Snake Handlers". The preachers of "With Signs Following" interprets certain passages in the Bible literally, especially the Gospel of Mark 16: 17-18: "And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues; They shall take up serpents; and if they drink any deadly thing, it shall not hurt them." The "With Signs Following" church follows the five signs: exorcism, speaking in tongues, laying on of hands, drinking poison (preferably strychnine or lye), and handling poisonous snakes. Faith is an incredibly powerful weapon. Not quite as many as you might expect have died from snake bites or by drinking poison, but the commitment has claimed its victims over the years. The handling of snakes is prohibited since the 1940s, but the long arm of the law is not always long enough to reach out in all capillaries in U.S., especially in rural areas. Snake handling still occurs.
The music consists of original and traditional songs, as well as an occasional cover. Creech Holler is not for everyone. The music can be described as "Southern Gothic set to stun." Creech Holler reminds of Woven Hand. It is dark, unsettling and enigmatic. The difference between them is that Creech Holler is more electric with feedback guitars and an extreme harsh treatment of the drums. In some cases it resembles of grunge-garage-blues. On the band's website, they write: "Creech Holler plays the music of midnight whiskey stills and front porches. of those whose sole act of contrition before god was to make song of their sin and sorrow. of those who have been to dark places, and who left their soul there. of those who deemed it necessary to kill some poor son of a bitch who had it coming to them, and then deemed it necessary to sing a song about it. of those who loved the sacred and the profane in equal measure; who played the devil's music on saturday night, and god's music on sunday morning. of those who have trod black paths so long that they have forgotten the light, but not so long so as to forget to bring their gun and a shovel. of those who saw fit to salve their wounds with the banjo, the fiddle, the guitar. of those who know no other way to touch the face of god than to take the venomous serpent to their breast, and drink deadly things, and take up fire, and live or die by the power of their faith and the force of their will and the sweat of their backs. creech holler is the hills and hollers of east tennessee and the fields of the delta, and the regret and desires and vain hopes of redemption buried under their soil. it's everywhere that america's bad blood flows and gives birth to hymns to the wrong that lives in low men's hearts. it's the ghosts of america's music reborn in furious electricity."
The authenticity of Creech Holler - with their roots deeply entrenched in the American South - is indisputable. Creech Holler is also represented with a song on one (Rodentia I) of the four compilations with The Best of Dark Roots from Devils Ruin Records. It is a mark of quality (let be an obscure one). Creech Holler is on an indefinite hiatus. Time will tell if the hiatus is permanent or not. A lot of time has now passed and I would be very surprised if Creech Holler took off again. There's however no discord between the members. Not even a commuting problem anymore, since everyone nowadays lives in Nashville, Tennessee. Jeff Zentner has released three solo albums: Hymns To The Darkness (2006), The Dying Days Of Summer (2009) and A Season Lost (2012). Creech Holler has released two albums: "With Signs Following" (2006) and "The Shovel And The Gun" (2008). The album covers are outstanding, but the back covers are even more spectacular. Both albums are designed by Gin Stevens. On the first album cover: a dead corkwood where the branches are decorated with bottles, back cover: a "Snake Handler" with his hands full of snakes. On the second album cover: a hand, tattooed with a gun and the word "fate". The hand rests on a playing card with two crossed shovels, back cover: a gravedigger with a firm grip on a shovel. Can it get any better than that in the "gothic country" genre? Probably not.
Below is a suggestion for a CD compilation.
With Signs Following
Lester Ballard
Little Mathie Grove
Red Rockin Chair
Poor Old Maddie
Plaugue Of Frogs
The Shovel And The Gun
Maggie Rose
Willie Williams
Darlin' Corey
When The Temptor Calls
Devils's Eyes
Serpent King
The Color Of Bone
Poor Pilgrim Of Sorrow
Best album: With Signs Following or The Shovel And The Gun (can't decide)
Best songs: Plague of Frogs, Devils's Eyes, The Cuckoo, Serpent King, Poor Pilgrim Of Sorrow
Konztroll
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ACCEPTED
#### According to
Index Fungorum
#### Published in
null
#### Original name
Pluteus magnus McClatchie {?}
### Remarks
null
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NEW RICHMOND, WI The 31st annual USA Nationals weekend kicked off on Thursday, August 2nd at the immaculate 3/8s-mile of Cedar Lake Speedway (WI) located just across the Minnesota/Wisconsin state line and northeast of Minneapolis, MN in New Richmond, WI. The first of three nights of racing for the World of Outlaws® Craftsman Late Model Series, would see the teams vie for a $6,000 to win payday and some important track time in anticipation of Friday and Saturday'sshow. After swapping the lead back and forth several times over the coarse of the race, Brandon Sheppard slipped by Jonathan Davenport for the final time coming down for the checkered to secure his 10th Feature Win of the season.
"Yeah that was fun! It was hard to know where to be most of the night, but we found a good groove in the middle of the track. I knew J.D. (Jonathan Davenport) was going to the top. He kept getting a run on me up there, but we were a little bit better in the middle." Explained the 25-year-old driver of the #1 Seubert Calf Ranches / Rocket XR1 Chassis / Durham Racing Engines machine. "I was pretty lucky that I could stay up to his quarter panel, so that last lap I was able to get a good run on him. I wasn't too sure I could get by him there at the end though. But, I was able to get into the corner with both rear tires and get gripped up really good and it just worked out for us." He added.
In continuation of the Outlaws "Week of Wisconsin" road trip and the series' 24th all-time appearance at Cedar Lake, it would be Davenport and Madden bringing the stellar 24-car field to the green flag for the 40-lap Feature and it would be Davenport powering his way to the front to lead the opening lap. Sheppard, who started right behind Davenport in third, was also able to get past Madden to place himself in second and set his sights on Davenport. On lap four, Sheppard maneuvered around the outside of Davenport to take the lead only to lose it back to Davenport two laps later. Sheppard regrouped on the next lap and retook the lead and pulled away from Davenport and the rest of the field.
Davenport lost the second spot to 2017 rookie of the year and PFC Brakes Fast Qualifier, Devin Moran on lap 11, but would regain the runner-up spot on lap 25 and reset his sights back on Sheppard. With three laps to go, Davenport pulled up along-side Sheppard and retook the lead again, but Sheppard stayed next to Davenport as the crowd rose to their feet over the closing laps. Davenport tried to hold back the continued advances of Sheppard, but the defending series champion was up to the task and with one final push, Sheppard edged back out ahead of Davenport and beat him to the line as the checkered flag flew by 0.266 seconds to score the thrilling victory.
For Sheppard, this is his 10th win of the season and 34th of his Outlaws career to move him to within three of fifth place all-time behind 2011 series champion, Rick Eckert who has 37 career Feature Wins. It was three races ago back on July 10th at Black Hills Speedway (SD) when Sheppard scored his 32nd career win to move him ahead of another former series champion, 2004 titlist, Scott Bloomquist to move into sixth all-time on the career wins list.
For the second race in a row, Davenport recorded a podium finish, this time one spot better than just two nights ago at Shawano Speedway (WI) where he finished third. This time, the Blairsville, GA driver in his #49 Crop Production Services / Longhorn Chassis / Cornett Racing engines entry settled for the runner-up spot. "Brandon (Sheppard) and I always race good together, we race hard and we race each other clean. I had him passed a couple of times and I could just about always get a decent run coming out of the corners. Stated the 34-year-old driver in the pits after the post-race ceremonies. "I tried to take his line away, but he knew what he was supposed to do there at the end and he did it. We know we can be better. We've got a good idea now of what we need to do for the rest of the weekend." He smiled.
O'Neal notched a career high in Outlaws competition, fourth place showing in his 11th career series appearance as Jimmy Mars rounded out the top five. Madden finished in sixth but took over the points lead outright while Chris Simpson advanced 10 spots to score a seventh place showing ahead of Ricky Weiss who picked up 11 positions to finish eighth. Brian Shirley was ninth as Jimmy Owens completed the top 10.
Earlier in the evening in PFC Brakes Qualifying, Moran won his third in a row, sixth of the season and ninth Fast Qualifier award of his career with a 13.563 over the 45-car field. Madden, Sheppard, Davenport and Babb won Qualifier Heat Races while Chris Simpson and Billy Moyer picked up the wins in the Last Chance Showdowns.
The World of Outlaws Craftsman Late Model Series continues the Week of Wisconsin on Friday, August 3rd with Qualifying night featuring the unique Double Heat Races format. Passing points will be accumulated based on positions gained in the two heat races each competitor competes in during the night. The top 16 drivers with the most passing points will be locked into the Feature on Saturday. Additionally, the top eight (8) drivers within the top 16 will race in the USA Nationals Dash to compete for starting spots in the top four rows of the $50,000 to Win Sears Craftsman Feature on Saturday. Also, on Friday night, the traditional FANS Fund Dash will close out the evening of racing.
Then on Saturday, August 4th, it'll be the Last Chance Showdowns followed by the $50,000 to Win USA Nationals that will wrap up the race weekend in the Cheese State. Don O'Neal pocketed $50,000 for his USA Nationals victory in 2017 while Chris Madden grabbed the checkered flag on preliminary night. Overall, three-time series champion, Billy Moyer leads the way with seven career wins at the track including five career USA Nationals titles while four-time series champion, Josh Richards has three career triumphs as two of those wins have come in the USA Nationals. Jonathan Davenport has two checkered flags as he swept both the prelim night and the USA Nationals in 2015 and now Sheppard has two wins, both coming on Prelim Nights.
There are 11 other drivers who have at least one victory with O'Neal, Jimmy Owens, 2006 series champion, Tim McCreadie, three-time series champion, Darrell Lanigan, 2004 series champion, Scott Bloomquist and Dale McDowell all getting their wins in the USA Nationals. Madden, Jimmy Mars, Donnie Moran and Rick Egersdorf have all scored victories at Cedar Lake as well.
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Bravehearts welcome tougher stance on child sex offenders
Jarrod Bleijie Tom Huntley
by adavies
Adam Davies Senior Journalist
Adam was born in New South Wales and was educated at the prestigious Scots College in Sydney. He has worked both in Australia and United Kingdom for some of the largest newspapers in the two respective countries. He joined APN as a senior journalist at The Chronicle in Toowoomba in 2010, before moving to APN'S Brisbane Newsdesk in 2013 where he covered politics and court. Adam won a 2015 Queensland Clarion Award - the state's premier journalism awards - and was named 2011 APN Daily Reporter of...
QUEENSLAND child protection organisation Bravehearts has welcomed the decision to introduce mandatory jail time for dangerous sex offenders who remove or tamper with their electronic monitoring bracelets.
Attorney-General Jarrod Bleijie said on Monday five offenders have been charged with removing their devices since 2011.
"Sex offenders who remove or tamper with their bracelets will be sentenced to one year's mandatory jail time with a maximum penalty of five years in prison," he said.
"This will be a strong deterrent for offenders who abscond and it will also ensure that those who do so will go back to prison.
"It sends a strong message to sex offenders that we are watching them and that we will not tolerate any attempts to breach their conditions."
Under sweeping changes to legislation, which will be introduced into State Parliament later this year, Mr Bleijie said offenders who procure a child or a person with an impairment of the mind for prostitution would also face increased penalties.
"The kind of people who would exploit innocent children and people with mental disabilities deserve tough sentences," he said.
"The maximum penalty will be increased from 14 years in prison to 20 years.
"The offence will also be classified as a serious violent offence meaning an offender will have to serve 80% of their sentence before being eligible for parole."
Bravehearts research and policy manager Carol Ronken said the proposed changes were definitely a step in the right direction.
"We are extremely supportive of the Queensland Government's policies in relation to sex offenders," she said.
"Generally the people who wear monitoring bracelets are the worst of the worst anyway.
"If they want to remove their bracelets then clearly they have ulterior motives for doing so and it raises a huge red flag."
Premier Campbell Newman said he "absolutely" endorsed proposed changes to the legislation.
"Queenslanders expect stronger protections for our kids and that is exactly what we are determined to do," he said.
Mandatory jail for sex offenders who break release rules
Police probe pedophile priest allegations from inquiry
Commission hears of cruel abuser who moved from home to home
Appeal on nine-month jail sentence of child sex offender
Moves for permanent prison for QLD sex offenders
Sex offender Fardon to stay out of jail as options run out
Bravehearts says children should be taught personal safety
Woman sold five underage girls for sex
Pensioner's shock: escort turns out to be son's girlfriend
Mowerthon man cutting path to realise child safety
jarrod bleijie
bravehearts child abuse jarrod bleijie sex offenders
Weather Severe thunderstorms have dumped almost 70mm in an hour to some regions as the latest alert warned of "life-threatening flooding". LATEST WARNINGS
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Loučenská hornatina je jeden ze dvou geomorfologických podcelků Krušných hor. Její severní hranice sleduje hranici s Německem, na jihu je oddělena od prostoru Podkrušnohorských pánví tzv. Krušnohorským zlomem. Na západě hraničí s Klínoveckou hornatinou, přibližně v linii Perštejn – České Hamry a na východě končí Nakléřovským průsmykem, který ji odděluje od Děčínské vrchoviny.
Zatímco jižní svahy pokrývají především zachovalé bučiny, smrkové porosty na hřebenu vinou neúnosného emisního zatížení z elektráren v podhůří většinou odumřely. Nyní probíhá jejich nákladná obnova. Důležitou složku zdejší přírody tvoří rašeliniště vrchovištního typu (např. NPR Novodomské rašeliniště).
Vrcholy
Pro Loučenskou hornatinu je charakteristické, že žádný z vrcholů nepřesahuje 1000 m n. m. Nejvyšším vrcholem je Jelení hora (993 m), ale pojmenována byla podle Loučné (956 m). Další významné body: Medvědí skála (923 m), Jedlová (853 m), Střelná (868 m), Stropník (856 m), Bouřňák (869 m), Pramenáč (911 m), Komáří hůrka (808 m) a Špičák u Krásného Lesa (723 m). Celá hornatina má podobu náhorní plošiny, nad níž vystupují ojedinělé vrcholy, a od pánve je oddělená výrazným svahem, dosahujícím místy až 500 metrového převýšení.
Geomorfologické členění
Loučenská hornatina (v členění Jaromíra Demka označená jako IIIA-2B) se dělí na okrsky pojmenované podle sídelních útvarů:
Přísečnická hornatina
Rudolická hornatina
Novoveská vrchovina
Flájská hornatina
Cínovecká hornatina
Nakléřovská vrchovina
Bolebořská vrchovina
Podrobné dělení včetně podokrsků je vidět v následující tabulce:
Externí odkazy
Geomorfologické jednotky Krušných hor
Pohoří v Česku
Geomorfologické podcelky v Česku
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"Botswana decriminalizes gay sex in landmark Africa case" – Associated Press
JOHANNESBURG (AP) — Botswana became the latest country to decriminalize gay sex on Tuesday in a landmark case for Africa when the High Court rejected as unconstitutional sections of the penal code…
Language Analysis
Sentiment Magnitude
-0.1 13.5
JOHANNESBURG – Botswana became the latest country to decriminalize gay sex on Tuesday when the High Court rejected as unconstitutional sections of the penal code that punish same-sex relations with up to seven years in prison.
It came less than a month after Kenya's High Court had upheld similar sections of its own penal code in another closely watched case.
More than two dozen countries in sub-Saharan Africa have laws criminalizing gay sex.
Earlier this year, the southern African nation of Angola also decriminalized same-sex activity and banned discrimination based on sexual orientation.
Those arguing against the laws criminalizing gay sex say they leave people in the LGBT community vulnerable to discrimination and abuse while making it difficult to access basic health and other services.
Tuesday's ruling led to rejoicing by rights groups that had expressed frustration with the Kenyan decision last month.
Botswana's High Court said in its ruling that penalizing people for who they are is disrespectful, and that the law should not deal with private acts between consenting adults.
https://apnews.com/3872487731374ea18b5b27e5fe16105a
Author: CARA ANNA
gay , right , ruling
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\section{Introduction} \label{intro}
The vast majority of numerical methods, such those of Newton, Euler, Lagrange, Gauss, Fourier, Jacobi, Runge-Kutta and so many others~\cite{Numerov6}, were introduced in the context of applications in physics, astronomy or in other areas of a technical nature, such as aerodynamics. Since then, numerical analysis was not being recognized as a mathematical discipline and this situation persisted during the first four decades of 20th century. Even today, although some numerical methods are taught in physics courses, within the disciplines of mathematics, little emphasis is given to them in physical applications.
In the las decades, the teaching of computing techniques has become more present and also increasingly essential in the development of students from all areas, and therefore, it would not be different for physics teaching. Having said that, it is of paramount importance that we always produce new teaching materials for new technologies such as the Python programming language, which, despite of being relatively new, has already dominated the market to become one of the most important languages today.
We will disclose here a powerful numerical calculation method originally developed by Boris Vasil'evich Numerov~\cite{Numerov, Numerov2}, see also~\cite{Numerov3, Numerov4, Numerov5, baugci2021efficient}, applying it to the time-independent Schr\"{o}dinger equation describing physical systems like the hydrogen atom, a diatomic molecule governed by the Morse potential and one model for the quantum dot atom~\cite{Caruso, caruso2017corrigendum, BJP}. These three examples will be solved and the parameters needed for each solution using Numerov's method will be shared in their respective sections.
In summary, this work aims to provide the complete code developed in Python with the {\it Jupyter Notebook} for the Numerov's numerical method. However, it is important to emphasize that we do not aim to teach Python to the reader, who must have a basic knowledge of programming to be able to keep up the examples.
\section{Numerov's Method} \label{NM}
Numerov's initial motivation was to be able to calculate corrections to the trajectory of comet Halley. Therefore, Numerov's method was initially developed to determine solutions to eigenvalue problems associated with ordinary differential equations of second order of celestial mechanics, which did not contain terms involving the first derivative of a function unknown $y(x)$, that is, equations of the form
\begin{equation}\label{dif}
\frac{\mbox{d}^2y}{\mbox{d}x^2} = f(y,x).
\end{equation}
Every differential equation equal to equation~(\ref{dif}) can be replaced by the following system of first order equations
\begin{equation*}
\left\{
\begin{array}{ll}
\displaystyle \frac{\mbox{d}z}{\mbox{d}x} = f(x,y),\\
\displaystyle z = \frac{\mbox{d}y}{\mbox{d}x}.\\
\end{array}
\right.
\end{equation*}
Traditional methods for numerically solving this system of equations, such as those of Euler or Runge-Kutta, consider that the values of $y(x)$ and of $\mbox{d}y/\mbox{d}x$ are known at a given point in the domain $[a, b]$ of system validity, \textit{i.e.}, are suitable for the so-called seed problems.
In non-relativistic quantum mechanics, more specifically in bound state problems involving a particle of mass $m$ confined in a well of potential $V(x)$, in a given interval $a < x < b$, the allowed energies $(E)$ and the corresponding wave functions $\psi(x)$ that describe these steady states satisfy the Schr\"{o}dinger's eigenvalue equation
\begin{equation}\label{sch1}
\frac{\mbox{d}^2\psi}{\mbox{d}x^2} + k^2(x) \psi = 0
\end{equation}
where $k = \sqrt{2m[E-V(x)]}/\hbar$ and $\hbar \simeq 1.055 \times 10^{-34} J.s$ is the reduced Planck constant.
In these cases, as the value of the first derivative of the wave function is not known, the Euler and Runge-Kutta cannot be employed. Nonetheless, it is possible to establish continuity conditions for the values of $\psi$ and $\mbox{d}\psi/\mbox{d}x$ at two or more points of the domain of the wave function, which characterizes the so-called boundary value problems.
In addition to making the transformation of a second order differential equation in a first order system, the Numerov method allows the simultaneous determination of the energy spectrum of the particle and of the eigenfunctions associated with each energy value.
Like any iterative numerical method, the solution of equation~(\ref{sch1}) is constructed by successive integrations. In Numerov's method, initially, the solution is considered to be known at two subsequent points of the interval $[a, b]$, for example, at $\psi(x - \delta)$ and $\psi(x)$, where $\delta$ is an arbitrarily small quantity, called the integration step. Next, we try to establish an algorithm to determine the solution at the next point, $\psi(x + \delta)$.
The starting point for establishing this algorithm is the expansion of $\psi(x \pm \delta)$ in Taylor series, up to fourth-order derivatives, that is,
\begin{equation}\label{taylor}
\psi(x\pm\delta)=\psi(x) \pm \delta \psi'(x) + \frac{\delta^2}{2}\psi''(x) \pm \frac{\delta^3}{6}\psi'''(x) + \frac{\delta^4}{24}\psi^{iv}(x)
\end{equation}
Adding the terms $\psi(x + \delta)$ and $\psi( x - \delta)$, only the derivatives of even order survive and, therefore, a relationship between the values of a function in three is reached. points and its second derivative, given by
\begin{equation}\label{taylor2}
\frac{\psi(x+\delta)+\psi(x-\delta)-2\psi(x)}{\delta^2} = \psi''(x)+\frac{\delta^2}{12}\psi^{iv}(x) \equiv \left(1+\frac{\delta^2}{12}\frac{\mbox{d}^2}{\mbox{d}x^2}\right)\psi''{x}
\end{equation}
Writing the unidimensional Schr\"{o}dinger equation, equation~(\ref{sch1}), in a more convenient form
\begin{equation}\label{taylor3}
\left(1 + \frac{\delta^2}{12}\frac{\mbox{d}^2}{\mbox{d}x^2}\right)\psi''(x) = -k^2(x) \psi(x) - \frac{\delta^2}{12}\frac{\mbox{d}^2}{\mbox{d}x^2}\left[k^2(x)\psi(x)\right]
\end{equation}
\noindent and using equation~(\ref{taylor2}) to replace the terms that contain second order derivatives, one obtains
\begin{eqnarray}\label{taylor4}
&&\frac{\psi(x+\delta) + \psi(x-\delta) - 2\psi(x)}{\delta^2} = -k^2(x)\psi(x) \\
&& - \frac{\delta^2}{12} \times \left[\frac{k^2(x+\delta)\psi(x+\delta)+k^2 (x-\delta)\psi(x-\delta) - 2k^2(x)\psi(x)}{\delta^2}\right] + \mathcal{O}(\delta^4) \nonumber
\end{eqnarray}
\noindent Regrouping the therm we obtain the Numerov difference formula for the problem of a particle under action of a one-dimensional potential
\begin{equation}\label{taylor5}
\left[1 + \frac{h^2}{12} k^2(x+\delta)\right]\psi(x+\delta) = 2\left[1-\frac{5\delta^2}{12}k^2(x)\right]\psi(x) - \left[1+\frac{\delta^2}{12}k^2(x-\delta)\right]\psi(x-\delta)
\end{equation}
In fact, it should be noted that the algorithm can be applied to any ordinary linear differential equation and second-order homogeneous that does not contain terms of first derivative.
Since the problem of interest is an eigenvalue problem, the numerical integration technique of the one-dimensional Schr\"{o}dinger equation for a particle in a well depends on attaching arbitrary values conveniently to eigenvalues and to the respective (possible) eigenfunctions in 2 points of the domain of the problem. But how to do it? Regarding the choice of the initial value for the energy (first eigenvalue), just remember that, according to Heisenberg uncertainty relation, the energy $E$ of a particle in a well of potential $V(x)$ must be greater than the minimum value of the well. Thus, it is considered, initially, that $E_{initial} = V_{min} + \Delta E$, with $\Delta E >0$
The choice of a energy value, determines two turning points, $x_{\ell}$ and $x_{r}$, where the energy value is equal to potential energy value, whose motion obeys the classical Newtonian mechanics. That is, from the point of view of classical mechanics, the movement of the particle is restricted only to the region $\left[x_{\ell},x_{r}\right]$, in which the energy is greater than or equal to the potential energy. The regions $x<x_{\ell}$ and $x>x_{r}$ are called classically prohibited regions, and are indicated in Fig.~\ref{fig1}
\begin{figure}[ht]
\centerline{\includegraphics[width=8.0cm]{figura1}}
\caption{Meeting points between the potential curve and the initial energy, also called turning points.}
\label{fig1}
\end{figure}
As the Schr\"{o}dinger equation admits solutions for these classically prohibited regions, for each energy value, initially, values are assigned to a possible eigenfunction at two points of the classically prohibited regions, in which the function practically cancels itself. In general, these are the boundary points $a$ and $b>a$ of the function's integration domain.
However, the implementation of Numerov's method to solve the problem still requires an iteration scheme that uses the Numerov formula in two steps: from $a$, or to the left of $a$ from the classic turning points, hereinafter called match point ($x_{match}$), and from $b$, or to the right of the match point.
Thus, arbitrarily taking a initial value for the energy, and two successive arbitrary values for the solution, starting from the lower extremes and upper part of the integration interval $\left[a,b\right]$, one can implement the method's iteration scheme in the two senses, such as:
\begin{itemize}
\item Solution to the left of match point $(x<x_{match})$
\end{itemize}
Being $E_{initial} = V_{min} + \Delta E \left(\Delta E/|V_{min}|\ll1\right)$ an arbitrary value for the energy of the particle. Also arbitrating values for the function of wave, in 2 successive points, from $a$,
\begin{equation*}
\left\{
\begin{array}{ll}
\psi^{\ell}(a)=0,\\
\psi^{\ell}(a+\delta) = \delta^\ell,\quad (\delta^\ell \ll 1)\\
\end{array}
\right.
\end{equation*}
\noindent and using the formula of differences, equation~(\ref{taylor5}), the solution on the left is built sequentially until match point $(x_{match})$, in what $\psi^\ell(x_{match}) = \psi^\ell_{match}$.
\begin{itemize}
\item Solution to the right of match point $(x>x_{match})$
\end{itemize}
From a similar way, for the same values $E_{initial}$, arbitrating
\begin{equation*}
\left\{
\begin{array}{ll}
\psi^{r}(b)=0,\\
\psi^{r}(b+\delta) = \delta^r,\quad (\delta^r \ll 1)\\
\end{array}
\right.
\end{equation*}
the solution to the right, from $b$, is constituted sequentially until the points $x_{match}$ and $x = x_{match}-\delta$, as
\begin{equation*}
\left\{
\begin{array}{ll}
\psi^{r}(x_{match})=\psi^{r}_{match},\\
\psi^{r}(x_{match} - \delta) = \psi^r_{match -1},\quad (\delta^r \ll 1)\\
\end{array}
\right.
\end{equation*}
To guarantee the boundary condition of the solution, we redefine the solution to the left according to equation~(\ref{eq8}) given below, and the boundary condition of the first derivatives, according to equation~(\ref{eq9}).
The procedure is repeated step by step, in the two ways, $a \rightleftharpoons b$. Starting from $a$, using the Numerov recurrence formula associated with an equation, if we build the solution $\psi^\ell$ until the classic rewind point, nearest of $b$, where $E = V(x_{match})$, called the match point. Then, from $b$, the analog is made, building a solution $\psi^r$ to the match point. In principle, the possible solutions $\psi^\ell$ and $\psi^r$ will not necessarily be equal in this $x_{match}$ stitch. To ensure the continuity of the solution redefines itself $\psi^\ell$ like
\begin{equation}\label{eq8}
\psi^\ell(x) \rightarrow \psi^\ell(x) \frac{\psi^r (x_{matxh})}{\psi^\ell (x_{matxh})} \quad (a \leq x \leq x_{match})
\end{equation}
Finally, it is verified how close are the values of the respective first derivatives of $\psi^r$ and the new function $\psi^\ell$ It is staggered, at match point. To test the boundary condition of the derivatives first, taking into account Taylor's series for $\psi(x+\delta$ and $\psi(x-\delta)$, up to the first order, you can write
\begin{equation}\label{eq9}
\left\{
\begin{array}{ll}
\frac{\mbox{d}\psi^\ell}{\mbox{d}x} \big{|}_{x_r} = \frac{\psi^\ell_{match+1}-\psi^\ell_{match-1}}{2\delta},\\
\frac{\mbox{d}\psi^r}{\mbox{d}x} \big{|}_{x_r} = \frac{\psi^r_{match+1}-\psi^r_{match-1}}{2\delta},\\
\end{array}
\right.
\end{equation}
\noindent in what, $\psi_{match\pm1} = \psi(x_{match\pm\delta})$.
If the difference between these values is less than the values of a predefined error, the process is interrupted, confirming the searched eigenvalue and the respective eigenfunction as being
\begin{equation*}
\left\{
\begin{array}{ll}
\psi^{\ell}(x), \quad (a \leq x < x_{match})\\
\psi^{r}(x), \quad (x_{match} \leq x \leq b)\\
\end{array}
\right.
\end{equation*}
If the continuity condition of the derivatives is not satisfied, the value of the energy is increased and we restarted a search for a new value which is really an eigenvalue of the problem, and its respective eigenfunction.
The process can be repeated until the desired number of eigenvalues and eigenfunctions of the problem.
Because it is based on Taylor's serial expansion to fourth order, the error in Numerov's method is much smaller than the errors that come out from the expansion-based methods in lower order, like that of Runge-Kutta.
\newpage
\section{Hidrogen Atom} \label{atom}
Numerical solutions of hydrogen atom was previously obtained in~\cite{Numerov6} using Numerov's method. The program was written in C++ for the ROOT cint compiler.
Although it was originally developed for second order linear and homogeneous ordinary differential equations that do not contain terms of the first derivative, the
Numerov's method can be generalized to cover the presence of terms that contain the first derivative in the differential equation, so that eigenvalue problems can also be considered.
In fact, in the case of linear equations, every equation second order differential of type
\begin{equation*}
\frac{\mbox{d}^2y}{\mbox{d}x^2} + P(x) \frac{\mbox{d}y}{\mbox{d}x} + Q(x)y = 0
\end{equation*}
\noindent can be written in its normal form
\begin{equation*}
\frac{\mbox{d}^2y}{\mbox{d}x^2} = q(x)y = 0
\end{equation*}
\noindent where
\begin{equation*}
q(x) = Q(x) - \frac{1}{4} P^2(x) - \frac{1}{2}\frac{\mbox{d}P}{\mbox{d}x}
\end{equation*}
Schr\"{o}dinger's radial equation for a particle of mass $m$ under the action of a Coulombian electric field, like the electron in the hydrogen atom, can be
written as
\begin{equation}\label{sch}
\frac{\mbox{d}^2R(r)}{\mbox{d}r^2} + \frac{2}{r} \frac{\mbox{d}R(r)}{\mbox{d}r} + \frac{2m}{\hbar^2}\left[E+\frac{e^2}{r} - \frac{\hbar^2}{2m} \frac{\ell(\ell+1)}{r^2}\right]R(r) = 0
\end{equation}
Making the substitution $r = xa_B$ with $a_B = \hbar^2/(me^2)$ being the Bohr radius, equation~(\ref{sch}) can be rewritten, for a new function $y(x) = R(r)$ as
\begin{equation}\label{sch2}
\frac{\mbox{d}^2y}{\mbox{d}x^2} = -\frac{2}{x}\frac{\mbox{d}y}{\mbox{d}x} - \left[\varepsilon - V(x)\right]y(x)
\end{equation}
\noindent where, $\varepsilon = \frac{E}{e^2/(2a_B)}$ and $V(x) = \frac{\ell(\ell+1)}{x^2} - \frac{2}{x}$ are, respectively, the energy and the so-called effective potential in atomic units. So, in possession of equation~(\ref{sch2}), we can start building our program code.
First of all, we must import the functions available in the Pylab module that bulk imports matplotlib.pyplot (for plotting) and NumPy (for Mathematics and working with arrays) in a single name space. We then declare who our effective potential $V(x)$ is, and during the construction of this example we will use $\ell=0$.
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
{\color{darkgreen}{\bf from}} pylab {\color{darkgreen}{\bf import}} {\color{purple}*}
x {\color{purple}=} linspace({\color{purple}-}{\color{darkgreen}10},{\color{darkgreen}10},{\color{darkgreen}1001})
{\color{darkgreen}{\bf def}} V(x):
L{\color{purple}=}{\color{darkgreen}0}
Vx{\color{purple}=}{\color{purple}-}{\color{darkgreen}2}.{\color{purple}{\color{purple}/}}x
{\color{darkgreen}{\bf return}} Vx
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
{\color{darkgreen}def} vec_max(dim,x): #left maximum
xmax{\color{purple}=}{\color{darkgreen}0}
N{\color{purple}=}dim
{\color{darkgreen}for} j in range(int(N)):
if j<int(N) and abs(x[j])>xmax:
xmax{\color{purple}=}abs(x[j])
else:
continue
{\color{darkgreen}return} xmax
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
The equation, in this case, that is intended to be solved by Numerov's method presents a term involving the first derivative, and can be expressed by
\begin{equation}\label{13}
\psi''(x) = -p(x)\psi'(x) - s (x)\psi(x),
\end{equation}
where
\begin{equation*}
\left\{
\displaystyle \begin{array}{ll}
\displaystyle p(x)=\frac{2}{x} \quad \Rightarrow \quad p'(x) = - \frac{2}{x^2},\\
\displaystyle s(x) = \varepsilon - V(x).\\
\end{array}
\right.
\end{equation*}
From the Taylor expansions, equation~(\ref{taylor}), we can rewrite equation~(\ref{13}) as
\begin{equation}\label{14}
\left(1+\frac{\delta^2}{12}\frac{\mbox{d}^2}{\mbox{d}x^2}\right)\psi''(x) = -p(x)\psi'(x) - s(x)\psi(x) - \frac{\delta^2}{12}\frac{\mbox{d}^2}{\mbox{d}x^2}\left[p(x)\psi'(x) + s(x)\psi(x)\right].
\end{equation}
In a similar way to the previous case, according to equation~(\ref{taylor2}), you can write the term on the right side of the equation~(\ref{14}) which contains derivatives of order 2, such as
\begin{eqnarray*}
&&\frac{\mbox{d}^2}{\mbox{d}x^2} \left[p(x)\psi'(x) + s(x)\psi(x)\right] = \frac{1}{\delta^2} \left[p(x+\delta)\psi'(x+\delta) + s(x+\delta)\psi(x+\delta) +\right. \\
&& + \left. p(x-\delta)\psi'(x-\delta) + s(x-\delta)\psi(x-\delta) + -2p(x)\psi'(x)-2s(x)\psi(x)\right]
\end{eqnarray*}
Replacing first order derivatives with approximations
\begin{equation*}
\left\{
\begin{array}{lll}
\psi'(x) = \left[\psi(x+\delta) - \psi(x-\delta)\right]/(2\delta),\\
\psi'(x+\delta) = \left[\psi(x+\delta) - \psi(x)\right]/(\delta),\\
\psi'(x-\delta) = \left[\psi(x) - \psi(x-\delta)\right]/(\delta),\\
\end{array}
\right.
\end{equation*}
\noindent we obtain
\begin{eqnarray*}
&& \frac{\mbox{d}^2}{\mbox{d}x^2}\left[p(x)\psi'(x) + s(x)\psi(x)\right] = \frac{1}{\delta^2} \left\{ \left[\frac{p(x+\delta)-p(x)}{\delta}+s(x+\delta)\right]\times\right. \\
&& \times \psi(x+\delta)+ \left.\left[\frac{p(x)-p(x-\delta)}{\delta}+s(x-\delta)\right]\psi(x-\delta) +\right. \\
&& + \left.2\left[\frac{p(x-\delta)-p(x+\delta)}{2\delta}+s(x)\right]\psi(x) \right\}
\end{eqnarray*}
\noindent or
\begin{eqnarray}\label{17}
&& \frac{\mbox{d}^2}{\mbox{d}x^2} \left[p(x)\psi'(x) + s(x)\psi(x)\right] = \frac{1}{\delta^2} \left\{ \left[p'(x)+s(x+\delta)\right]\psi(x+\delta)+\right. \nonumber\\
&& + \left.\left[p'(x)+s(x-\delta)\right]\psi(x-\delta) - 2\left[p'(x)+s(x)\right]\psi(x) \right\}
\end{eqnarray}
Taking into account that the left side of the equation~(\ref{14}) is equal to
\begin{equation*}
\left[\psi(x+\delta)+\psi(x-\delta)-2\psi(x)\right]/\delta^2
\end{equation*}
\noindent we can write
\begin{eqnarray*}
&&\frac{\psi(x+\delta)+\psi(x-\delta) - 2\psi(x)}{\delta^2} = -p(x)\left[\frac{\psi(x+\delta)-\psi(x-\delta)}{2\delta}\right] \\
&& - s(x)\psi(x) + \frac{1}{12}\left[p'(x)+s(x+\delta)\right]\psi(x+\delta) \\ &&
- \frac{1}{12}\left[p'(x)+s(x-\delta)\right]\psi(x-\delta) + \frac{1}{6}\left[p'(x)+s(x)\right]\psi(x)
\end{eqnarray*}
Regrouping the terms, and making
\begin{equation*}
\left\{
\begin{array}{lll}
\psi(x-\delta)=\psi_0,\\
r\psi(x)=\psi_1,\\
\psi(x+\delta) = \psi_2,\\
\end{array}
\right.
\end{equation*}
\noindent one obtains the Numerov difference equation for the problem, suitable for the propagation of the solution from of the limits of the integration interval
\begin{equation}\label{19}
\psi_2 = \frac{2\left\{1-\left[s(X)-\frac{p'(x)}{5}\right]\frac{5\delta^2}{12}\right\}\psi_1 -\left\{1-p(x) \frac{\delta}{2} + \left[s(x-\delta)+p'(x)\right]\frac{\delta^2}{12} \right\}\psi_0}{\left\{1+p(x)\frac{\delta}{2}+\left[s(x+\delta)+p'(x)\right]\frac{\delta}{12}\right\}}
\end{equation}
From this formula, a procedure analogous to the previous case can be implemented for the construction of solutions of the radial Schr\"{o}dinger equation in the interval $(0,\infty)$.
Now, in order to introduce the Numerov diference formula~(\ref{19}), we first need to insert equation~(\ref{taylor5}) in our code, for that, let's break it down into different pieces $p_0$, $p_1$ and $p_2$, with $h=\delta$, $q_0 = s(x)$. Thus, equation~(\ref{19}) is now called $y_2$, where $\psi_i = y_i$.
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
{\color{darkgreen}def} nrovl(y0, y1, x0, E, h, iflag):
q0 {\color{purple}=} (E{\color{purple}-}V(x0))
q1 {\color{purple}=} (E{\color{purple}-}V(x0{\color{purple}+}h))
q2 {\color{purple}=} (E{\color{purple}-}V(x0{\color{purple}+}h{\color{purple}+}h))
p0 {\color{purple}=} ({\color{darkgreen}1} {\color{purple}+} h{\color{purple}*}h{\color{purple}*}q0{\color{purple} /}{\color{darkgreen}12})
p1 {\color{purple}=} {\color{darkgreen}2}{\color{purple}*}({\color{darkgreen}1} {\color{purple}-} {\color{darkgreen}5}{\color{purple}*}h{\color{purple}*}h{\color{purple}*}q1{\color{purple} /}{\color{darkgreen}12})
p2 {\color{purple}=} {\color{darkgreen}1} {\color{purple}+} h{\color{purple}*}h{\color{purple}*}q2{\color{purple} /}{\color{darkgreen}12}
y2 {\color{purple}=} (p1{\color{purple}*}y1{\color{purple}-}p0{\color{purple}*}y0){\color{purple} /}p2
if iflag<{\color{darkgreen}1}:
print(" x0 {\color{purple}=} ", x0," y0 {\color{purple}=} ", y0," V {\color{purple}=} ",V(x0))
print(" x1 {\color{purple}=} ", x0{\color{purple}+}h," y1 {\color{purple}=} ",y1," V {\color{purple}=} ",V(x0{\color{purple}+}h),
" y2 {\color{purple}=} ",y2)
{\color{darkgreen}return} y2
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
And, for the case $x-\delta$, we repeat the previous step, changing the appropriate sign.
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
{\color{darkgreen}def} nrovr(y0, y1, x0, E, h, iflag):
q0 {\color{purple}=} (E{\color{purple}-}V(x0))
q1 {\color{purple}=} (E{\color{purple}-}V(x0{\color{purple}-}h))
q2 {\color{purple}=} (E{\color{purple}-}V(x0{\color{purple}-}h{\color{purple}-}h))
p0 {\color{purple}=} ({\color{darkgreen}1} {\color{purple}+} h{\color{purple}*}h{\color{purple}*}q0{\color{purple} /}{\color{darkgreen}12})
p1 {\color{purple}=} {\color{darkgreen}2}{\color{purple}*}({\color{darkgreen}1} {\color{purple}-} {\color{darkgreen}5}{\color{purple}*}h{\color{purple}*}h{\color{purple}*}q1{\color{purple} /}{\color{darkgreen}12})
p2 {\color{purple}=} {\color{darkgreen}1} {\color{purple}+} h{\color{purple}*}h{\color{purple}*}q2{\color{purple} /}{\color{darkgreen}12}
y2 {\color{purple}=} (p1{\color{purple}*}y1{\color{purple}-}p0{\color{purple}*}y0){\color{purple} /}p2
if iflag<{\color{darkgreen}1}:
print(" x_100 {\color{purple}=} ", x0," y0_100 {\color{purple}=} ", y0," V {\color{purple}=} ",V(x0))
print(" x_99 {\color{purple}=} ", x0{\color{purple}-}h," y_99 {\color{purple}=} ",y1," V {\color{purple}=} ",V(x0{\color{purple}-}h),
" y_98 {\color{purple}=} ",y2)
{\color{darkgreen}return} y2
{\color{darkgreen}def} espectro(xl,xu,h,delta,eps,dim,nmax,kmax,Ein,Vmax,dE,iflag):
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
We now create a list for each variable up to the value of {\it dim} or {\it nmax} which will also be defined in a future step.
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
xx{\color{purple}=}list(range(dim)); yy{\color{purple}=}list(range(dim))
ww{\color{purple}=}list(range(dim)); yl{\color{purple}=}list(range(dim))
yr{\color{purple}=}list(range(dim)); ee{\color{purple}=}list(range(nmax))
ff{\color{purple}=}list(range(nmax)); ff2{\color{purple}=}list(range(nmax))
yy1{\color{purple}=}list(range(dim)); yy2{\color{purple}=}list(range(dim))
yy3{\color{purple}=}list(range(dim))
colors {\color{purple}=}['b','r','g','m','c']; nk{\color{purple}=}list(range(nmax))
E_old {\color{purple}=} Ein; E {\color{purple}=} Ein {\color{purple}+} dE
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
In the next steps, the program will determine the interaction for the eigenvalue candidates and determine their solutions as well as printing the parameters found on the screen.
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
{\color{darkgreen}for} M in range(nmax):
print(" ******* Eigenvalue #",M{\color{purple}+}{\color{darkgreen}1}," ******* ")
f_old{\color{purple}=}{\color{darkgreen}0}
{\color{darkgreen}for} k in range(kmax): #iteration for eigenvalue candidate
imatch{\color{purple}=}{\color{darkgreen}0}
{\color{darkgreen}for} j in range(dim{\color{purple}-}1): #classical right turning point
xx[{\color{darkgreen}0}]{\color{purple}=}xl; xx[dim{\color{purple}-}{\color{darkgreen}1}]{\color{purple}=}xu
DE1 {\color{purple}=} E {\color{purple}-} V(xx[j])
xx[j{\color{purple}+}{\color{darkgreen}1}] {\color{purple}=} xx[j]{\color{purple}+}h
DE2 {\color{purple}=} E {\color{purple}-} V(xx[j{\color{purple}+}{\color{darkgreen}1}])
D1D2{\color{purple}=}DE1{\color{purple}*}DE2
if D1D2<{\color{purple}=}{\color{darkgreen}0} and DE1 > {\color{darkgreen}0}: #match point
imatch {\color{purple}=} j{\color{purple}+}{\color{darkgreen}1}
print(" imatch {\color{purple}=} ",imatch," xmatch {\color{purple}=}
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
xmatch{\color{purple}=}xx[imatch]
ii{\color{purple}=}range(imatch{\color{purple}+}{\color{darkgreen}2})
i_lim {\color{purple}=} ii[{\color{darkgreen}2}:imatch{\color{purple}+}{\color{darkgreen}2}]
xx[{\color{darkgreen}0}]{\color{purple}=}xl; xx[{\color{darkgreen}1}]{\color{purple}=}xl{\color{purple}+}h #valores iniciais
yy[{\color{darkgreen}0}]{\color{purple}=}{\color{darkgreen}0}; yy[{\color{darkgreen}1}] {\color{purple}=} delta
{\color{darkgreen}for} i in i_lim: #numerov left solution
yy[i]{\color{purple}=}nrovl(yy[i{\color{purple}-}2],yy[i{\color{purple}-}1],xx[i{\color{purple}-}2],E,h,iflag)
xx[i]{\color{purple}=} xx[i{\color{purple}-}1]{\color{purple}+}h
jjj{\color{purple}=}list(range(dim{\color{purple}+}1))
j_lim {\color{purple}=} list(jjj[imatch{\color{purple}-}1:dim{\color{purple}+}1])
comp_j{\color{purple}=}len(j_lim)
jj{\color{purple}=}sorted(j_lim,key{\color{purple}=}abs,reverse{\color{purple}=}True)
{\color{darkgreen}for} i in range(dim):
if i<{\color{purple}=}imatch{\color{purple}+}1:
yl[i]{\color{purple}=}yy[i]
if i>imatch{\color{purple}+}1:
yl[i]{\color{purple}=}0
{\color{darkgreen}for} i in jj: #numerov right solution
if i{\color{purple}=}{\color{purple}=}dim:
yr[dim{\color{purple}-}1]{\color{purple}=}0
if i{\color{purple}=}{\color{purple}=}(dim{\color{purple}-}2):
yr[dim{\color{purple}-}2]{\color{purple}=}2{\color{purple}*}delta
if i<(dim{\color{purple}-}2):
yr[i]{\color{purple}=}nrovr(yr[i{\color{purple}+}2],yr[i{\color{purple}+}1],xx[i{\color{purple}+}2],E,h,iflag)
xx[i]{\color{purple}=} xx[i{\color{purple}+}1]{\color{purple}-}h
{\color{darkgreen}for} i in range(imatch{\color{purple}-}1):
yr[i]{\color{purple}=}0
ymatch{\color{purple}=}yy[imatch]
yrmatch{\color{purple}=}yr[imatch]
ylmatch{\color{purple}=}yl[imatch]
if ymatch !{\color{purple}=} 0:
scale{\color{purple}=}yrmatch{\color{purple} /}ymatch
else:
continue
{\color{darkgreen}for} t in range(imatch{\color{purple}+}1): # y_left
yy[t] {\color{purple}=} yy[t]{\color{purple}*}scale
yl[t] {\color{purple}=} {\color{purple}-}yl[t]{\color{purple}*}scale
yl[imatch{\color{purple}+}1]{\color{purple}=}{\color{purple}-}yl[imatch{\color{purple}+}1]{\color{purple}*}scale
ymatch{\color{purple}=}yy[imatch]
dlmatch{\color{purple}=}yy[imatch{\color{purple}+}1]{\color{purple}*}scale{\color{purple}-}yy[imatch{\color{purple}-}1] # dif1_left
t_lim{\color{purple}=}list(range(dim{\color{purple}+}1))
tt{\color{purple}=}list(t_lim[imatch{\color{purple}+}1:dim])
drmatch{\color{purple}=}yr[imatch{\color{purple}+}1]{\color{purple}-}yr[imatch{\color{purple}-}1] # dif1_right
f {\color{purple}=}(dlmatch{\color{purple}-}drmatch){\color{purple} /}(2{\color{purple}*}h)
{\color{darkgreen}for} t in tt: # y_right
yy[t] {\color{purple}=} yr[t]
delta_E{\color{purple}=}{\color{purple}-}f{\color{purple}*}(E{\color{purple}-}E_old){\color{purple} /}(f{\color{purple}-}f_old)
if abs(delta_E)<eps: # determinacao da raiz (energia)
# de f(E) pelo metodo da secante
ee[M] {\color{purple}=} E
nk[M] {\color{purple}=} k
ff[M] {\color{purple}=} f
k {\color{purple}=} kmax
break
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
So far, the only thing we need to change in our program is the equation that defines our effective potential $V(x)$. The rest of the code will be the same for any equation that is in the same form as equation~(\ref{eq9}). From now on, we must change the code whenever we are looking for solutions with a different potential.
The parameter $M$ indicates the eigenvalue that we are determining, in the next step, in order to avoid that the program needs to sweep the entire potential well in search of solutions, we can give increments between one eigenvalue and another in the form of multiples of the $\mbox{d}E$ parameter, which will be duly defined in a next step.
Usually, this process involves trial and error, where we adjust the $\mbox{d}E$ multiplier for each case, until we find the desired eigenvalue. However, as we are developing this first example for the hydrogen atom, which already has its energy eigenvalues well defined, this task becomes much easier. Before we find the ground state ($M=0$) we must use the step $24 \times \mbox{d}E$. Thus, we find for ground state energy the value of $\varepsilon = -0.99453$, which must be compared with the known value of the ground state energy for the hydrogen atom $\varepsilon = -1$. And the next multipliers so that we can find at least the first three solutions witch are:
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
else:
f_old{\color{purple}=}f; E_old{\color{purple}=}E; E {\color{purple}=} E {\color{purple}+} 24{\color{purple}*}dE
if M{\color{purple}=}{\color{purple}=}0:
E {\color{purple}=} E {\color{purple}+} 126{\color{purple}*}dE
{\color{darkgreen}for} j in range(dim):
yy1[j]{\color{purple}=}yy[j]
if M{\color{purple}=}{\color{purple}=}1:
E {\color{purple}=} E {\color{purple}+} 3{\color{purple}*}dE
{\color{darkgreen}for} j in range(dim):
yy2[j]{\color{purple}=}yy[j]
if M{\color{purple}=}{\color{purple}=}2:
E {\color{purple}=} E_old {\color{purple}+} 6{\color{purple}*}dE
{\color{darkgreen}for} j in range(dim):
yy3[j]{\color{purple}=}yy[j]
print(" k {\color{purple}=}
f_old {\color{purple}=}
print()
{\color{darkgreen}return} ee, xx, yy1, yy2, yy3
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
If you are interested in finding other solutions, you should add the steps for large values of $M$.
We finally reach the part of the program where we must introduce the initial values to proceed with the solution. Whenever we start to develop a new code, these must be the first values to be changed, right after choosing the effective potential $V(x)$.
The parameters $a$ and $b$ correspond to the boundary points mentioned in the second section. At first, our wave function should have its initial value ($a$) equal to 0, however, to avoid divisions by 0 throughout the program we should start from a relatively small value ($a=0.001$). In the piece of code below $h$ represents the $\delta$ increment, $kmax$ is the maximum number of interactions for each eigenvalue, $nmax$ is the number of eigenvalues that we are trying to find, $Ein$ is the minimum energy of de effective potential that we are trying to solve, and $Vmax$ is the maximum energy of the same effective potential.
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
a{\color{purple}=}0.001; b{\color{purple}=} 60.001; h{\color{purple}=}0.01
xl{\color{purple}=}a; xu{\color{purple}=}b; D {\color{purple}=} xu{\color{purple}-}xl
delta {\color{purple}=} 0.02; eps {\color{purple}=} 0.0001
dim{\color{purple}=}int(D{\color{purple} /}h); kmax{\color{purple}=}300; nmax{\color{purple}=}3
n {\color{purple}=}0; iflag{\color{purple}=}0
Rydberg{\color{purple}=}13.605693122994
x0{\color{purple}=}xl; y0{\color{purple}=}0. ; y1{\color{purple}=}delta; iflag{\color{purple}=}1
nrovl(y0,y1,x0,0,h,iflag)
nrovr(y0,y1,xu,0,h,iflag)
dE {\color{purple}=} delta{\color{purple} /}4
Ein {\color{purple}=} {\color{purple}-}1.6
Vmax{\color{purple}=} 0.
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
With the inputs given in the previous step, we can now print the initial values of our program on the screen.
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
print(" =================================================")
print(" ")
print(" Potential : V(x) {\color{purple}=} {\color{purple}-}2{\color{purple} /}x (Hydrogen L=0) ")
print(" ")
print(" =================================================")
print(" E_in {\color{purple}=}
print(" ")
corlors {\color{purple}=}['b','r','g','m','c']
ee,xx,yy1,yy2,yy3{\color{purple}=}espectro(xl,xu,h,delta,eps,dim,nmax,kmax,
Ein,Vmax,dE,iflag)
A{\color{purple}=}1. # amplitude normalization in 1 unit
ymax1{\color{purple}=}vec_max(dim,yy1)
ymax2{\color{purple}=}vec_max(dim,yy2)
ymax3{\color{purple}=}vec_max(dim,yy3)
{\color{darkgreen}for} i in range(dim): # amplitude normalization
yy1[i] {\color{purple}=} yy1[i]{\color{purple} /}ymax1; yy2[i] {\color{purple}=} yy2[i]{\color{purple} /}ymax2
yy3[i] {\color{purple}=} yy3[i]{\color{purple} /}ymax3
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
Finally, at this point the program was able to determine the eigenvalues and eigenfunctions associated with the first three states of the hydrogen atom. Initially, the program prints the eigenvalues ($Eingen$) on the screen according to the Figure~\ref{fig2}.
\begin{figure}[ht]
\centerline{\includegraphics[width=12.0cm]{output}}
\caption{Output of eigenvalues displayed by the code.}
\label{fig2}
\end{figure}
\newpage
Table~\ref{tabela1} shows the comparison between our results, extract from the Figure~\ref{fig2}, and the well known analytical values for the hydrogen atom, in Rydberg units, given by the formula $E_n = -1/n^2$.
\renewcommand{\arraystretch}{0.9}
\begin{table}[ht]
\caption{Comparison between the energy values, in Rydberg units, found by the Numerov's method and the analytical ones for $\ell=0$ and n=1, 2 and 3.}\label{tabela1}
\vspace*{0.2cm}
\begin{center}
\begin{tabular}{c|c|c}
\hline
\hline
n &Numerov's Energy &Analytical value \\ \hline
1 & -0.995 & -1 \\
2 &-0.245 & -0.25 \\
3 &-0.110 & -0.111 \\
\hline
\hline
\end{tabular}
\end{center}
\end{table}
\renewcommand{\arraystretch}{1}
From now on we will introduce the codes necessary to generate the graphs, as well as calculate the normalization of the wavefunctions. First, let's plot the effective potential graph. During the process of setting the code for different potentials, it is important to know the effective potential in order to adjust the parameters accordingly.
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
print(" ")
print("
figure(figsize{\color{purple}=}(8, 6), dpi{\color{purple}=}800)
plot(x,V(x),'k{\color{purple}-}',linewidth{\color{purple}=}2)
ylim({\color{purple}-}10,1)
xlim(a,10)
xlabel('x')
ylabel('Effective potential')
grid()
show())
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
\noindent The code above plots the effective potential, as we can see in figure~\ref{fig3}
\begin{figure}[ht]
\centerline{\includegraphics[width=12.0cm]{effective_potential}}
\caption{effective potential of equation~(\ref{sch2}) for $\ell=0$.}
\label{fig3}
\end{figure}
And the graph for the eigenfunctions with an arbitrary normalization, is built by
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
print(" ")
print("
figure(figsize{\color{purple}=}(8, 6), dpi{\color{purple}=}800)
plot(xx,yy1,'b{\color{purple}-}',linewidth{\color{purple}=}1)
plot(xx,yy2,'r{\color{purple}-}')
plot(xx,yy3,'g{\color{purple}-}')
legend([' y1',' y2',' y3'],prop{\color{purple}=}{"size":10},frameon{\color{purple}=}False)
ylim({\color{purple}-}0.7,1.1)
xlim(0,40)
xlabel('x')
ylabel('Eigenfunctions')
grid()
show()
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
\noindent Which generates the plot shown in the figure~\ref{fig4}
\begin{figure}[ht]
\centerline{\includegraphics[width=12.0cm]{eigenfunctions}}
\caption{First three eigenfunctions of equation~(\ref{sch2}), with $\ell=0$, calculated with the Numerov method.}
\label{fig4}
\end{figure}
As a last step, let's include in our code, the calculation of the normalization of the wave functions, given by:
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
efic{\color{purple}=}list(range(nmax)); I{\color{purple}=}list(range(nmax))
eI{\color{purple}=}list(range(nmax))
S{\color{purple}=}A{\color{purple}*}(xu{\color{purple}-}xl) # Born normalization
l0{\color{purple}=}0; l1{\color{purple}=}0; l2{\color{purple}=}0
N{\color{purple}=}10000
{\color{darkgreen}for} i in range(N): # integral de y{\color{purple}*}y
y {\color{purple}=} A{\color{purple}*}random(1)
j{\color{purple}=}randint(dim)
yj1{\color{purple}=}yy1[j]{\color{purple}*}yy1[j]; yj2{\color{purple}=}yy2[j]{\color{purple}*}yy2[j]; yj3{\color{purple}=}yy3[j]{\color{purple}*}yy3[j]
if y <{\color{purple}=} yj1:
l0 {\color{purple}+}{\color{purple}=} 1
if y <{\color{purple}=} yj2:
l1 {\color{purple}+}{\color{purple}=} 1
if y <{\color{purple}=} yj3:
l2 {\color{purple}+}{\color{purple}=} 1
efic[0] {\color{purple}=} float(l0){\color{purple} /}N; efic[1] {\color{purple}=} float(l1){\color{purple} /}N
efic[2] {\color{purple}=} float(l2){\color{purple} /}N
I[0] {\color{purple}=} S{\color{purple}*}efic[0]; I[1] {\color{purple}=} S{\color{purple}*}efic[1]; I[2] {\color{purple}=} S{\color{purple}*}efic[2]
eI[0] {\color{purple}=} (S{\color{purple} /}sqrt(N)){\color{purple}*}sqrt(efic[0]{\color{purple}*}(1{\color{purple}-}efic[0]))
eI[1] {\color{purple}=} (S{\color{purple} /}sqrt(N)){\color{purple}*}sqrt(efic[1]{\color{purple}*}(1{\color{purple}-}efic[1]))
eI[2] {\color{purple}=} (S{\color{purple} /}sqrt(N)){\color{purple}*}sqrt(efic[2]{\color{purple}*}(1{\color{purple}-}efic[2]))
print(" ")
print(" probability normalization ")
print("efic1{\color{purple}=
print("efic2{\color{purple}=
print("efic2{\color{purple}=
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
{\color{darkgreen}for} i in range(dim): # probability normalization
yy1[i]{\color{purple}=}yy1[i]{\color{purple} /}sqrt(I[0]); yy2[i]{\color{purple}=}yy2[i]{\color{purple} /}sqrt(I[1])
yy3[i]{\color{purple}=}yy3[i]{\color{purple} /}sqrt(I[2])
ymax1{\color{purple}=}vec_max(dim,yy1); ymax2{\color{purple}=}vec_max(dim,yy2)
ymax3{\color{purple}=}vec_max(dim,yy3)
S0{\color{purple}=}ymax1{\color{purple}*}ymax1{\color{purple}*}(xu{\color{purple}-}xl); S1{\color{purple}=}ymax2{\color{purple}*}ymax2{\color{purple}*}(xu{\color{purple}-}xl)
S2{\color{purple}=}ymax3{\color{purple}*}ymax3{\color{purple}*}(xu{\color{purple}-}xl)
l0{\color{purple}=}0; l1{\color{purple}=}0; l2{\color{purple}=}0 # checking probability
N{\color{purple}=}10000
{\color{darkgreen}for} i in range(N):
y1 {\color{purple}=} ymax1{\color{purple}*}ymax1{\color{purple}*}random(1); y2 {\color{purple}=} ymax2{\color{purple}*}ymax2{\color{purple}*}random(1)
y3 {\color{purple}=} ymax3{\color{purple}*}ymax3{\color{purple}*}random(1)
j{\color{purple}=}randint(dim)
yj1{\color{purple}=}yy1[j]{\color{purple}*}yy1[j]; yj2{\color{purple}=}yy2[j]{\color{purple}*}yy2[j]; yj3{\color{purple}=}yy3[j]{\color{purple}*}yy3[j]
if y1<{\color{purple}=} yj1:
l0 {\color{purple}+}{\color{purple}=} 1
if y2 <{\color{purple}=} yj2:
l1 {\color{purple}+}{\color{purple}=} 1
if y3 <{\color{purple}=} yj3:
l2 {\color{purple}+}{\color{purple}=} 1
efic[0] {\color{purple}=} float(l0){\color{purple} /}N; efic[1] {\color{purple}=} float(l1){\color{purple} /}N
efic[2] {\color{purple}=} float(l2){\color{purple} /}N
I[0] {\color{purple}=} S0{\color{purple}*}efic[0]; I[1] {\color{purple}=} S1{\color{purple}*}efic[1]; I[2] {\color{purple}=} S2{\color{purple}*}efic[2]
eI[0] {\color{purple}=} (S0{\color{purple} /}sqrt(N)){\color{purple}*}sqrt(efic[0]{\color{purple}*}(1{\color{purple}-}efic[0]))
eI[1] {\color{purple}=} (S1{\color{purple} /}sqrt(N)){\color{purple}*}sqrt(efic[1]{\color{purple}*}(1{\color{purple}-}efic[1]))
eI[2] {\color{purple}=} (S2{\color{purple} /}sqrt(N)){\color{purple}*}sqrt(efic[2]{\color{purple}*}(1{\color{purple}-}efic[2]))
print(" ")
print(" checking probability ")
print(" efic1{\color{purple}=
print(" efic2{\color{purple}=
print(" efic3{\color{purple}=
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
print("
colors {\color{purple}=}['b','r','g','m','c']
figure(figsize{\color{purple}=}(8, 6), dpi{\color{purple}=}800)
plot(xx,yy1,color{\color{purple}=}cores[0])
plot(xx,yy2,color{\color{purple}=}cores[1])
plot(xx,yy3,color{\color{purple}=}cores[2])
#plot(xx,yy4,color{\color{purple}=}cores[3])
#plot(xx,yy5,color{\color{purple}=}cores[4])
legend(['y1','y2','y3'],prop{\color{purple}=}{"size":10},frameon{\color{purple}=}False)
ylim({\color{purple}-}0.3,0.8)
xlim(0,40)
xlabel('x')
ylabel('Normalized Eigenfunctions')
grid(True)
show()
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
Thus, we were able to obtain our final graph, composed of the first three wave functions for the hydrogen atom.
\begin{figure}[ht]
\centerline{\includegraphics[width=12.0cm]{norm_eigenfunctions}}
\caption{First three normalized eigenfunctions of equation~(\ref{sch2}), with $\ell=0$, calculated with the Numerov method.}
\label{fig42}
\end{figure}
\newpage
\section{Morse Potential}
The Morse potential is a common model for the interatomic interaction of a diatomic molecule~\cite{morse, morse2}. In this section, in order to learn how we can use the Phyton code in other problems, we will see what we must change in the code that was made available in the previous section so that the program will be able to solve equation~(\ref{sch1}) for the quantum number $\ell=0$ and the Morse potential with arbitrary parameters given by:
\begin{equation}\label{morse}
V(x) = 16 \left(1-e^{-2x} \right)^2
\end{equation}
In this example, we will calculate the first two bounded states, for that, we must adjust the $\mbox{d}E$ multiplier for each case as:
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
else:
f_old{\color{purple}=}f; E_old{\color{purple}=}E; E {\color{purple}=} E {\color{purple}+} 7.2{\color{purple}*}dE
if m{\color{purple}=}{\color{purple}=}0:
E {\color{purple}=} E {\color{purple}+} 70{\color{purple}*}dE
{\color{darkgreen}for} j in range(dim):
yy1[j]{\color{purple}=}yy[j]
if m{\color{purple}=}{\color{purple}=}1:
E {\color{purple}=} E {\color{purple}+} dE{\color{purple}/}10
{\color{darkgreen}for} j in range(dim):
yy2[j]{\color{purple}=}yy[j]
if m{\color{purple}>}{\color{purple}=}2:
E {\color{purple}=} E_old {\color{purple}+} 50{\color{purple}*}dE
{\color{darkgreen}for} j in range(dim):
yy3[j]{\color{purple}=}yy[j]
print(" k {\color{purple}=}
f_old {\color{purple}=}
print()
{\color{darkgreen}return} ee, xx, yy1, yy2, yy3
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
And, the most important part, which is the adjustment of the initial data of our problem. Analyzing the effective potential we can verify that the value os parameter $a$ must be negative, and its minimum value is zero, so the code must be set as follows:
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
a{\color{purple}=}-1.01; b{\color{purple}=} 5.01; h{\color{purple}=}0.006
xl{\color{purple}=}a; xu{\color{purple}=}b; D {\color{purple}=} xu{\color{purple}-}xl
delta {\color{purple}=} 0.01; eps {\color{purple}=} 0.00001
dim{\color{purple}=}int(D{\color{purple} /}h); kmax{\color{purple}=}100; nmax{\color{purple}=}2
n {\color{purple}=}0; iflag{\color{purple}=}0
Rydberg{\color{purple}=}13.605693122994
x0{\color{purple}=}xl; y0{\color{purple}=}0. ; y1{\color{purple}=}delta; iflag{\color{purple}=}1
nrovl(y0,y1,x0,0,h,iflag)
nrovr(y0,y1,xu,0,h,iflag)
dE {\color{purple}=} delta
Ein {\color{purple}=} 0.0
Vmax{\color{purple}=} 16.
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
From now on, the program is able to find the energies of the first two states, which are respectively $7.1380$ and $15.0380$. As well as already determined the wave functions also for the first two states.
Then, all that remains is to get all the aesthetic part of the code right, adjusting the limits of graphics, subtitles and other factors. Thus we first get the effective potential, as shown in Figure~\ref{fig5} and finally arrive at the normalized wave functions shown in Figure~\ref{fig6}.
\begin{figure}[htb]
\centerline{\includegraphics[width=12.0cm]{pot_morse}}
\caption{Effective Potential given by equation~(\ref{morse}).}
\label{fig5}
\end{figure}
\begin{figure}[htb]
\centerline{\includegraphics[width=12.0cm]{norm_eigenfunctions_morse}}
\caption{Normalized Eigenfunctions of equation~(\ref{sch2}), with the potential given by equation~(\ref{morse}) with $\ell=0$.}
\label{fig6}
\end{figure}
\newpage
In Table~\ref{tabela2}, we can compare the eigenvalues found by the Numerov's method with the analytical values given by $E_n = 16 \left[\left(n+\frac{1}{2}\right)-\frac{1}{4}\left(n+\frac{1}{2}\right)\right]$.
\renewcommand{\arraystretch}{0.9}
\begin{table}[ht]
\caption{Comparison between the energy values for the Morse potential, in Rydberg units, found by the Numerov's method and the analytical ones for $\ell=0$ and n=0 and 1.}\label{tabela2}
\vspace*{0.2cm}
\begin{center}
\begin{tabular}{c|c|c}
\hline
\hline
n &Numerov's Energy &Analytical value \\ \hline
0 & 7.1380 & 7.0 \\
1 & 15.0380 & 15.0 \\
\hline
\hline
\end{tabular}
\end{center}
\end{table}
\renewcommand{\arraystretch}{1}
\newpage
\section{Quantum Dot}
The development of technology based on quantum dots is quite recent, but it is already showing signs that it is the next great technology, when we talk about optics. In a simple model for a quantum dot
composed of two electrons, they can be described with a external harmonic oscillator potential of frequency $\Omega = 2\omega$. Following the steps of reference~\cite{BJP}, we have the
effective potential to be introduced into equation~(\ref{sch1}) for the quantum number $\ell=0$ is given by:
\begin{equation}\label{qd}
V(x) = \frac{1}{x} + \omega^2 x - \frac{0.25}{x^2}
\end{equation}
\noindent introducing this potential into our code, let's now calculate the first five solutions that the program is capable of finding. We can observe that in our code used so far, we only have up to three wave functions,
in this example we will show how we included two more solutions in the code. The procedure is very simple, just add the $yy4$ and $yy5$ functions along the code and all the other parts that are related to them, for example,
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
xx{\color{purple}=}list(range(dim)); yy{\color{purple}=}list(range(dim))
ww{\color{purple}=}list(range(dim)); yl{\color{purple}=}list(range(dim))
yr{\color{purple}=}list(range(dim)); ee{\color{purple}=}list(range(nmax))
ff{\color{purple}=}list(range(nmax)); ff2{\color{purple}=}list(range(nmax))
yy1{\color{purple}=}list(range(dim)); yy2{\color{purple}=}list(range(dim))
yy3{\color{purple}=}list(range(dim)); {\color{red} yy4{\color{purple}=}list(range(dim))}
{\color{red} yy5{\color{purple}=}list(range(dim))}
colors {\color{purple}=}['b','r','g','m','c']; nk{\color{purple}=}list(range(nmax))
E_old {\color{purple}=} Ein; E {\color{purple}=} Ein {\color{purple}+} dE
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
Now, as in the previous example, let's include the $dE$ multipliers, remembering to include the new wave functions.
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
else:
f_old{\color{purple}=}f; E_old{\color{purple}=}E; E {\color{purple}=} E {\color{purple}+} dE{\color{purple}/}25
if m{\color{purple}=}{\color{purple}=}0:
E {\color{purple}=} E {\color{purple}+} 6{\color{purple}*}dE
{\color{darkgreen}for} j in range(dim):
yy1[j]{\color{purple}=}yy[j]
if m{\color{purple}=}{\color{purple}=}1:
E {\color{purple}=} E {\color{purple}+} 6{\color{purple}*}dE
{\color{darkgreen}for} j in range(dim):
yy2[j]{\color{purple}=}yy[j]
if m{\color{purple}>}{\color{purple}=}2:
E {\color{purple}=} E_old {\color{purple}+} 13{\color{purple}*}dE{\color{purple}/}2
{\color{darkgreen}for} j in range(dim):
yy3[j]{\color{purple}=}yy[j]
if m{\color{purple}>}{\color{purple}=}3:
E {\color{purple}=} E_old {\color{purple}+} 13{\color{purple}*}dE{\color{purple}/}2
{\color{darkgreen}for} j in range(dim):
yy4[j]{\color{purple}=}yy[j]
if m{\color{purple}>}{\color{purple}=}4:
E {\color{purple}=} E_old {\color{purple}+} 4{\color{purple}*}dE
{\color{darkgreen}for} j in range(dim):
yy5[j]{\color{purple}=}yy[j]
print(" k {\color{purple}=}
f_old {\color{purple}=}
print()
{\color{darkgreen}return} ee, xx, yy1, yy2, yy3. yy4, yy5
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
And finally, we must include the initial conditions for our problem, as shown below.
\vspace*{0.1cm}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\begin{Verbatim}[commandchars=\\\{\}, baselinestretch=1.0]
a{\color{purple}=}0.001; b{\color{purple}=} 60.001; h{\color{purple}=}0.02
xl{\color{purple}=}a; xu{\color{purple}=}b; D {\color{purple}=} xu{\color{purple}-}xl
delta {\color{purple}=} 0.01; eps {\color{purple}=} 0.00001
dim{\color{purple}=}int(D{\color{purple} /}h); kmax{\color{purple}=}100; nmax{\color{purple}=}5
n {\color{purple}=}0; iflag{\color{purple}=}0
Rydberg{\color{purple}=}13.605693122994
x0{\color{purple}=}xl; y0{\color{purple}=}0. ; y1{\color{purple}=}delta; iflag{\color{purple}=}1
nrovl(y0,y1,x0,0,h,iflag)
nrovr(y0,y1,xu,0,h,iflag)
dE {\color{purple}=} delta{\color{purple}/}2.8
Ein {\color{purple}=} 0.086857
Vmax{\color{purple}=} 2.
\end{Verbatim}
\end{tcolorbox}
\vspace*{0.1cm}
Thus, adjusting the rest of the code, we obtain the first five eigenvalues. The effective potential and the eigenfunctions can be seen in Figures~\ref{fig7} and \ref{fig8}.
\begin{figure}[hbt]
\centerline{\includegraphics[width=9.0cm]{effective_potential_qd}}
\caption{Effective Potential given by equation~(\ref{qd}).}
\label{fig7}
\end{figure}
\begin{figure}[!htb]
\centerline{\includegraphics[width=9.0cm]{norm_eigenfunctions_qd}}
\caption{Normalized Eigenfunctions of equation~(\ref{qd}), with the potential given by equation~(\ref{morse}) with $\ell=0$.}
\label{fig8}
\end{figure}
In Table \ref{tabela3}, we can compare the eigenvalues found by the Numerov's method with the analytical values for the quantum dot given by $\eta_{n\ell} = 2(n+\ell+1)\omega$.
\renewcommand{\arraystretch}{0.9}
\begin{table}[!ht]
\caption{Comparison between the energy values for the Quantum dot, in Rydberg units, found by the Numerov's method and the analytical ones for $\ell=0$ and n=0 and 1.}\label{tabela3}
\vspace*{0.2cm}
\begin{center}
\begin{tabular}{c|c|c}
\hline
\hline
n &Numerov's Energy &Analytical value \\ \hline
4 & 0.1046 & 0.10 \\
6 & 0.1403 & 0.14 \\
8 & 0.1760 & 0.18 \\
10 & 0.2134 & 0.22 \\
12 & 0.2507 & 0.26 \\
\hline
\hline
\end{tabular}
\end{center}
\end{table}
\renewcommand{\arraystretch}{1}
\newpage
\section{Conclusion}
Analyzing the results arranged in Tables~\ref{tabela1}, \ref{tabela2} and~\ref{tabela3} we can conclude that the method used here is able to reproduce the analytical results within small errors.
Therefore, it is evident that the numerical method of Numerov is a powerful tool, easy to use, which can help in the development of not only new knowledge in the area of programming,
but also the solution of Schr\"{o}dinger equations outside the usual results found in the examples of modern physics books. We hope that this short introduction to the code, which can be found
in full at \url{https://1drv.ms/u/s!Ai_Lqkgh1kiskp5_cfOtwCfqX-LpTw?e=srdmzS}, will open doors for students to create their own versions, increasingly improving the versatility of this tool.
\section*{Acknowledgment}
One of us (FS) was financed in part by the Coordena\c{c}\~{a}o de Aperfei\c{c}oamento de Pessoal de N\'{\i}vel Superior -- Brazil (CAPES), Finance Code 001.
\renewcommand\refname{References}
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UK Price Comparison has over 5 products listed for Le'Xpress price comparison offered by more than 30 online retailers.
You can get the best deals of Le'Xpress products simply by searching for a product you are looking to buy in brand new, used or even refurbished condition.
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{"url":"http:\/\/wiki.freepascal.org\/Why_Pascal_is_Not_My_Favorite_Programming_Language","text":"# Why Pascal is Not My Favorite Programming Language\n\n\"Why Pascal is Not My Favorite Programming Language\" is an article (can be found here) written about by Brian W. Kernighan, April 2, 1981. The article is often used in language comparison discussions even today, typically by critics of Pascal-family. Despite of the fact that the article is talking about the language that is there no more. The description of the language that B Kernighan is referring to in the article could be found here.\n\nThe purpose of this page, is to show that the article is quite out-dated. People who are still trying to refer to the article don't know what the current Pascal (Delphi\/FPC) are.\n\n## Article\n\n### Types and Scopes\n\nInteger variables may be declared to have an associated range of legal values, and the compiler and run-time support\nensure that one does not put large integers into variables that only hold small ones. This too seems like a service,\nalthough of course run-time checking does exact a penalty.\n\n\nIt needs to be noted here, that compiler allows to remove the range run-time check completely.\n\n### The size of an array is part of its type\n\nWithout quoting of the article - the complain is about an arrays of different size (though still the same type) are considered a different type. Since Pascal is strict type routines cannot be shared among array of different size. The task of sorting is used as an example in the article.\n\nThe 1985 Ansi\/ISO standards have an (optional) section about conformant arrays fixing this. Currently neither FPC (ISO mode) nor Borland derivatives implement it.\n\nDynamic and Open arrays were introduced in Delphi that overcomes the limitation at the cost of the lower bound always being 0. The desired result could be achieved even back at the time, using pointers.\n\n### There are no static variables and no initialization\n\nAs well as Static variables are just \"implementation\"-only variables per unit. Global variable initialization were added in some version of Delphi, as well as type constants (which are variables) requires the initialization to be present.\n\nAlso, each unit provides an initialization section (which is executed in run-time), that provides a very flexible and convenient way for initialization (of dynamic storages).\n\n### Related program components must be kept separate\n\nNo such strict order limitation in Object Pascal.\n\n### There is no separate compilation\n\nFixed mid eighties by the module(ISO)\/units(UCSD\/Borland) system in a way that doesn't need a separate interpreter (make) to manage building and without the infinate header reparsing problem that causes C and C++ compilers to be relatively slow in practice.\n\n### Some miscellaneous problems of type and scope\n\nIt is not legal to name a non-basic type as the literal formal parameter of a procedure;\n\n\nThis is actually still true.\n\nIt is nice to have the declaration 'var' for formal parameters of functions and procedures;\nthe procedure clearly states that it intends to modify the argument. But the calling program\nhas no way to declare that a variable is to be modified - the information is only in one place,\nwhile two places would be better.\n\n\nconst is available to identified unmodified parameter and passing a parameter by reference (where applicable)\n\nPascal's 'set' construct seems like a good idea, providing notational convenience and some free type checking.\nFor example, a set of tests like\n\nif (c = blank) or (c = tab) or (c = newline) then ...\n\ncan be written rather more clearly and perhaps more efficiently as\n\nif c in [blank, tab, newline] then ..\n\n\nAnd they're!\n\n### There is no escape\n\nType casting is available (and causing issues for some developers)\n\n## Control Flow\n\nThere is no guaranteed order of evaluation of the logical operators 'and' and 'or' - nothing like && and || in C.\nThis failing, which is shared with most other languages, hurts most often in loop control:\n\nwhile (i <= XMAX) and (x[i] > 0) do ...\n\n\nConditions are short-cut evaluated. Thus loops can be implemented the way above without a risk breaking out of the range.\n\nWith no 'break' statement...\n\n\nThere's break\n\nThe increment of a 'for' loop can only be +1 or -1, a minor restriction.\n\n\nStill true.\n\nThere is no 'return' statement, again for one in-one out reasons.\n\n\nThere's Exit statement (FPC only Exit() ) available.\n\nThe 'case' statement is better designed than in C, except that there is no 'default' clause and the behavior\nis undefined if the input expression does not match any of the cases. This crucial omission renders the 'case' construct\nalmost worthless.\n\n\nThere's default in case statement.\n\n## The Environment\n\nNo problems with using System APIs and any I\/O routines provided by an underlying environment.\n\n## Cosmetic Issues\n\nBut if something must be inserted before b, it no longer needs a semicolon, because it now precedes an 'end':\n\n\nA statement before \"end\" might have or not have a semicolon. Not-having a semicolon is not enforced.\n\nC and Ratfor programmers find 'begin' and 'end' bulky compared to { and }.\n\n\nIs still true and there're no plans to change that.\n\nA function name by itself is a call of that function; there is no way to distinguish such a function call from a simple variable\nexcept by knowing the names of the functions\n\n\nIs still true, except for FPC\/objFPC mode, where a function call must come with ()\n\nIn particular, there are no bit-manipulation operators (AND, OR, XOR, etc.).\nI simply gave up trying to write the following trivial encryption program in Pascal:\n\ni\u00a0:= 1;\nwhile getc(c) <> ENDFILE do begin\nputc(xor(c, key[i]));\ni\u00a0:= i mod keylen + 1\nend\n\n\nBit-manipulation operators are available.\n\nThere is no null string, perhaps because Pascal uses the doubled quote notation to indicate a quote embedded in a string\n\n'This is a character'\n\nThere is no way to put non-graphic symbols into strings. In fact, non-graphic characters are unpersons in a stronger\nsense, since they are not mentioned in any part of the standard language. Concepts like newlines, tabs, and so on\nare handled on each system in an 'ad hoc' manner, usually by knowing something about the character set\n(e.g., ASCII newline has decimal value 10)\n\n\nEscape characters are available.\n\n 'new line'#13#10\n\n\nNeedless to say, that Unicode escaping is available too.\n\nThere is no macro processor.\n\n\nGod bless Pascal!\n\nThe 'const' mechanism for defining manifest constants takes care of about 95 percent of the uses of simple\n#define statements in C, but more involved ones are hopeless. It is certainly possible to put a macro\npreprocessor on a Pascal compiler. This allowed me to simulate a sensible 'error' procedure as\n\n#define error(s)begin writeln(s); halt end\n\n\nObviously the error(s) should implemented as a function. Since nothing is executed after Halt(). Though these days \"raising\" an exception might be a better approach.\n\nThe language prohibits expressions in declarations, so it is not possible to write things like\nconst SIZE = 10;\ntype arr = array [1..SIZE+1] of integer;\n\n\nConstant expressions are allowed as value of an expression.\n\n## Perspective\n\nTo close, let me summarize the main points in the case against Pascal.\n1. 2. 3. 4. 5. 6. 7. 8. ...\n9. There's no escape\n\nThis last point is perhaps the most important. The language is inadequate but circumscribed, because there\nis no way to escape its limitations. There are no casts to disable the type-checking when necessary.\nThere is no way to replace the defective run-time environment with a sensible one, unless one controls\nthe compiler that defines the standard procedures. The language is closed.\n\n\nModern Pascals are easily extensible, but still, if you don't like the run-time environment. You can introduce your own. After all, FPC is open source.","date":"2018-01-23 17:22:26","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4880913197994232, \"perplexity\": 2538.4214627758165}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-05\/segments\/1516084892059.90\/warc\/CC-MAIN-20180123171440-20180123191440-00167.warc.gz\"}"}
| null | null |
# TABLE OF CONTENTS
## Southwest USA Cover
## How to Use This Guide
## Southwest USA Map
## PLAN YOUR TRIP
## ON THE ROAD
## UNDERSTAND SOUTHWEST USA
## SURVIVAL GUIDE
## Behind the Scenes
## Map Legend
## Our Writers
### GETTING THE MOST OUT OF LONELY PLANET MAPS
E-reader devices vary in their ability to show our maps. To get the most out of the maps in this guide, use the zoom function on your device. Or, visit media.lonelyplanet.com/ebookmaps and grab a PDF download or print out all the maps in this guide.
### Plan Your Trip
Welcome to Southwest USA
Top Experiences
Need to Know
If You Like...
Month by Month
Route 66 & Scenic Drives
Itineraries
Southwest USA Outdoors
Travel with Children
Regions at a Glance
# welcome to Southwest USA
Top of section
_The Southwest is America's playground, luring adventurers and artists with the promise of red-rock landscapes, the legends of shoot-'em-up cowboys and the kicky delights of a green chile stew._
### The Great Outdoors
Beauty and adventure don't just join hands in the Southwest. They crank up the whitewater, unleash the single track, add blooms to the trail and drape a sunset across the red rocks. Then they smile and say, 'Come in.' This captivating mix of scenery and possibility lures travelers who want to rejuvenate physically, mentally and spiritually. The big draw is the Grand Canyon, a two-billion-year-old wonder that shares its geologic treasures with a healthy dose of fun. Next door in Utah, the red rocks will nourish your soul while thrashing your bike. In southern Colorado ice climbing and mountain biking never looked so pretty. Tamp down the adrenaline in New Mexico with a scenic drive, an art walk or a lazy slide down a shimmery dune. And Vegas? Your willpower may be the only thing exercised, but chasing the neon lights will certainly add verve to your vacation.
### This is the Place for History
The Southwest wears its history on its big, sandy sleeve. Ancient cultures left behind cliff dwellings and petroglyphs while their descendants live on in reservations and pueblos. Navajos and Apaches arrived next, followed by Spanish conquistadors. Next up? The missionaries, who left a string of stunning missions in their wake. Mormon religious refugees arrived with Brigham Young, who famously declared, 'This is the place' when he reached the Salt Lake Valley. Their cities have flourished, proving more durable than the region's abandoned mining towns. Which brings us to the Old West. There was gold and copper in them thar hills and plenty of land for cattle-grazing. Tombstone is one Old West town that lives to fight another day – well, every day at 2pm – while dude ranches lure wannabe cowboys.
### Multicultural Meanderings
It's the multicultural mix – Native American, Hispanic, Anglo – that makes a trip to the Southwest unique. There are 19 Native American pueblos in New Mexico, and the Navajo Reservation alone covers more than 27,000 sq miles. Monument Valley and Canyon de Chelly, two of the most striking geologic features in the Southwest, are protected as sacred places. Tribal traditions and imagery influence art across the region. The Spanish and Mexican cultures are also a part of daily life, from the food to the language to the headlines about illegal immigration. In Utah 58% of the population identifies as Mormon, and the religion's stringent disapproval of 'vices' keeps the state on an even keel. So savor the cultural differences – and start with that green chile stew.
The Mittens, Monument Valley
RUTH EASTHAM & MAX PAOLI/LONELY PLANET IMAGES ©
# TOPexperiences
Top of section
### Grand Canyon National Park
1 Go ahead, don't hold back. Let out that 'Whoa!' as you peek over the edge for the very first time. The sheer immensity of the canyon is what grabs you first: it's a two-billion-year-old rip across the landscape that reveals the Earth's geologic secrets with commanding authority. But it's Mother Nature's artistic touches – from sun-dappled ridges and crimson buttes to lush oases and a ribbon-like river – that hold your attention and demand your return. As Theodore Roosevelt said, this natural wonder is 'unparalleled throughout the rest of the world.'
RALPH HOPKINS/LONELY PLANET IMAGES ©
### Sedona
2 The beauty of the red rocks hits you on an elemental level. Yes, the jeep tours, crystal shops and chichi galleries add to the fun, but it's the crimson buttes – strange yet familiar – that make Sedona unique. Soak up the beauty by hiking to Airport Mesa, bicycling beneath Bell Rock or sliding across Oak Creek. New Agers may tell you to seek out the vortexes, which allegedly radiate the Earth's power. The science may be hard to confirm, but even non-believers can appreciate the sacred nature of this breathtaking tableau.
CHEYENNE ROUSE/LONELY PLANET IMAGES ©
### Las Vegas
3 Just as you awaken from your in-flight nap – rested, content, ready for red-rock inspiration – here comes Vegas shaking her thing on the horizon like a showgirl looking for trouble. As you leave the airport and glide beneath the neon of the Strip, she puts on a dazzling show: dancing fountains, a spewing volcano, the Eiffel Tower. But she saves her most dangerous charms for the gambling dens – seductive lairs where the fresh-pumped air and bright colors share one goal: separating you from your money. Step away if you can for fine restaurants, Cirque du Soleil and a shark-filled reef.
DOUG MICKINLAY/LONELY PLANET IMAGES ©
### Old West Towns of Arizona
4 If you judge an Old West town by the quality of its nickname, then Jerome, once known as the Wickedest Town in the West, and Tombstone, the Town Too Tough to Die, are the most fascinating spots in Arizona. While Bisbee's moniker – Queen of the Copper Camps – isn't quite as intriguing, the town shares key traits with the others: a rough-and-tumble mining past, a remote location capping a scenic drive, and a quirky cast of entrepreneurial citizens putting their spin ongalleries, B&Bs and restaurants. Pardner, they're truly the best of the West.
Bisbee
RICHARD CUMMINS/LONELY PLANET IMAGES ©
### Santa Fe
5 Santa Fe may be celebrating her 400th birthday, but she's kicking up her stylish heels like a teenager. On Friday night, art lovers flock to Canyon Rd to gab with artists, sip wine and explore more than 100 galleries. Art and history partner up within the city's consortium of museums, with international crafts, Native American art, world-class collections and a new history museum competing for attention. And oh, the food and the shopping. With that crystal-blue sky as a backdrop, dining and shopping on the Plaza isn't just satisfying, it's sublime.
RICHARD CUMMINS/LONELY PLANET IMAGES ©
### Route 66
6 As you step up to the counter at the Snow Cap Drive-In in Seligman, Arizona, you know a prank is coming – a squirt of fake mustard or ridiculously incorrect change. And though it's all a bit hokey, you'd be disappointed if the owner forgot to 'get you'. It's these kitschy, down-home touches that make the Mother Road so memorable. Begging burros, the Wigwam Motel, the neon signs of Tucumcari – you gotta have something to break up the scrubby Southwest plains. We'll take a squirt of fake mustard over a mass-consumption McBurger every time.
SABRINA DALBESIO/LONELY PLANET IMAGES ©
### Angels Landing (Zion)
7 The climb to Angels Landing in Zion National Park may be the best day-hike in North America. The 2.2-mile trail crosses the Virgin River, hugs a towering cliffside, squeezes through a narrow canyon, snakes up Walter's Wiggles then traverses a razor-thin ridge – where steel chains and the encouraging words of strangers are your only reliable friends. Your reward after the final scramble to the 5790-ft summit? A lofty view of Zion Canyon. The hike encapsulates what's best about the park: beauty, adventure and the shared community of travelers who love the outdoors.
CAROL POLICH/LONELY PLANET IMAGES ©
### Moab
8 The Slickrock Trail won't kick my butt, dude, no way. I'm fit, I'm ready, I'm – ow! I'm flat on my back. That rock just ate my bike, bro. Awesome! Oh yes, the bike-thrashing, 12.7-mile Slickrock Trail is the signature ride in this gnarly gateway town, and with a trail that tough, you gotta have the appropriate backup: a sunrise java joint, a cool indie bookstore, outdoor shops and a post-ride brewery that smells of beer and adventure. Moab scores on all points.
PHILIP & KAREN SMITH/LONELY PLANET IMAGES ©
### Mesa Verde National Park
9 You don't just walk into the past at Mesa Verde, the site of 600 ancient cliff dwellings. You scramble up 10ft ladders, scale a 60ft rock face and crawl 12ft through a tunnel. Yes, it's interactive exploring at its most low-tech, but it's also one of the most exhilarating adventures in the Southwest. It's also a place to puzzle out the archaeological and cultural clues left by its former inhabitants – Ancestral Puebloans who vacated the site in AD 1300 for reasons still not fully understood.
WITOLD SKRYPCZAK/LONELY PLANET IMAGES ©
### Flagstaff
10 Flagstaff is finally the perfect mountain town. For years this outdoorsy mecca – think hiking, biking, skiing and star-gazing – fell short of perfection due to the persistent blare of passing trains, up to 125 daily. Today, the horns have been silenced and Grand Canyon travelers can finally enjoy a decent night's sleep. Well-rested? Stay longer to walk the vibrant downtown, loaded with ecofriendly eateries, indie coffee shops, convivial breweries and atmospheric hotels. It's a liberal-minded, energetic place fueled by students at North Arizona University – and it's ready to share the fun.
DAVID KADLUBOWSKI/CORBIS ©
### Monument Valley & Navajo Nation
11 'May I walk in beauty' is the final line of a famous Navajo prayer. Beauty comes in many forms on the Navajo's sprawling reservation but makes its most famous appearance at Monument Valley, a majestic cluster of rugged buttes and stubborn spires. Beauty swoops in on the wings of birds at Canyon de Chelly, a lush valley where farmers till the land near age-old cliff dwellings. Elsewhere, beauty is in the connections, from the docent explaining Navajo clans to the cafe waiter offering a welcoming smile.
Canyon de Chelly
CATHERINE KARNOW/CORBIS ©
### Taos
12 The grab bag of celebrities who are crazy for Taos is as eclectic as the town itself. In the 1840s, mountain man Kit Carson chose Taos as the end of the trail. Today, outdoorsy types hike and ski in the surrounding mountains while history buffs wander Carson's home and the Taos Pueblo. Georgia O'Keeffe and DH Lawrence led the artists' charge, and now more than 80 galleries line the streets. Carl Jung and Dennis Hopper? Maybe they came for the quirky individualism, seen today in the wonderfully eccentric Adobe Bar and the off-the-grid Earthship community.
Earthship community
PETER PTSCHELINZEW/LONELY PLANET IMAGES ©
### Carlsbad Caverns National Park
13 As the elevator drops, it's hard to comprehend the ranger's words. Wait, what? We're plunging the length of the Empire State Building? I'm not sure that's such a great idea. But then the doors open. Hey, there's a subterranean village down here. A snack bar, water fountains, restrooms and, most impressive, the 255ft-high Big Room where geologic wonders line a 2-mile path. But you're not the only one thinking it's cool – 250,000 Mexican free-tailed bats roost here from April to October, swooping out to feed at sunset.
DIEGO LEZAMA/LONELY PLANET IMAGES ©
### Georgia O'Keeffe Country
14 O'Keeffe's cow-skull paintings and mesa-filled landscapes are gateway drugs for New Mexico – one look will have you hankering for arid landscapes framed by brilliant blues. What drew the state's patron artist? As she explained, 'It's something that's in the air, it's different. The sky is different. The wind is different.' Travelers can experience this uniqueness with a stroll through Santa Fe, stopping by the Georgia O'Keeffe Museum for background and a close-up view of her paintings. From there, the best stops include Abiquiú and the atmospheric Ghost Ranch where the views are superb.
HOLGER LEUE/LONELY PLANET IMAGES ©
### Tucson
15 Like so many Arizonan towns, Tucson sprawls. Yet it still manages to feel like a cohesive whole. From the pedestrian-friendly anchor of 4th Ave, you can walk past indie clothing boutiques and live music clubs that balance cowboy rock with East Coast punk, stopping to eat the original chimichanga and see a show at a Gothy burlesque club. With wheels, you can follow the saguaros to their namesake park then catch a sunset at Gates Pass. Conclude with a Sonoran hotdog, a festival of delicious excess that celebrates the city's muticultural heritage.
RICHARD CUMMINS/LONELY PLANET IMAGES ©
### White Sands National Monument
16 Frisbee on the dunes, colorful umbrellasin the sand, kids riding wind-blown swells – the only thing missing at this beach is the water. But you don't really mind its absence, not with 275 sq miles of gypsum draping the landscape with a hypnotic whiteness that rolls and rises across the southern New Mexico horizon. A 16-mile scenic drive loops past one-of-a-kind views, but to best get a handle on the place, full immersion is key: buy a disc at the gift store, trudge to the top of a dune, run a few steps and...wheee!
RICHARD CUMMINS/LONELY PLANET IMAGES ©
### Salt Lake City
17 The 2002 Winter Olympics dropped the world at the door, and Salt Lake City is riding the momentum. Outdoorsy tourists and new residents are swooping in for world-class hiking, climbing and skiing, and they're infusing this Mormon enclave with rebel spirit. For decades, the populace was like its streets: orderly and square, with the Mormon influence keeping change at bay. But no more. It's a post-Olympic world with bustling brewpubs, eclectic restaurants and a flourishing arts scene.
VISIONSOFAMERICA/JOE SOHM/GETTY ©
### Phoenix
18 Sometimes you just have to ask: what about me? Phoenix answers that question with a stylish grin. Golfers have their pick of more than 200 courses. Posh resorts cater to families, honeymooners and even dear old Fido. The spas are just as decadent, offering aquatic massages, citrusy facials and healing desert-clay wraps. Add in world-class museums, patio-dining extraordinaire, chichi shopping and more than 300 days of sunshine, and it's easy to condone a little selfishness.
LEE FOSTER/LONELY PLANET IMAGES ©
### Arches & Canyonlands National Parks
19 More than 2500 arches cluster within 116 miles at Arches, a cauldron of geologic wonders that includes a balanced rock, a swath of giant fins and one span that's so photogenic it's emblazoned on Utah license plates. Just north is equally stunning Canyonlands, a maze of plateaus, mesas and canyons as forbidding as it is beautiful. How best to understand the subtle power of the landscape? As eco-warrior Edward Abbey said in _Desert Solitaire_ , 'you can't see anything from the car.' So get out, breathe in, walk forward.
IZZET KERIBAR/LONELY PLANET IMAGES ©
### Bryce National Park
20 At sunrise and sunset, the golden-red spires of Utah's smallest national park shimmer like trees in a magical stone forest – a hypnotic, Tolkien-esque place that is surely inhabited by nimble elves and mischievous sprites. The otherworldly feelingcontinues as you navigate the maze of crumbly hoodoos beside the 1.4-mile Navajo Loop trail, which drops 521ft from Sunset Point. Geologically, the park is magical too; the spires are the limestone edges of the Paunsaugunt Plateau – eroded by rain, shaped by freezing water.
NEIL SETCHFIELD/LONELY PLANET IMAGES ©
### Park City
21 Park City, how'd you get to be so cool? Sure, you hosted events in the 2002 Winter Olympics, and you're home to the US Ski Team, but it's not just the snow sports. There's the Sundance Film Festival, which draws enough glitterati to keep the world abuzz. We're also digging the stylish restaurants; they serve fine cuisine but never take themselves too seriously. Maybe that's the key – it's a world-class destination comfortable with its small-town roots.
CHEYENNE ROUSE/LONELY PLANET IMAGES ©
### Pueblos
22 Nineteen Native American pueblos are scattered across New Mexico. These adobe villages – often rising several stories above the ground – offer a glimpse into the distinct cultures of some of America's longest running communities. Not all are tourist attractions, but several offer unique experiences that may be among your most memorable in the Southwest. Marvel at the mesa-top views at Acoma, shop for jewelry at Zuni and immerse yourself in history at the Taos Pueblo – where the fry bread at Tewa's makes a tasty distraction.
ANN CECIL/LONELY PLANET IMAGES ©
### Hwy 50: The Loneliest Road in America
23 You say you want to drop off the grid? Are you sure? Test your resolve on this desolate strip of pavement that stretches across the white-hot belly of Nevada. The highway passes through a poetic assortment of tumbleweed towns following the route of the Overland Stagecoach, the Pony Express and the first transcontinental telephone line. Today, it looks like the backdrop for a David Lynch film, with scrappy ghost towns, hardscrabble saloons, singing sand dunes and ancient petroglyphs – keeping things more than a little off-kilter.
STEPHEN SAKS/LONELY PLANET IMAGES ©
### San Juan Mountains
24 Adventure lovers, welcome home. The San Juans are a steep, rugged playground renowned for mountain biking, hut-to-hut hiking and high-octane skiing. But it's not all about amped-up thrills in the towns lining US 550, also known as the San Juan Byway (or the Million Dollar Highway between Ouray and Silverton). Both glitzy and gritty, secluded Telluride draws travelers to its outdoor festivals while Ouray lures 'em in with hot springs and ice climbing. In summer, a historic train chugs into Silverton daily from Durango. Leaf-peepers, start your engines for the yellow-aspen shimmer in the fall.
ED DARACK/SCIENCE FACTION/CORBIS ©
### Native American Art
25 Native American art is not stuck in the past. While designs often have a ceremonial purpose or religious significance, the baskets, rugs and jewelry that are crafted today often put a fresh spin on the ancient traditions – in Phoenix's Heard Museum, dedicated to Southwest cultures, you'll even see pottery emblazed with a Harry Potter theme. From Hopi kachina dolls and Navajo rugs to Zuni jewelry and the baskets of the White Mountain Apaches, art is a window into the heart of the native Southwest peoples.
LEE FOSTER/LONELY PLANET IMAGES ©
# need to know
Top of section
##### CURRENCY
» US dollars ($)
##### LANGUAGE
» English
##### MONEY
»ATMs widely available in cities and towns, but less prevalent on Native American land. Credit cards accepted in most hotels and restaurants.
##### VISAS
»Generally not required for stays up to 90 days for countries included in the Visa Waiver Program.
##### CELL PHONES
»Local SIM cards can be used in unlocked European and Australian phones. Cell phone reception can be non-existent in remote or mountainous areas.
##### DRIVING/TRANSPORTATION
»Best option for exploring is a car. Amtrak and Greyhound buses typically do not stop in national parks or small towns.
### When to Go
###### HIGH SEASON (JUN–AUG, NOV–FEB)
»Enjoy warm temperatures and sunny skies in New Mexico, Utah and northern Arizona.
»In winter, hit the slopes in Utah, New Mexico and Colorado or giddy-up at Arizona dude ranches.
###### SHOULDER SEASON (MAR–MAY, SEP–OCT)
»In fall, check out colorful aspens and cottonwoods in southern Colorado and northern New Mexico.
»Cooler temperatures and lighter crowds on the Grand Canyon South Rim.
###### LOW SEASON (NOV–FEB, JUN–AUG)
»National parks in northern Arizona and Utah clear out as the snow arrives.
»In summer, locals flee the heat in southern Arizona.
### Your Daily Budget
###### BUDGET LESS THAN $100
»Campgrounds and hostels: $20-40
»Taquerias, sidewalk vendors, supermarkets for self-caterers
»Share a rental car; split cost of park vehicle entry fees
###### MIDRANGE $100–250
»Mom-and-pop motels, low-priced chains: $50-90
»Diners, good local restaurants
»Visit museums, theme parks, national and state parks
###### TOP END OVER $250
»Boutique hotels, B&Bs, resorts, national park lodges: $120-650
»Upscale restaurants
»Hire an outdoor outfitter; take a guided tour; book ahead for top performances
### Websites
»National Park Service (www.nps.gov) Current information about national parks.
»Lonely Planet (www.lonelyplanet.com/usa/southwest) Summaries, travel news, links and traveler forum.
»Recreation.gov (www.recreation.gov)Camping reservations on federally managed lands.
»American Southwest (www.americansouthwest.net) Comprehensive site for national parks and natural landscapes.
»Grand Canyon Association (www.grandcanyon.org) Online bookstore with helpful links.
### Exchange Rates
Australia | A$1 | $1.04
---|---|---
Canada | C$1 | €1.02
Europe | €1 | $1.43
Japan | ¥100 | $1.28
Mexico | 10 pesos | $ .83
New Zealand | NZ$1 | $ .84
UK | £1 | $1.64
For current exchange rates see www.xe.com.
### Important Numbers
Country code | 1
---|---
International access code | 011
Emergency | 911
National sexual assault hotline | 800-656-4673
Statewide road conditions | 511
### Arriving in the Southwest
»McCarran International Airport, Las Vegas, NV
»Shuttles – $7 to the Strip; take exit door 9 to Bell Trans
»Taxis – $10-15 to the Strip; 30 min in heavy traffic
»Sky Harbor International Airport, Phoenix, AZ
»Shuttles – $14 to downtown, $20 to Old Town Scottsdale
»Taxis – $17-19 to downtown, $24 to Old Town Scottsdale
### Time
Most of the Southwest is on Mountain Time, which is seven hours behind Greenwich Mean Time. Nevada is one hour behind Mountain Time, on Pacific Time.
Daylight saving time currently begins in mid-March, when clocks are put forward one hour, and ends in early November, when clocks are turned back one hour.
Arizona does not use daylight saving time, so during that period it's one hour behind the other Southwestern states. The Navajo Reservation, which lies in Arizona, New Mexico and Utah, does use daylight-saving time (ie the whole reservation is on the same time zone). The small Hopi Reservation, which is surrounded by the Navajo Reservation in Arizona, follows the rest of Arizona. At hotels and restaurants on the Utah and Arizona border, you're likely to see two clocks on the wall – one for each state.
# if you like...
Top of section
### Green Chile
Green chile is to New Mexico what breath is to life – essential. Chiles are picked green, roasted in special barrel-shaped contraptions then sold at roadside stands statewide in September and October.
Hatch The soil and water in this town 40 miles north of Las Cruces are perfect for chile-growing, earning it the nickname 'Chile Capital of the World.' Read more on Click here.
Green chile cheeseburgers Restaurants across the state boast about the tastiness of their green chile-topped burgers. Our favorites are Sparky's Burgers (Click here) and the Owl Bar Café (Click here).
Chile Pepper Institute Part of the Chile Pepper Breeding and Genetics Program at NMSU, the institute has chile-filled demonstration gardens (Click here).
Horseman's Haven Serving the HOTTEST green chile in Santa Fe, this horse bites (Click here)!
Red or green? This is New Mexico's official state question. It's typically asked by waiters wondering whether to serve your dish with red or green chile.
### Wine & Microbrews
Whether it's après-ski in Park City, post-ride brews in Durango or wine sipping after shopping in Sedona and Jerome, it just feels right to celebrate your adventures – and the scenery – with a post-workout toast. And with brewpubs, microbreweries and wineries scattered across the region, celebrating is not hard to do.
Polygamy Porter Lip-smacking Utah microbrew with a catchy slogan: 'Why drink just one?' Try one, or two, at the Wasatch Brew Pub (Click here).
Beaver Street Brewery The perfect brewery: darn good food, friendly service, convivial patrons and beer that goes down smooth (Click here).
Verde Valley Wine Country Home to an up-and-coming Arizona wine trail that winds past wineries and vineyards in Cottonwood, Jerome and Cornville (Click here).
Durango, CO This knobby-tired mountain town hosts the San Juan Brewfest (Click here).
Napoleon's More than 100 types of champagne? _Mais oui_ at this 19th-century French theme bar (Click here).
### Hiking
As you descend the South Kaibab Trail past 2 billion years of geologic history, it's easy to feel insignificant. Until you hike back up and your pain becomes rather, well, significant. The Southwest is a rambler's paradise, with scenery to satisfy every type of craving: mountain, riparian, desert and red rock.
Grand Canyon Trails The Rim Trail offers inspiring views, but to really appreciate the age and immensity of the canyon you've got to hike into its depths (Click here).
Santa Fe National Forest Nearly 1000 miles of trail twist through forests and meadows in the forest's Pecos Wilderness (Click here).
Zion National Park Slot canyons, hidden pools and lofty scrambles make this stunner Utah's top national park for hiking (Click here).
Piestewa Peak Stroll past saguaros and scale a 2608ft peak in the scrubby heart of Phoenix (Click here).
Red Rock Country Hike to vortexes in Sedona (Click here), hoodoos in Bryce Canyon (Click here) and slender spans in Arches (Click here) and Canyonlands (Click here) National Parks.
### Small Towns
The small towns of the Southwest may have been settled by ornery miners, greedy cattle barons and single-minded Mormon refugees, but today these places have adjusted comfortably into welcomingartist communities and outdoorsy outposts that typically offer a warm hello.
Bisbee One-time mining town merges artsy, grungy and quirky with thoroughly engaging flair (Click here).
Torrey Mecca for outdoor lovers headed into Capital Reef National Park. Also has a bad-movie festival, pioneer buildings and the fantastic Café Diablo (Click here).
Billy the Kid Highway Named for the outlaw, this scenic byway swoops past shoot-'em-up Lincoln, Smokey the Bear's El Capitan and woodsy Ruidoso (Click here).
Ouray Hooray for you-ray, and sometimes ooh-ray, an ice climber's paradise in winter and a haven for hikers in summer that's plunked beside the Million Dollar Hwy (Click here).
Wickenburg Channels the 1890s with an ice cream parlor, an Old West museum, home-cooked breakfast joints and several range-riding dude ranches (Click here).
### Film Locations
From glowing red buttes to scrubby desert plains to the twinkling lights of Vegas, the landscape glows with undeniable cinematic appeal. It's simultaneously a place of refuge, unknown dangers and breathtaking beauty. In other words, it's catnip to movie directors looking to drop their heroes into inspirational settings.
Monument Valley Stride John Wayne–tall beneath the iconic red monoliths that starred in seven of the Duke's beloved Westerns (Click here).
Las Vegas Bad boys and their hi-jinks brought Sin City back to the big screen in _Oceans Eleven_ and _The Hangover_ (Click here).
Moab & around Directors of _Thelma & Louise_ and _127 Hours_ shot their most dramatic scenes in nearby parks (Click here).
Butch Cassidy & The Sundance Kid Cassidy roamed southwestern Utah; Grafton ghost town is the site of the movie's bicycle scene (Click here).
Very Large Array 27 giant antenna dishes look to the stars in extraterrestrial-themed movies like _Contact_ and _Cocoon_ (Click here).
### Kitsch & Offbeat
There's a lot of empty space in the Southwest, and this empty space draws the weird out of people. And we mean that as a compliment. Dinosaur sculptures. Museums of the bizarre. Festivals that spotlight cannibals and desert creativity. Perhaps the bumper sticker we saw in Jerome says it best: 'We're all here because we're not all there.'
Route 66 This two-lane ode to Americana is dotted with wacky roadside attractions, especially in western Arizona (Click here).
Burning Man A temporary city in the Nevada desert attracts 55,000 for a week of self-expression and blowing sand (Click here).
Roswell, NM Did a UFO crash outside Roswell in 1947? Museums and a UFO festival explore whether the truth is out there (Click here).
Ogden Eccles Dinosaur Park Roadside dinosaurs at their kitschy, animatronic best (Click here).
Wacky museums The death mask of John Dillinger (Click here), mummified bobcats and Doc Holliday's card table (Click here)keep things kitschy in Arizona.
### Art
Cranes etched on rocks. Georgia O'Keeffe's cow skulls. Black-and-white photographs by Ansel Adams. The Southwest has inspired self-expression in all its forms. Today, former mining towns have re-emerged as artists' communities, and you'll find galleries and studios lining 1800s-era main streets. For artists and shoppers alike, northern New Mexico reigns supreme.
Santa Fe Sidewalk artisans, chichi galleries and sprawling museums are framed by crisp skies and the Sangre de Cristos (Click here).
Heard Museum The art, craftsmanship and culture of Southwestern tribes earn the spotlight at this engaging Phoenix museum (Click here).
Abiquiú & the Ghost Ranch Captivating red rock landscapes that Georgia O'Keeffe claimed as her own (Click here).
Bellagio Gallery of Fine Art Art? On the Las Vegas Strip? You betcha, and the exhibits here draw from top museums and collections (Click here).
Jerome This former mining town lures weekend warriors with artist cooperatives, an art walk and one-of-a-kind gift shops (Click here).
### Historic Sights
Across the Southwest, dinosaurs left their footprints, ancient civilizations left their cliff dwellings and outlaws and sheriffs left behind enough legends to fill hundreds of books. Many of these sights have barely changed over the centuries, making it easy to visualize how history unfolded, sometimes just a few steps away.
Dinosaur National Monument Touch a 150-million-year-old fossil at one of the largest dinosaur fossil beds in North America, discovered in 1909 (Click here).
Mesa Verde Climb up to cliff dwelling that housed Ancestral Puebloans more than 700 years ago (Click here).
Virginia City Site of the Comstock Lode, which begat an 1859 silver rush (Click here).
Picacho Peak State Park On April 15, 1862 this desolate place witnessed the westernmost battle of the Civil War (Click here).
Golden Spike National Historic Site Union Pacific Railroad and Central Pacific Railroad met here on May 10, 1869, completing the transcontinental railroad (Click here).
### Water Adventures
Water adventures? In a land of deserts, red rocks and cacti? Thank the big dams like Hoover, Glen Canyon and Parker for the region's big lakes and all their splashy activities. Elsewhere, hurtle over whitewater, paddle over ripples, slide through a plastic tube or simply sip a cocktail beside a Sin City pool – there's something here to fit your speed.
Grand Canyon Rafting the Colorado through the Big Ditch is the Southwest's most thrilling, iconic expedition (Click here).
Pools & theme parks Las Vegas pools are playgrounds for adults (Click here); Phoenix water parks are the ideal splash grounds for the kiddies (Click here).
Big lakes Water-skiers zip across Lake Mead (Click here) and house-boaters putter below crimson rocks on Lake Powell (Click here).
Moab rivers The Colorado and Green Rivers win Most Well-Rounded, offering rafting, canoeing and kayaking (Click here).
Fly fishing McPhee Lake in Dolores, CO has the best catch ratio in the Southwest (Click here).
### Old West
The legend of the Wild West has always been America's grandest tale, capturing the imagination of writers, singers, filmmakers and travelers around the world. At atmospheric sites across the region, you can compare the truth to the myth.
Lincoln Billy the Kid's old stomping – and shooting – ground during the Lincoln County War (Click here).
Tombstone Famous for the Gunfight at the OK Corral, this dusty town is also home to Boothill Cemetery and the Bird Cage Theater (Click here).
Whiskey Row This block of Victorian-era saloons has survived fires and filmmakers (Click here).
Kanab Hundreds of Westerns were filmed near this rugged Mormon outpost known as Utah's Little Hollywood (Click here).
Steam train Channel the Old West on the steam-driven train that's chugged between Durango and Silverton for 125 years (Click here).
### Spas & Resorts
When it comes to lavish resorts, the Southwest serves up everything except an oceanfront view. But what Phoenix and Santa Fe lack in beachfront property, they make up for with world-class shopping, dining, art and pampering.
Truth or Consequences Built over Rio Grande–adjacent hot springs, the bathtubs and pools here bubble-up with soothing, hydro-healing warmth (Click here).
Ten Thousand Waves The soaking tubs at this intimate Japanese spa are tucked on a woodsy hillside (Click here).
Phoenix & Scottsdale Honeymooners, families, golfers – there's a resort for every type of traveler within a few miles of Camelback Rd (Click here).
Las Vegas Many four- and five-star hotels – Encore, Bellagio, Wynn – offer resort-like amenities (Click here).
Sheraton Wild Horse Pass Resort & Spa On the Gila Indian Reservation, this resort embraces its Native American heritage with style (Click here).
### Different Cultures
Cowboys and miners showed up late for the party, following on the heels of several vibrant cultures that had already laid claim to the region. Descendants of these early inhabitants (Native Americans, Spanish and Mexican settlers, and Mormons) live in the region today, giving the Southwest a multicultural flair evident in its art, food and festivals.
Hopi Reservation The past and present merge atop the Hopi's long-inhabited mesas, the center of their spiritual world (Click here).
Temple Square Trace the history of Mormon pioneers and their leaders on a 10-acre block in Salt Lake City (Click here).
National Hispanic Cultural Center Galleries and a stage spotlight Hispanic arts (Click here).
Pueblos Multi-level adobe villages, some dating back centuries, are home to a diverse array of Native American tribes in northern New Mexico (Click here).
Canyon de Chelly Learn about the history and traditions of the Navajo on a guided tour into this remote but stunning canyon (Click here).
### Geology
The Southwest's geologic story starts with oceans, sediment and uplift, continues with a continental collision and more oceans, then ends with wind, water and erosion.
Grand Canyon A 277-mile river cuts through two-billion-year-old rock whose geologic secrets are layered and revealed within a mile-high stack (Click here).
Chiricahua National Monument A rugged wonderland of rock chiseled by rain and wind into pinnacles, bridges and balanced rocks (Click here).
Sand dunes The white and chalky gypsum dunes at White Sands National Monument are, simply put, mesmerizing (Click here).
Arches National Park Sweeping arcs of sandstone create windows on the snowy peaks and desert landscapes (Click here).
Caverns Head to Carlsbad Caverns for an 800ft plunge to a subterranean wonderland (Click here) or step into the pristine confines of Kartchner Caverns for an educational tour (Click here).
### Wildlife
You'd be surprised how much wildlife you can see from the confines of your car – roadrunners, coyotes, elk, maybe a condor. But really, how much fun is that? As descendants of hunting nomads isn't it in our genes to scan the horizon for signs of life?
Bird-watching Southern Arizona is the place to be in April, May and September for migrating birds attracted to its riparian forests (Click here).
Valles Caldera National Preserve Dormant crater of a super-volcano is now home to New Mexico's largest elk herd (Click here).
Gila National Forest Javelina, bear and trout live in this remote and rugged corner of New Mexico (Click here).
California Condors This prehistoric bird, recently on the verge of extinction, is making a comeback near the Vermilion Cliffs (Click here)
Arizona-Sonora Desert Museum Education-minded wildlife repository spotlights desert denizens (Click here).
### Shopping
High quality Native American jewelry and crafts make shopping in the Southwest unique. The stunning landscapes here attract artists galore, and their paintings make for wonderful gifts. There's also plenty of upscale shopping for those who seek it, but remember to save five dollars for that kitschy key chain from Route 66.
Trading Posts Scattered across the southwest, these were the first go-to shops for Native American crafts (Click here).
Scottsdale Honey, Manolo up: we don't have _malls_ in Scottsdale, we have borgatas, commons and fashion squares (Click here).
Santa Fe boutiques Eclectic specialty stores dot downtown and 100+ galleries hug Canyon Road (Click here and Click here).
The Strip Over-the-top goes over-the-top at Vegas' newest designer-label malls: Crystal's at City Center and the Shoppes at Palazzo (Click here).
Singing Wind Bookshop Destination indie bookstore has everything you'll ever want to read about the Southwest, and a whole lot more (Click here).
# month by month
Top of section
### Top Events
Sundance Film Festival, January
Cactus League, March
Telluride Bluegrass Festival, June
Burning Man, September
Balloon Festival, October
January
Start the New Year swooshing down mountain slopes in New Mexico, Utah and yes, even Arizona. Artsy events like film festivals and poetry readings will turn your mind from the cold. Snowbirds keep warm in Phoenix and Yuma.
###### COWBOY POETRY
Wranglers and ropers gather in Elko, NV for a week of poetry readings and folklore performances. Started in 1985, this event has inspired cowboy poetry gatherings across the region.
###### ICE CLIMBING
Billed as 'The Biggest Ice Festival in North America,' this mid-January party offers chills and thrills with four days of climbing competitions, clinics and microbrew beer – all in Ouray, CO.
###### SUNDANCE FILM FESTIVAL
Hollywood moves to Park City in late January when aspiring filmmakers, actors and industry buffs gather for a week of cutting-edge films.
February
Wintery sports not your thing? Hit an urban center for indoor distractions like shopping, gallery hopping or attending the symphony. If your family wants to rope and ride on a dude ranch, now is the time to finalize reservations in southern Arizona.
###### TUCSON GEM & MINERAL SHOW
At the largest mineral and gem show in the US, held the second full weekend in February, about 250 dealers sell jewelry, fossils, crafts and lots and lots of rocks. Lectures, seminars and a silent auction round out the weekend.
###### ARTFEAST
Eat, drink and be merry while gallery hopping in Santa Fe, NM during this weekend-long festival in late February that comes at just the right time – the fashion shows and wine tastings do a good deal to temper the late-winter cold.
March
March is spring break season in the US. Hordes of rowdy college students descend on Arizona's lakes while families head to the region's national parks. Lodging prices may jump in response. Skiers will want to enjoy their last runs in Telluride.
###### SPRING TRAINING
Major league baseball fans have it good in March and early April. That's when Arizona hosts the preseason Cactus League, when some of the best pro teams play ball in Phoenix and Tucson.
Blooming cactus flowers along Camino del Diablo in the Sonoran Desert
MICHAEL BENANAV/LONELY PLANET IMAGES ©
###### WILDFLOWER VIEWING
Depending on rainfall, spring is wildflower season in the desert. Check www.desertusa.com for wildflower bloom reports at your favorite national and state parks.
April
Birders flock (sorry) to nature preserves across the region to scan for migrating favorites. Spring is also the season for outdoor art and music festivals. Runners might consider the Salt Lake City marathon.
###### NATIVE AMERICAN POWWOW
More than 3000 Native American dancers and singers from the US and Canada come together at the Gathering of Nations Powwow to compete in late April in Albuquerque, NM. There's also an Indian market with more than 800 artists and craftsmen.
###### ROUTE 66 FUN RUN
Classic cars, not joggers, 'run' down Route 66 between Seligman and Golden Shores in western Arizona in late April. Roadster enthusiasts can check out the cars, vans and buses at the Powerhouse Visitor Center parking lot in Kingman on Saturday afternoon.
May
As the school year winds down, May is a good time to enjoy pleasant weather and lighter crowds at the Grand Canyon and other national parks. Southern Arizona starts to heat up, so get that shopping spree done before Phoenix starts to melt. Memorial Day weekend marks the start of summer fun.
###### CINCO DE MAYO
Mexico's 1862 victory over the French in the Battle of Puebla is celebrated on May 5 with parades, dances, music, arts and crafts and street fairs. And lots of Mexican beer.
'Aliens' at the UFO Festival, Roswell (Click here)
RAY LASKOWITZ/LONELY PLANET IMAGES ©
June
###### UTAH SHAKESPEAREAN FESTIVAL
Head to Cedar City for a dramatic 'Shakesperience' with performances, literary seminars and educational backstage tours from mid-June to October. 2011 marked its 50th anniversary.
###### BLUEGRASS IN THE MOUNTAINS
In mid-June enjoy the high lonesome sounds of bluegrass in the mountain-flanked beauty of Telluride. Favorites like Old Crow Medicine Show, Sam Bush and Emmylou Harris keep festivarians happy.
July
Summer is in full swing, with annual 4th of July celebrations reminding us that the season is almost halfway over. If you've always wanted to luxuriate in a fancy Phoenix spa, now's your chance. The 100+ heat drives away tourists, so it's a fantastic time to score awesome deals. Mountain bikers can hit the trails at ski resorts in Utah and Colorado.
###### INDEPENDENCE DAY
Cities and towns across the region celebrate America's birth with rodeos, music, parades and fireworks on the 4th of July. For something different, drive Route 66 to Oatman for the 4th of July sidewalk egg fry.
###### UFO FESTIVAL
Held over the 4th of July weekend, this festival beams down on Roswell, NM with an otherworldly costume parade, guest speakers and workshops. There's even an Alien Battle of the Bands.
Art installation at the Burning Man festival (Click here)
AURORA PHOTOS/ALAMY ©
###### SPANISH MARKET
This weekend festival draws huge crowds to Santa Fe in late July. The main event is the acclaimed juried show when traditional Spanish Colonial arts – from small religious devotionals like _retablos_ to _bultos_ to handcrafted furniture and metalwork – are shown.
August
This is the month to check out Native American culture, with arts fairs, markets and ceremonial gatherings in several cities and towns. Popular parks like the Grand Canyon will likely be booked up, so try for cancellations or grab your tents and water jugs for dispersed camping in nearby national forests and on the Bureau of Land Management (BLM) acreage.
###### NAVAJO FESTIVAL OF ARTS & CULTURE
Artists, dancers and storytellers share the customs and history of the Diné in Flagstaff on a weekend in early August.
###### SANTA FE INDIAN MARKET
Only the best get approved to show their work at Santa Fe's most famous festival, held the third week of August on the historic plaza, that includes a world-famous juried show where more than 1100 artists from 100 tribes and pueblos exhibit.
###### AUGUST DOIN'S – WORLD'S OLDEST CONTINUOUS RODEO
Steer wrestling and barrel racing are on tap in Payson, where the annual rodeo has been held for 127 continuous years.
September
It's back to school for the kiddies, which means lighter crowds at the national parks. Fall is a particularly nice time for an overnight hike to the bottom of the Grand Canyon. Leaf-peepers may want to start planning fall drives in northern mountains.
###### BURNING MAN
In 2011 an estimated 54,000 people attended this outdoor celebration of self-expression known for its elaborate art displays, barter system, blowing sand and final burning of the man. This temporary city rises in the Nevada desert before Labor Day.
###### NAVAJO NATION FAIR
The country's largest Native American Fair, with a rodeo, a parade, dances, songs, arts, crafts and food, is held in early September in Window Rock, AZ.
###### BEER TASTING
Mountain bikers, microbrews, an outdoorsy town and a late-August weekend. The only thing missing is a beer festi-oh wait, there is one. The San Juan Brewfest in Durango serves samples of more than 60 beers.
October
Shimmering aspens lure road trippers to Colorado and northern New Mexico for the annual fall show. Keep an eye out for goblins, ghouls and ghost tours as Halloween makes its annual peek-a-boo appearance on October 31.
###### SEDONA ARTS FESTIVAL
This fine-art show overflows with jewelry, ceramics, glass and sculptures in early October. More than 150 artists exhibit their art at Sedona's Red Rock High School.
Albuquerque's International Balloon Festival in full swing (Click here)
MARK NEWMAN/LONELY PLANET IMAGES ©
###### INTERNATIONAL BALLOON FESTIVAL
The world's biggest gathering of hot-air balloons, with daily mass lift-offs in early October that invoke childlike awe in Albuquerque, NM.
December
It's Christmas season in the Southwest, which means nativity pageants and holiday lights displays. It's also high season at resorts across the region, from Phoenix to ski resort towns.
###### FESTIVAL OF LIGHTS
Some 6000 luminaries twinkle in Tlaquepaque Arts & Crafts Village in Sedona with Santa Claus and a mariachi band.
# Route 66 & Scenic Drives
Top of section
### Buckle Up
Route 66
758 to 882 miles (depending on segments driven)
A classic journey through small town America, with a side of kitsch.
Hwy 89/89A: Wickenburg to Sedona
120 miles
The Old West meets the New West on this drive past dude ranches, mining towns, art galleries and stylish wineries.
Billy the Kid Highway
84 miles
This outlaw loop shoots through Billy the Kid's old stomping grounds.
Kayenta-Monument Valley Scenic Road
40 miles
Star in your own western on an iconic drive past cinematic red rocks in Navajo Country.
Highway 50: The Loneliest Road
320 miles
An off -the-grid ramble mixing the quirky, historic and dry lonesome in tumbleweed Nevada.
Million Dollar Highway
25 miles
There's gold in them thar mountain views, but don't squint too hard or you might run off the ro-whoa!
High Road to Taos
85 miles
Drive into your own landscape painting on this picturesque mountain romp between Santa Fe and Taos.
The Southwest is chock-full of picturesque drives and we've dedicated a chapter to the very best. From Route 66 to the Million Dollar Highway to the Loneliest Road in America, we've got a drive for every corner of the region.
For more drives in a particular region, check the destination chapters.
### Route 66
'Get your kitsch on Route 66' might be a better slogan for the scrubby stretch of Mother Road running through Arizona and New Mexico. Begging burros. Lumbering dinosaurs. A wigwam motel. It's a bit off beat, but all the folk along the way sure seem glad that you're stopping by.
#### Why Go?
History, scenery and the open road. This alluring combination is what makes a road trip on Route 66 so fun. From Topock, Arizona, heading east, highlights include the begging burros of Oatman, the Route 66 Museum in Kingman and an eclectic general store in tiny Hackberry. Kitsch roars its dinosaury head at Grand Canyon Caverns, luring you 21 stories underground for a tour and even an overnight stay. Burma-Shave signs spout amusing advice on the way to Seligman, a funny little village that greets travelers with retro motels, a roadkill cafe and a squirt of fake mustard at the Snow Cap Drive-In.
Next up is Williams, a railroad town lined with courtyard motels and brimming with small-town charm. Route 66 runs parallel to the train tracks through Flagstaff, passing the wonderful Museum Club, a cabinlike roadhouse where everyone's having fun. From here, must-sees include Meteor Crater and the 'Take it Easy' town of Winslow where there's a girl, my Lord, in a flatbed Ford... Snap a photo of the famous corner then savor a spectacular dinner in the Turquoise Room at La Posada hotel. Finish Arizona in kitschy style with a snooze in a concrete teepee in Holbrook.
In New Mexico, look for the 1937 El Rancho hotel (John Wayne slept here!) in Gallup then slurp green-chile stew at Albuquerque's beloved eatery, Frontier. Route 66 runs uninterrupted through Gallup, passing the restored 1926 Spanish Colonial El Morro Theatre. Next up? Santa Rosa's scuba-ready Blue Hole and the neon signs of Tucumcari, comforting reminders of civilization as dusk falls over the lonesome plains.
#### When to Go
The best time to travel Route 66 is from May to September, when the weather is warm and you'll be able to take advantage of more open-air activities.
#### The Route (882 miles)
This journey starts in Topock, Arizona then continues northeast to Kingman. After crossing I-40, Route 66 travels east and cuts through Flagstaff , Winslow and Holbrook. In New Mexico, it passes through Gallup and Grants before entering Albuquerque, Santa Rosa and Tucumcari.
#### Time
If you're racing down the Mother Road, this trip will take about two days because the route is primarily two-lane and there are lots of stoplights in the cities. If you have some time, it's best explored over the course of a week.
### Hwy 89 & 89A: Wickenburg to Sedona
Hwy 89 and its sidekick Hwy 89A are familiar to Arizona road-trippers because they cross some of the most scenic and distinct regions in the center of the state. The section described here travels from Wickenburg over the Weaver and Mingus Mountains before rolling into Sedona.
#### Why Go?
This is our favorite drive in Arizona. It may not be the prettiest or the wildest, but the trip is infused with a palpable sense of the Old West, like you've slipped through the swinging doors of history. But the route's not stuck in the 19th century – far from it. Weekend art walks, a burgeoning wine trail, stylish indie shops and top-notch restaurants all add some 21st-century spark. For those interested in cowboy history, Wickenburg and its dude ranches are a good place to spend some time. Hwy 89 leaves town via Hwy 93 and soon tackles the Weaver Mountains, climbing 2500ft in 4 miles. The road levels out at mountain-topping Yarnell, 'where the desert breeze meets the mountain air,' then swoops easily past grassy buttes and grazing cattle in the Peeples Valley. From here, highlights include Prescott's Whiskey Row, towering Thumb Butte and the unusual boulders at Granite Dells.
Follow Hwy 89A to Jerome and hold on tight. This serpentine section of road brooks no distraction, clinging tight to the side of Mingus Mountain. If you dare, glance east for stunning views of the Verde Valley. The zigzagging reaches epic proportions in Jerome, a former mining town cleaved into the side of Cleopatra Hill. Pull over for art galleries, tasting rooms, quirky inns and an unusually high number of ghosts. Hwy 89A then drops into Clarkdale, Tuzigoot National Monument and Old Town Cottonwood. On the way to the red rocks of Sedona and Oak Creek Canyon, detour to wineries on Page Springs Rd or loop into town via the Red Rock Loop Rd past Cathedral Rock.
#### When to Go
This route is best traveled in spring, summer and fall to avoid winter snow – although you might see a few flakes in the mountains in April. In the dead of summer, you won't want to linger in low-lying, toasty Wickenburg.
#### The Route (120 miles)
From Wickenburg, follow Hwy 93 to Hwy 89 then drive north to Prescott. North of town pick up Hwy 89A, following it to Sedona.
#### Time
This trip takes about a half-day to drive without stopping, assuming you don't get stuck behind a slow-moving recreational vehicle. To fully enjoy the scenery and the towns, give yourself four to five days.
### ROADSIDE ODDITIES: ROUTE 66
»Grand Canyon Caverns tour & underground motel room A guided tour 21 stories below the earth's surface loops past mummified bobcats, civil-defense supplies and a $700 motel room.
»Porís de Abona Our favourite east-coast beach; pretty, pocket-sized black-sand beach in a working fishing village. Largely undeveloped.
»Burma-Shave signs Red-andwhite ads from a bygone era line the roadside, offering tongue-in-cheek advice for life.
»Seligman's Snow Cap Drive-In Juan Delgadillo opened this prankish burger joint and ice-creamery in 1953.
»Meteor Crater A fiery rock slammed into the earth 50,000 years ago, leaving a 550ft-deep pockmark that's nearly 1 mile across.
»Holbrook's Wigwam Motel Concrete wigwams will flash you back to the 1950s with retro hickory log-pole furniture.
### Billy the Kid Highway
Named for the controversial outlaw famous for his role in the Lincoln County War, the Billy the Kid National Scenic Byway loops around his old stomping grounds in the rugged mountains of Lincoln National Forest in central New Mexico.
El Rancho Hotel and Motel (Click here), a National Historic Landmark on Route 66
RICHARD CUMMINS/LONELY PLANET IMAGES ©
#### Why Go?
This mountain-hugging loop provides a cool respite from the heat and hustle-bustle of Roswell and Alamogordo. For a primer on Billy the Kid, also known as William Bonney, the best place to start is Lincoln, population 50 (see also Click here). This one-road hamlet was the focal point of the Lincoln County war, a bloody rivalry between two competing merchants and their gangs in the late 1870s. Billy took an active role in the conflict and evidence of his involvement can be seen today at the courthouse: a bullet hole in the wall left after he shot his way to freedom during a jailbreak. From here, you can visit Smokey the Bear's grave in Capitan, hike up Sierra Blanca Peak, or take in a bit of horse racing at Rui doso Downs. End with dinner at Rickshaw, serving the best Asian food in the region.
Hairpin bend on Million Dollar Highway (Click here)
JOHN ELK III/LONELY PLANET IMAGES ©
#### When to Go
Although there's skiing in the area in winter, the best time for a scenic drive is during summer, when average temperatures hover between 77°F and 82°F (25°C and 28°C). It's also a pleasant time to enjoy hiking and fly-fishing in the surrounding national forest.
#### The Route (84 miles)
From Roswell, follow Hwy 70 west to Hwy 380, following it through Hondo, Lincoln and Capitan before looping south on Hwy 48 to Ruidoso then take Hwy 70 east to close the loop at Hondo.
#### Detour
For art galleries, antique shops and a few members of the herd of Painted Burros – a mulish spin on the colorful painted cows in New York and Chicago – head to tiny Carrizozo sitting 20 miles west of Capitan on Hwy 360. Curious kids will enjoy a short hike through a lava field at Valley of Fires Recreation Area.
#### Time
If you're not stopping, this route should take about half a day. To see the sights, including Carrizozo, allow three days.
### Kayenta-Monument Valley Scenic Road
One of the cool things about road-tripping to Monument Valley – and there are many – is that the place isn't easy to reach. Upon arrival, you can't help but feel a special sense of accomplishment, that you're in on a secret that's saved only for the most worthy of travelers.
#### Why Go?
From a distance, the rugged sandstone formations of Monument Valley look like a prehistoric fortress, a huddled mass of red and gold protecting ancient secrets. But as you approach, individual buttes and craggy formations break from the pack, drawing you closer with sun-reflected beauty and unusual shapes. Up close they're downright hypnotic, an alluring mix of familiar and elusive. Yes, we've seen them in the John Ford Westerns, but the big screen doesn't quite capture the changing patterns of light, the imposing height, or the strangeness of the angles and forms.
The closest town to Monument Valley is Kayenta, a cluster of gas stations, motels and restaurants at the junction of Hwys 160 and 163. The Burger King there has a small exhibit on the Navajo Code Talkers. Like Monument Valley, Kayenta is part of the sprawling Navajo Reservation; at 27,000 sq miles it's the country's largest reservation. Hwy 163 leads to the entrance of the Monument Valley Navajo Tribal Park and the 17-mile drive that loops around the major formations. Goulding's Lodge is across from the entrance, on the other side of Hwy 163 (Harry Goulding opened a trading post here in 1925 and enticed director John Ford to the area) and there's a small movie-themed museum on the grounds.
The Monument Valley loop ($5) is a dusty, bumpy dirt road that winds beneath the sandstone formations, most named for the objects or animals they resemble, from the Mittens to Elephant Butte. Budget about an hour and a half for the drive. SUVs will find the drive easy, compact cars may have to drive more carefully. A new addition to the landscape is the View Hotel, which blends in well with the surrounding rocks.
#### When to Go
Temperatures remain comfortable April through November, reaching the low-tomid 90s (or low 30s in Celsius) in July and August. With average lows in the 20s (around -6°C) in December and January, winter can be a bit chilly!
#### The Route (40 miles)
From Tuba City, Arizona, take Hwy 160 northeast to Kayenta. Follow Hwy 163 north 22 miles to the park entrance.
#### Time
This trip can be done in a day, but to spend some time exploring the area, allow two to three days.
### Highway 50: The Loneliest Road
Stretching east from Fallon, Nevada, to Great Basin National Park and the Nevada state line, remote Highway 50 follows some of Americas most iconic routes – the Pony Express, the Overland Stagecoach and the Lincoln Highway – across the heart of the state.
#### Why Go?
Why would you drive the Loneliest Road in America? As mountaineer George Mallory said about Everest: 'Because it's there.' And yes, Mallory disappeared while attempting the feat, but the lesson still applies. You drive Highway 50 because something might just...happen. So take the blue pill Neo, wake up from your slumber and point your ride toward Fallon, a former pioneer town now home to the US Navy's TOPGUN fighter-pilot school. From here, listen for the singing dunes at Sand Mountain Recreation Area then pull over and hike to the ruins of a Pony Express station – the FedEx office of its day.
Just east of Austin (population 340 last we checked) look for petroglyphs, then yell 'Eureka!' for the tiny town that coughed up $40 million in silver in the 1800s. Then check out the beehive-shaped buildings at Ward Charcoal Ovens State Park near Ely, where charcoal was created to use in the silver smelters. End at Great Basin National Park, gaining 4000ft in elevation on the 12-mile Wheeler Peak Scenic Drive and earning expansive views of the Great Basin Desert.
### HISTORY OF ROUTE 66
Built in 1926, Route 66 stretched from Chicago to Los Angeles, linking a ribbon of small towns and country byways as it rolled across eight states. The road gained notoriety during the Great Depression, when migrant farmers followed it west from the Dust Bowl across the Great Plains. It's nickname, 'Mother Road', first appeared in John Steinbeck's novel about the era, The Grapes of Wrath. Things got a little more fun after World War II, when newfound prosperity prompted Americans to get behind the wheel and explore. Sadly, just as things got going, the Feds rolled out the interstate system, which eventually caused the Mother Road's demise. The very last town on Route 66 to be bypassed by an interstate was Arizona's very own Williams, in 1984.
#### When To Go
Your best bet is summer. Sections of the road get hit with snow and rain in winter and early spring; in a few towns the road requires 4WD and chains during the worst conditions.
#### The Route (320 miles)
From Fallon, Nevada – about 75 miles east of Lake Tahoe – follow Hwy 50 east to Austin, Eureka, Ely and then Great Basin National National Park, bordering Utah.
#### Time
The Loneliest Road can be driven in less than a day but to check out a few sites and the national park, allow for two or three.
### Million Dollar Highway
Stretching between old Colorado mining towns Ouray and Silverton is one of the most gorgeous alpine drives in the US. Part of the 236-mile San Juan Skyway, this section of US 550 is known as the Million Dollar Highway, most likely because its roadbed is filled with ore.
#### Why Go?
Twenty-five miles of smooth, buttery pavement twists over three mountain passes, serving up views of Victorian homes, snow-capped peaks, mineshaft headframes and a gorge lined with rock. But the allure isn't just the beauty – there is also the thrill of driving. Hairpin turns,occasional rock slides and narrow, mountain-hugging pavement flip this Sunday afternoon drive into a NASCAR-worthy dventure.
Charming Ouray sits at nearly 7800ft, surrounded by lofty peaks. It also fronts the Uncompahgre Gorge, a steep, rocky canyon famous for its ice climbing. While here, take a hike or soak in the town's hot springs. From Ouray, the Million Dollar Highway – completed in 1884 after three years of construction – hugs the side of the gorge, twisting past old mines that pock the mountainsides. Stay vigilant for the masochistic, spandex-clad cyclists pumping over the passes on the ribbon-thin road. In Silverton, step away from the car and enjoy the aspencovered mountains or watch the steampowered Durango & Silverton Narrow Gauge Railroad chug into town.
#### When to Go
In winter, Red Mountain Pass south of Ouray may close if there is too much snow; at other times you may need chains. You might even see snow on the ground in summer, though it likely won't be on the road.
#### The Route (25 miles)
From Ouray, follow Hwy 550 south to Silverton.
#### Detour
The drive between Ouray and Telluride is 50 miles – if you take the paved route. If you're feeling adventurous (and have the right vehicle) consider the 16-mile road over Imogene Pass. On this old mining road you'll cross streams, pass through alpine meadows, negotiate one of the state's highest passes, and even drive by the old mine itself. But we should mention one thing: this 'shortcut' takes three hours. Still game?
#### Time
Travel time depends on who's traveling in front of you and weather conditions, but at a minimum allow yourself half a day to drive it. If you have time, spend two to three days exploring the region.
### High Road to Taos
This picturesque byway in northern New Mexico links Santa Fe to Taos, rippling through a series of adobe villages and mountain-flanked vistas in and around the Truchas Peaks.
#### Why Go?
Santa Fe and Taos are well-known artists' communities, lovely places brimming with galleries, studios and museums that are framed by turquoise skies and lofty mountains. Two cities this stunning should be linked by an artistically pleasing byway. The High Road to Taos, a wandering route that climbs into the mountains, obliges.
In Nambé, hike to waterfalls or simply meditate at Lake Nambé. From here, the road leads north to picturesque Chimayo. Ponder the crutches left in the Santuario de Chimayo (the 'Lourdes of America') or admire fine weaving and wood carving in familyrun galleries. Near Truchas, a village of galleries and century-old adobes, you'll find the High Road Marketplace. This cooperative on SR 676 sells a variety of artwork by area artists.
Further up Hwy 76, original paintings and carvings remain in good condition inside the Church of San José de Gracia, considered one of the finest surviving 18th-century churches in the USA. Next is the Picuris Pueblo, once one of the most powerful pueblos in the region. This ride ends at Penasco, a gateway to the Pecos Wilderness that's also the engagingly experimental Penasco Theatre. From here, follow Hwy 75 and 518 to Taos.
#### When to Go
Catch blooms in spring, the high season in summer and changing leaves in the fall. With the mountains on this route, winter is not the best time to visit.
#### The Route (85 miles)
From Santa Fe, take 84/285 west to Pojoaque and turn right on Hwy 503, toward Nambé. From Hwy 503, take Hwy 76 to Hwy 75 to Hwy 518.
#### Time
You can spend a half day enjoying just the scenery, or two days checking out the history and galleries as well.
# itineraries
Top of section
Whether you've got six days or 60, these itineraries provide a starting point for the trip of a lifetime. Want more inspiration? Head online to lonelyplanet.com/thorntree to chat with other travelers.
### Two Weeks Vegas, Grand Canyon & Southern Utah Loop
If you only have time for a short loop, this tour offers a taste of the Southwest's most famous city, canyon and scenery. Start in Las Vegas and dedicate a few days to traveling the world on the Strip. When you've soaked up enough decadence, head east to canyon country – Grand Canyon country, that is. You'll want a couple of days to explore America's most famous park. For a once-in-a-lifetime experience, descend into the South Rim chasm on the back of a mule and spend the night at Phantom Ranch on the canyon floor.
From the Grand Canyon head northeast through Monument Valley, with scenery straight out of a Hollywood Western, to the national parks in Utah's southeast corner – they're some of the most visually stunning in the country. Hike the shape-shifting slot canyons of Canyonlands National Park, watch the sun set in Arches National Park, or mountain-bike sick slickrock outside Moab. Then drive one of the most spectacular stretches of pavement, Hwy 12, west until it hooks up with I-15 and takes you back to Las Vegas.
### Three Weeks to One Month Grand Tour
Throw a pair of cowboy boots, hiking boots and comfy walking shoes into the saddlebag, pardner, and get ready to ride. Suspend judgments and roll the dice for two days on the Las Vegas Strip before crossing the new Mike Callaghan-Pat Tillman Memorial Bridge – be sure to ogle Hoover Dam – as you swoop into Arizona. Next up is Route 66, which chases trains and Burma-Shave signs as it unfurls between Kingman and Williams. Funky Flagstaff is a welcoming spot to regroup before venturing into the Grand Canyon National Park, where a hike is always a must-do. After three days in the park, end the week among the red rocks of Sedona.
Heading south, get in touch with your shabby-chic side in Jerome before driving into Phoenix for two days of shopping and museum hopping. Mellow out on 4th Avenue, Tucson, then study the cacti at Saguaro National Park. Fancy yourself a gunslinger in Tombstone before ending the week with a two-day stay in charming Bisbee.
Next up is New Mexico, where you can sled down sand dunes in the remote White Sands National Monument. Spend a day exploring the caves at Carlsbad Caverns National Park then head north to Roswell to ponder its UFO mysteries. Plan to spend two days in Santa Fe, a foodie haven and a magnet for art fiends. Atomic-age secrets are revealed at nearby Los Alamos, which are an interesting contrast to the laid-back musings of the hippies and ski bums just north in Taos. Drive the luscious Enchanted Circle then chill out with a microbrew and bike ride in Durango. Next up? Pondering the past inside the amazing cliff dwellings at Mesa Verde National Park. You'll be equally amazed by the towering red buttes at Monument Valley.
For the most stunning wilderness in the US, spend your last week in Utah's national parks, including Canyonlands National Park and Arches National Park, for which Moab serves as a staging area. From Moab follow Hwy 12 back to Las Vegas, stopping at Capitol Reef National Park, Grand Staircase-Escalante National Monument, the spires of Bryce Canyon National Park and the sheer red rock walls at Zion National Park along the way.
### Ten to 12 Days Southern Arizona
This crazy-eight loop starts in Phoenix, where the multitude of posh spas, top museums and upscale dining and shopping options on offer will have you primed for exploring. Escape the urban crush with a long drive south on Hwy 85 to the lonely but rejuvenating Organ Pipe Cactus National Park. Hike, explore and relax for two days. From there, take Hwy 85 north to Hwy 86. Follow this lonely two-lane road east to lofty Kitt Peak National Observatory, site of 24 optical telescopes – the largest collection in the world. Take a tour or reserve a spot for nighttime stargazing.
Just northeast, laid-back Tucson is a pleasant place to chill out for a day or two. Indie shops line 4th Ave, and Congress St is the place to catch live music. Stop and smell the cacti in Saguaro National Park before spending the night in Benson, a good launchpad for the pristine Kartchner Caverns and the gloriously eclectic Singing Wind Bookshop. Wander the odd rock formations at Chiricahua National Monument then loop south on Hwys 191 and 181 for eye-catching galleries, great restaurants and an interesting mine tour in Bisbee. And you can't drive this far south without swinging by Tombstone for a reenactment of Wyatt and Doc's shootout with the Clantons. From Tombstone, Hwy 82 unfurls across sweeping grasslands, the horizon interrupted by scenic mountain ranges (known in these parts as sky islands).
Enjoy a day of wine-tasting in the villages of Sonoita and Elgin capped off with a slice of Elvis-inspired pizza in Patagonia. Close the loop with a swing back through Tucson on I-10 West, grabbing a Sonoran dog for the drive back to Phoenix.
### One Week Four Corners/Native American Journey
Start in Durango and spend a day exploring the historic mining town. The next day, ride the narrow-gauge railway to Silverton and quaff a beer at a Durango microbrewery on your return. Climb ladders into the haunting ruins at Mesa Verde National Park before heading to Arizona, stopping on the way at the recently revamped Four Corners Monument – check out that snazzy new plaza – to snap a cheesy picture with your hands and feet in four different states.
As you head into New Mexico, ogle Shiprock, a stunning, ragged red-rock formation. Spend the night at a motel in nearby Farmington or enjoy a snooze inside Kokopelli's Cave, a B&B room 70ft underground – complete with hot tub. A dusty, rutted drive leads to the isolated Chaco Culture National Historical Park, an amazing architectural sight. Stay near Window Rock, the capital of the Navajo Reservation, and be sure to check out the namesake rock. The old-world Hubbell Trading Post was the reservation's lifeline when it was established in the 1870s. Detour (65 miles each way) to Second Mesa, the heart of the Hopi Reservation, where you will find artisans and the Hopi Cultural Center.
Next up? The relatively verdant Canyon de Chelly National Monument, an inhabited, cultivated canyon with hogans and sheep herds. Remember to breathe as you approach the out-of-this-world beautiful Monument Valley. Drive the 17-mile loop around the towering buttes then spend the night at the adjacent View Hotel, you'll want to spend time – a lot of time – gaping at the monuments from your balcony. Finish the trip with a drive north to Mexican Hat in Utah – trust us, you can't miss it.
# Southwest USA Outdoors
Top of section
### Best Short Hikes to Big Views
South Kaibab Trail to Cedar Ridge South Rim, Grand Canyon National Park
Bright Angel Point Trail North Rim, Grand Canyon National Park
Angels Landing Zion National Park Mesa Arch Trail, Canyonlands National Park
Spider Rock Overlook Canyon de Chelly National Monument
### Best Wildlife Watching
Birds Patagonia-Sonoita Creek Preserve and Ramsey Canyon Preserve, Arizona
Elk Jemez Trail, Valles Caldera, New Mexico
Eagles Mesa Canyon near Durango, Colorado
Bears Gila National Forest, New Mexico and southern Colorado mountains
California condors Zion National Park and Vermilion Cliffs area, Arizona
### Best Water Activities
Splashing Beneath Havasu Falls, Havasupai Reservation, Arizona
Tubing On the Virgin River, Springdale, Utah
One-day rafting trip On the Rio Grande near Taos, New Mexico or the Colorado and Green Rivers in Moab, Utah
Multi-day rafting trip On the Colorado River through Grand Canyon National Park
Fly fishing Dolores, Colorado
The Southwest earns its reputation as the USA's land of adventure with a dizzying array of outdoor landscapes begging to be explored. Plunging canyons, lofty peaks, prickly deserts and red rock formations galore – with this embarrassment of riches it's hard to know where to start. Our advice? Pick one small pocket of the Southwest and get to know it well, rather than crisscrossing the region in search of the next best thing. Many of the towns and parks here are multisport destinations, and you get a different perspective depending on whether you travel by foot, bike, raft or skis.
### Hiking
#### Planning
It's always hiking season somewhere in the Southwest. When temperatures hit the 100s (about 40°C) in Phoenix, cooler mountain trails beckon in Utah and New Mexico. When highland paths are blanketed in snow, southern Arizona provides balmy weather. Parks near St George in southwestern Utah offer pleasant hiking possibilities well into midwinter. Of course, hardy and experienced backpackers can always don cross-country skis or snowshoes and head out for beautiful wintertime mountain treks.
More and more people venture further from their cars and into the wilds these days, so logistics isn't the only reason for careful planning. Some places cap the number of backpackers due to ecological sensitivity or limited facilities. Reservations are essential in highly visited areas such as the Grand Canyon (Click here) and during the busy spring and fall months in more seasonal areas like Canyonlands National Park (Click here). Consider going to the less heavily visited Bryce Canyon National Park (Click here) or Bureau of Land Management (BLM) lands and state parks, for a backpacking trip during busy months. Not only are they less restrictive than the national parks, but usually you can just show up and head out.
Backcountry areas are fragile and cannot support an inundation of human activity, especially when insensitive and careless. The key is to minimize your impact, leaving no trace of your visit and taking nothing but photographs and memories. To avoid erosion and damage, stay on main trails.
#### Safety
The climate is partly responsible for the epic nature of the Southwestern landscape. The weather is extraordinary in its unpredictability and sheer, pummeling force – from blazing sun to blinding blizzards and deadly flash floods. When there's too much water – the amounts necessary to scour slot canyons smooth – drownings can occur. Too little water combined with unforgiving heat leads to crippling dehydration (see Click here). A gallon (3.8L) of water per person per day is the recommended minimum in hot weather. Sun protection (brimmed hats, dark glasses and sunblock) is vital to a desert hiker. Know your limitations, pace yourself accordingly and be realistic about your abilities and interests.
Solo travelers should always let someone know where they are going and how long they plan to be gone. At the very least, use sign-in boards at trailheads or ranger stations. Travelers looking for hiking companions can inquire or post notices at ranger stations, outdoors stores, campgrounds and hostels.
### Mountain Biking & Cycling
As with hiking and backpacking, perfect cycling weather can be found at any time of year in different parts of the Southwest. Southern Arizona is a perfect winter destination; Tucson (Click here), considered a bicycle-friendly city, has many bike lanes and parks with bike trails. In spring and fall, Utah's Moab (Click here) is an incredibly popular destination for mountain bikers who want to spin their wheels on scenic slickrock trails.
In southern Colorado, the area around Durango has numerous trails (see Click here) as do Crested Butte (Click here) and the Four Corners area (see Click here). Hut-to-hut biking is also available in the San Juans (see Click here).
Local bike shops in all major and many minor cities rent bikes and provide maps and information. Visitor information offices and chambers of commerce usually have brochures with detailed trail maps. See Click here for info on rules, costs and so on.
The following are some additional choice mountain-biking spots.
#### Black Canyon of the Gunnison National Park
A dark, narrow gash above the Gunnison River leads down a 2000ft-deep chasm that's as eerie as it is spectacular. Head to the 6-mile-long South Rim Rd, which takes you to 11 overlooks. To challenge your senses, cycle along the smooth pavement running parallel to the rim.
The nearest town to this area is Montrose. For more info contact Black Canyon of the Gunnison National Park ( 970-249-1915; www.nps.gov/blca; 7-day admission per vehicle $15). See also Click here.
#### Carson National Forest
Carson contains an enormous network of mountain-bike and multiuse trails between Taos, Angel Fire and Picuris Peak. The nearest town is Taos (Click here), where you can rent bikes from Gearing Up Bicycle Shop ( 575-751-0365; www.gearingupbikes.com; 129 Paseo del Pueblo Sur; 9am-6:30pm) for $35 per day. For more info contact Carson National Forest ( 575-758-6200; www.fs.fed.us/r3/carson).
#### Kaibab National Forest
One of the premier mountain biking destinations in Arizona is the 800-plus-mile Arizona Trail. A popular section that's great for families is the Tusayan Bike Trail System (Click here). East of the town of Tusayan it's a pretty easy ride mostly on an old logging road that cuts through the Kaibab National Forest to the South Rim of the Grand Canyon. If you ride or walk the trail into the park, you've got to pay the $12 entrance fee that's good for seven days. For more info contact the Tusayan Ranger Station ( 928-638-2443; www.fs.fed.us/r3/kai).
#### NATIONAL PARKS & MONUMENTS
### PARK | ### FEATURES | ### ACTIVITIES | ### PAGE
---|---|---|---
Arches NP | sandstone arches, diverse geologic formations | hiking, camping, scenic drives | Click here
Black Canyon of the Gunnison NP | rugged deep canyon, ancient rocks | rock climbing, rafting, hiking, horseback riding | Click here
Bosque del Apache NWR | cottonwood forest along Rio Grande, abundant cranes & geese each winter | birding | Click here
Bryce Canyon NP | eroded hillsides, red & orange hoodoos & pillars | camping, hiking, scenic drives, stargazing, cross-country skiing | Click here
Canyon de Chelly NM | ancient cliff dwellings, canyons, cliffs | hiking and backpacking (guided only), horseback riding, scenic verlooks | Click here
Canyonlands NP | sandstone formations at confluence of Green & Colorado Rivers | rafting, camping, mountain biking, backpacking | Click here
Capitol Reef NP | buckled sandstone cliffs along the Waterpocket Fold | mountain biking, hiking, camping, wilderness, solitude | Click here
Carlsbad Caverns NP | underground cave system, limestone formations, bat flight in evening | ranger-led walks, spelunking (experienced only), backpacking | Click here
Dinosaur NM | fossil beds along Yampa & Green Rivers, dinosaur fossils & exhibits | hiking, scenic drives, camping, rafting | Click here
Grand Canyon NP | canyon scenery, geologic record, remote wilderness, condors | rafting, hiking, camping, mountain biking, road cycling | Click here
Grand Staircase-Escalante NM | desert wilderness, mountains, canyons, wildlife | mountain biking, hiking, camping, solitude | Click here
Great Basin NP | desert mountains, canyons, wildlife, fall colors | hiking, camping | Click here
Mesa Verde NP | Ancestral Puebloan sites | hiking, cross-country skiing | Click here
Monument Valley Navajo Tribal Park | desert basin with sandstone pillars & buttes | scenic drive, guided tours, horseback riding | Click here
Natural Bridges NM | premier examples of stone architecture | hiking, camping, sightseeing | Click here
Organ Pipe Cactus NM | Sonoran Desert, cactus bloom May & Jun | cactus viewing, scenic drives, mountain biking | Click here
Petrified Forest NP | Painted Desert, fossilized logs | scenic drives, backcountry hiking | Click here
Red Rock Canyon NCA | unique geologic features close to Las Vegas, waterfalls | scenic drives, hiking, rock climbing | Click here
Saguaro NP | desert slopes, giant saguaro, wildflowers, Gila woodpeckers, wildlife | cactus viewing, hiking, camping | Click here
San Pedro Riparian NCA | 40 miles of protected river habitats | birding, picnicking, fishing, horseback riding | Click here
Sunset Crater Volcano NM | dramatic volcanic landscape | hiking, sightseeing | Click here
White Sands NM | white sand dunes, specially adapted plants & animals | scenic drives, limited hiking, moonlight bicycle tours, range of walks | Click here
Zion NP | sandstone canyons, high mesas | hiking, camping, scenic drives, backpacking, rock climbing | Click here
NP – National Park; NM – National Monument; NCA – National Conservation Area; NWR – National Wildlife Refuge
#### Moab
Bikers from around the world come to pedal the steep slickrock trails and challenging 4WD roads winding through woods and into canyon country around Moab (Click here). The legendary Slickrock Trail is for experts only. This 12.7-mile, half-day loop will kick your butt. Intermediate riders can learn to ride slickrock on Klondike Bluffs Trail, a 15.6-mile round-trip that passes dinosaur tracks. For a family-friendly ride, try the 8-mile Bar-M Loop.
Full-suspension bikes start at around $43 a day at Rim Cyclery ( 435-259-5333; www.rimcyclery.com; 94 W 100 N, Moab) – check out its museum.
Visit www.go-utah.com/Moab/Biking and www.discovermoab.com/biking.htm for excellent Moab biking info. Both have loads of easy-to-access pictures, ratings and descriptions about specific trails.
### Snow Sports
All five states offer snow sports on some level. Yes, you can even ski in Arizona. Southwestern Colorado is riddled with fabulous ski resorts, while the Lake Tahoe area reigns in Nevada. In New Mexico head to the steeps at Taos and in Utah the resorts outside Salt Lake City – they were worthy of hosting the Winter Olympic Games!
#### Downhill Skiing & Snowboarding
Endless vistas, blood-curdling chutes, sweet glades and ricocheting half-pipes: downhill skiing and boarding are epic, whether you're hitting fancy resorts or local haunts. The season lasts from late November to April, depending on where you are.
Salt Lake City and nearby towns hosted the 2002 Winter Olympics, and have riproaring routes to test your metal edges. Slopes are not crowded at Snowbasin (Click here), where the Olympic downhill races were held. The terrain here is, in turns, gentle and ultra-yikes. Nearby Alta (Click here) is the quintessential Utah ski experience: unpretentious and packed with powder fields, gullies, chutes and glades.
New Mexico's Taos Ski Valley (Click here) is easily one of the most challenging mountains in the US, while the Santa Fe ski area (Click here), just 15 miles outside town, allows you the chance to ski in the morning and shop Canyon Rd galleries come afternoon.
### ACCESSIBLE ADVENTURES
If you're disabled but want to run white water, canoe, rock climb or Nordic ski, head to Salt Lake City–based Splore (www.splore.org), which runs outdoor trips in the area. For outdoor fun in Arizona, check out Accessing Arizona (www.accessingarizona.com).
In Colorado you'll want to head to Telluride (Click here) or Crested Butte (Click here). For extreme skiing, try Silverton (Click here). All three are wonderfully laid-back old mining towns turned ski towns, offering the opportunity to ride some of the best powder in the state by day, then chill in some of the coolest old saloons at night. For something completely local and low-key, check out family-run Wolf Creek (Click here). For more details about where to ride powder in the state visit www.coloradoski.com. The website lists 'ski and stay' specials and provides resort details and snow reports.
The Lake Tahoe area, straddling the Nevada–California border, is home to nearly a dozen ski and snowboard resorts. See Click here for more.
And then there's Arizona. Yes, you can ski. The snow isn't anything to write home about, but the novelty value may be. Head to the Arizona Snowbowl (Click here) outside Flagstaff.
Ski areas generally have full resort amenities, including lessons and equipment rentals (although renting in nearby towns can be cheaper). Got kids? Don't leave them at home when you can stash them at ski school for a day. For 'ski, fly and stay' deals check out web consolidators and the ski areas' own websites.
#### Cross-Country & Backcountry Skiing
Backcountry and telemark skiing are joining cross-country skiing and snowshoeing as alternative ways to explore the untamed Southwestern terrain.
A must-ski for cross-country aficionados? Utah's serene Soldier Hollow (Click here), which was the Nordic course used in the 2002 Winter Olympics. It's accessible to all skill levels.
The North and South Rims of the Grand Canyon both boast cross-country trails. The North Rim is much more remote. On the south side, you'll find several trails of easy to medium difficulty groomed and signed within the Kaibab National Forest (Click here).
### FLASH FLOODS: A DEADLY DESERT DANGER
Flash floods, which occur when large amounts of rain fall suddenly and quickly, are most common during the 'monsoon months' from mid-July to early September, but heavy precipitation in late winter can also cause these floods. They occur with little warning and reach a raging peak in minutes. Rainfall occurring miles away is funneled from the surrounding mountains into a normally dry wash or canyon and a wall of water several feet high can appear seemingly out of nowhere. There are rarely warning signs – perhaps you'll see some distant rain clouds – but if you see a flash flood coming, the only recommendation is to reach higher ground as quickly as possible.
Floods carry a battering mixture of rocks and trees and can be extremely dangerous. A swiftly moving wall of water is much stronger than it appears; at only a foot high, it will easily knock over a strong adult. A 2ft-high flood sweeps away vehicles.
Heed local warnings and weather forecasts, especially during the monsoon season. Avoid camping in sandy washes and canyon bottoms, which are the likeliest spots for flash floods. Campers and hikers are not the only potential victims; every year foolhardy drivers driving across flooded roads are swept away. Flash floods usually subside fairly quickly. A road that is closed will often be passable later on the same day.
The San Juan Hut Systems (see Click here) consist of a great series of shelters along a 60-mile route in Colorado from Telluride to Ouray – the scenery is fantastic.
### Rock Climbing
If Dr Seuss had designed a rock-climbing playground, it would look a lot like the Southwest: a surreal landscape filled with enormous blobs, spires, blobs on spires and soaring cliffs. While southern Utah seems to have the market cornered on rock climbing, the rest of the region isn't too shabby when it comes to the vertical scene. Just keep an eye on the thermometer – those rocks can really sizzle during summer. Help keep climbing spaces open by respecting access restrictions, whether they are set by landowners harried by loud louts or because of endangered, cliff-dwelling birds that need space and silence during nesting season.
Southwestern Utah's Snow Canyon State Park (Click here) offers more than 150 bolted and sport routes. Zion Canyon has some of the most famous big-wall climbs in the country, including Moonlight Buttress, Prodigal Son, Touchstone and Space Shot. In southeastern Utah, Moab (Click here) and Indian Creek (Click here) make awesome destinations.
Otherwise, make a swift approach to central Arizona's Granite Mountain Wilderness, which attracts rock climbers in warmer months. Pack your rack for the rocky reaches of Taos Ski Valley (Click here) or pack your picks for the Ouray Ice Park (Click here), where a 2-mile stretch of the Uncompahgre Gorge has become world renowned for its sublime ice formations. Chicks with Picks ( 970-316-1403, office 970-626-4424; www.chickswithpicks.net; 163 County Rd 12; prices vary) makes it easy for women to get involved too.
### Caving & Canyoneering
Much of the Southwest's most stunning beauty is out of sight, sitting below the earth's surface in serpentine corridors of stone that make up miles of canyons and caves. Visit Carlsbad Caverns National Park (Click here) and not only will you feel swallowed whole by the planet, you'll be amply rewarded with a bejeweled trove of glistening, colorful formations.
### TOP SPOTS FOR WHITE WATER RAFTING
Grand Canyon National Park (Click here) Arizona
Cataract Canyon (Click here) Moab, Utah
Westwater Canyon (Click here) Moab, Utah
Taos Box (Click here) Pilar, New Mexico
Animas River (Click here) Durango, Colorado
Canyoneering adventures vary from pleasant day hikes to multiday technical climbing excursions. Longer trips may involve technical rock climbing, swimming across pools, shooting down waterfalls and camping. Many experienced canyoneers bring inflatable mattresses to float their backpacks and sleep on.
### DIVING
If you're into diving, check out Blue Hole (www.santarosanm.org) near Santa Rosa, NM. It has an 81ft-deep artsesian well; blue water leads into a 131ft-long submerged cavern.
Arizona and Utah offer some of the best canyoneering anywhere. The first canyoneers in the huge gashes of the Colorado Plateau were Native Americans, whose abandoned cliff dwellings and artifacts mark their passage. See for yourself at the many-fingered Canyon de Chelly (Click here), which is accessible with a Navajo guide intimately familiar with its deep mazes.
The Grand Canyon (Click here) is the mother of all canyoneering experiences, attracting thousands to its jaw-dropping vistas.
Then there are slot canyons, hundreds of feet deep and only a few feet wide. These must be negotiated during dry months because of the risk of deadly flash floods. Always check with the appropriate rangers for weather and safety information. The Paria Canyon (Click here), carved by a tributary of the Colorado River on the Arizona–Utah border, includes the amazing Buckskin Gulch, a 12-mile-long canyon, hundreds of feet deep and only 15ft wide for most of its length. Perhaps the bestknown (though now highly commercialized) slot canyon is Antelope Canyon (Click here), near Lake Powell. You can also drive through magical Oak Creek Canyon (Click here), with dramatic red, orange and white cliffs sweetened with aromatic pine. A nimbus of giant cottonwoods crowd the creek.
Zion National Park (Click here) offers dozens of canyoneering experiences for day hikers and extreme adventurers, with weeping rocks, tiny grottoes, hanging gardens and majestic, towering walls.
#### HORSEBACK RIDING
### WHERE | ### WHAT | ### INFORMATION
---|---|---
Southern AZ dude ranches | cowboy up in Old West country; most ranches closed in summer due to the heat | www.azdra.com
Grand Canyon South Rim, AZ | low-key trips through Kaibab National Forest; campfire ride | www.apachestables.com
Santa Fe, NM | themed trail rides; sunsets | www.bishopslodge.com
Telluride, CO | all-season rides in the hills | www.ridewithroudy.com
Durango, CO | day rides and overnight camping in the Weminuche Wilderness | www.vallecitolakeoutfitter.com
### Water Sports
Water in the desert? You betcha. In fact, few places in the US offer as much watery diversity as the Southwest. Bronco-busting rivers share the territory with enormous lakes and sweet trickles that open into great escapes.
#### Boating
Near the California–Arizona state line, a series of dammed lakes on the lower Colorado River is thronged with boaters year-round. Area marinas rent canoes, fishing boats, speedboats, water-skiing boats, jet skis and windsurfers. On the biggest lakes – especially Arizona's Lake Powell (Click here) in the Glen Canyon National Recreation Area near the Grand Canyon and Lake Mead (Click here) in the Lake Mead National Recreation Area near Las Vegas – houseboat rentals sleep six to 12 people and allow exploration of remote areas difficult to reach on foot.
The thrill of speed mixed with alcohol makes popular houseboat areas dangerous for kayakers and canoeists. If you're renting a big rig, take the same care with alcohol as you would when driving a car. Travel at a speed that is safe based on the conditions, which include the amount of traffic on the water and the likelihood of underwater hazards (more common when water levels drop). Carbon monoxide emitted by houseboat engines is a recently recognized threat. Colorless and odorless, the deadly gas is heavier than air and gathers at water level, creating dangerous conditions for swimmers and boaters. In recent years, several swimmers have drowned after being overcome by carbon monoxide.
### RANKING RAPIDS
White-water rapids are rated on a class scale of I to V, with Class V being the wildest and Class I being nearly flat water. Most beginner trips take rafters on Class III rivers, which means you'll experience big rolling waves and some bumps along the way, but nothing super technical. In Class IV water you can expect to find short drops, big holes (meaning giant waves) and stronger undertows, making it a bit rougher if you get thrown off the boat. Class V rapids are the baddest of all and should only be attempted by strong swimmers with previous white-water experience – you should expect to be thrown out of the boat and perhaps sucked under for a few moments. You'll need to know what to do and not panic.
Tip: if you do get thrown, float through the rapid, lying on your back – your life vest will keep you afloat. Point your feet downriver and keep your toes up. Protect your head and neck with your arms (don't leave them loose or they can get caught in rocks).
Of course the difficulty of the rafting will depend a lot on the kind of trip you're on – it's much harder to kayak a Class V rapid than it is to ride it out in a motorized pontoon boat or even in a boat being oared by a professional. If you aren't a world-class kayaker, but want more interaction beyond being rowed down the river, try a paddle trip. On these, each person in the boat paddles, following the directions shouted by the experienced guide at the helm of the ship.
The I to V class system applies to all Southwestern rivers except for a portion of one. The part of the Colorado River running through the Grand Canyon is just too wild to play by traditional rules and requires its own scale system – from Class I to Class X – to classify its 160-plus rapids. Many of the Grand's rapids are ranked Class V or higher; two merit a perfect 10.
#### Swimming & Tubing
Most lakes and many reservoirs in the Southwest allow swimmers. The exception will be high-traffic areas of the bigger lakes, where swimming is very dangerous due to the number of motorboats. It's not unusual to see locals swimming in rivers during the hot summer months, and tubing on creeks throughout the Southwest is popular. If you happen to see a bunch of people riding down a creek, and wish to join, just ask where they go for their tires – where there's tubing in this region there is usually an entrepreneur renting tubes from a van in the nearest parking lot. Swimming in lakes and rivers is generally free but if you are in a state or national park, or on a reservoir you may have to pay an entrance fee to enter the property itself.
### Golfing
With more than 300 golf courses, Arizona is ranked the number-one golf destination in North America by the International Association of Golf Tour Operators. The state has some of the top golf resorts in the country, with the best ones designed by famous pros. Just about every sizable town in Arizona has a course and the bigger cities have dozens, a few of which are listed in this book. The Phoenix area alone has about 200.
In many desert areas, golf courses are viewed as welcome grassy amenities that also bring in tourist dollars, but this comes at a high price – the courses need lots of water, and conservationists decry the use of this most precious of desert resources for entertainment. In 2010 about 15% of the state's courses were considered at-risk because of a dip in tourism, increased competition and higher costs for water and labor.
Golf is also expensive for players. Some courses don't allow golfers to walk from hole to hole. A round of 18 holes on the best courses, often in upscale resorts that specialize in golf vacations, can cost hundreds of dollars (including use of a golf cart) during the balmy days of a southern Arizona winter. In the heat of summer, rates can drop to under $100 for the same resort. If you don't have that kind of money, try the public city courses where rounds are more reasonable. Several Phoenix city courses charge less than $50 for 18 holes in winter.
# travel with children
Top of section
### Best Regions for Kids
#### Arizona
Outdoorsy families can hike Grand Canyon trails and ponder the cacti outside Tucson. Water parks lure kiddies to Phoenix, while dude ranches, ghost towns and cliff dwellings are only a scenic drive away.
#### New Mexico
Swoop up a mountain on the Sandia Peak Tramway, drop into Carlsbad Caverns or scramble to the Gila Cliff Dwellings.
#### Utah
National parks in Utah sprawl across swaths of red rock country, offering fantastic hiking, biking and rafting. In the mountains, skis, alpine slides or snow tubes are equally fun.
#### Southwestern Colorado
Chug through the San Juans on a historic steam train, relax in Ouray's hot springs or take your pick of adventures - hiking, fishing, skiing - in low-key Telluride.
#### Las Vegas & Nevada
Children are not allowed in the gaming areas, but roller coasters and animal exhibits cater to the kiddies. For outdoor adventure, head to Great Basin National Park or Valley of Fire State Park.
### Southwest USA for Kids
The Southwest is a great place to travel with kids. Yes, the long drives, unforgiving desert landscapes and oppressive summer heat can be daunting, but the rewards for families far outweigh the challenges. These rewards can be found in the most mundane of activities – an afternoon splashing in a creek in New Mexico's Jemez Mountains (Click here), picnicking on the edge of the Grand Canyon in Kaibab National Forest (Click here), watching an old Western on the big screen at Parry Lodge's Old Barn Playhouse (Click here) in Kanab, UT. To make it even more enticing, the region's geology, human history and wildlife, accessible in concrete ways at every turn, make the Southwest as educational as it is fun – kids learn without even trying.
#### Lodging
Most hotels and motels offer cribs and rollaway beds, sometimes for a minimal fee. Ask about bed configurations, suites, adjoining rooms and rooms with microwaves or refrigerators. While many hotels allow children to stay free with adults, some can charge as much as $90 extra per night – always ask.
Full-scale resorts with kids' programs, lovely grounds, full service and in-house baby sitting can be found throughout the region, but particularly in Phoenix and, to a lesser degree, Tucson. There are far fewer resorts in New Mexico – try Bishop's Lodge Resort & Spa (Click here) in Santa Fe and the Native American–owned Hyatt Tamaya (Click here), on the Santa Ana Pueblo, just north of Albuquerque. For the real Western-immersion cowboy experience, complete with trail rides through the chamisa, cattle wrangling and beans 'n' corn bread round the fire, consider a stay at a dude ranch, such as the Flying E Ranch (Click here) in Wickenburg, AZ.
If it's late, you're tired and you don't want any surprises, head to a chain motel. Hilton perches at the high end of the scale, while Motel 6 and Super 8, usually the least expensive, offer minimal services, and Best Western is notoriously inconsistent. Your best bets are Holiday Inn Express and Fairfield Inn & Suites.
Finally, even the most novice campers will find beautiful campsites in national and state forests and parks throughout the region to be perfect for car-camping. You can't beat the flexibility and price, and kids love it.
#### Dining
While the Southwest offers the usual fast-food suspects, you may find yourself driving mile after mile, hour after hour without a neon-lit fast-food joint anywhere. Be prepared with snacks and, if appropriate, a cooler packed with picnic items. Many lodgings offer free breakfast.
Don't sacrifice a good meal or attractive ambience because you have kids. All but a handful of upscale restaurants welcome families and many provide crayons and children's menus. To avoid the dilemma of yet another fried meal, ubiquitous on kids' menus, simply ask for small adaptations to the standard menu, such as grilled chicken with no sauce, a side of steamed vegetables or rice with soy sauce.
### Children's Highlights
#### Outdoor Adventure
»Explore Grand Canyon National Park in Arizona.
»Ride the range at a Wickenburg dude ranch in southern Arizona.
»Chug into the San Juan Mountains on the Durango & Silverton Narrow Gauge Railroad in Colorado.
»Ride horses at Ghost Ranch in New Mexico.
»Ski the slopes at Wolf Mountain in Utah.
#### Theme Parks & Museums
»Relive the rootin', tootin' Old West with gold panning, burro rides and shoot-outs at Rawhide Western Town & Steakhouse in Mesa, AZ.
»Take in coyotes, cacti and demos at the Arizona-Sonora Desert Museum.
»Check out the Hall of Jurassic Supergiants at the Museum of Natural History & Science in Albuquerque, AZ.
»Visit with local artists and scientists at the Santa Fe Children's Museum in New Mexico.
»Have fun at Thanksgiving Point in Salt Lake City, UT, which has 55 acres of gardens, a petting farm, a movie theater and golf.
#### Wacky Attractions
»Get close to the begging burros that loiter in the middle of downtown Oatman, AZ.
»Marvel at the fake dinosaurs and mummified bobcats at Grand Canyon Caverns in Arizona – Route 66 kitsch at its best.
»Gaze at the world's most comprehensive collection of rattlesnake species at the Rattlesnake Museum in Albuquerque, AZ.
»Discover the truth, and lots of wild theories, at the International UFO Museum & Research Center in Roswell, NM.
»Visit Mexican Hat in Utah – hey, that rock looks like a sombrero!
#### Native American Sites
»Climb four ladders to a ceremonial cave that combines education with adventure at Bandelier National Monument in New Mexico.
»Explore ancient living history inside Taos Pueblo, NM, a multistory pueblo village dating to the 1400s.
»Discover Acoma Pueblo in New Mexico, also known as Sky City, which sits atop a mesa 7000ft above sea level.
»Climb into cliff dwellings in Mesa Verde National Park in southwestern Colorado for hands-on learning at its best.
»Match the names to the butte – Mittens, Eagle Rock – at Monument Valley Navajo Tribal Park in Arizona.
### Transportation
#### Car Seat Laws
Child restraint laws vary by state and are subject to change. The requirements should be checked before departure. Currently, Arizona law states that children under the age of five must be properly secured in a child-restraint device. Children five to eight years old are not required to use safety seats, but a federal car-safety board has asked the state to consider tightening its requirements. The website for the Arizona Governor's office (www.azgohs.gov/transportation-safety) provides booster-seat specifics. Children between five and 15 must wear a seatbelt if sitting in the front seat
In Colorado, infants under the age of one year and weighing less than 20lbs must be in a rear-facing infant seat, children aged one to three years and between 20lbs and 40lbs must be in a car seat and four- to seven-year-olds must use a booster. Nevada requires children five and under, and those weighing less than 80lbs, to use a booster. In New Mexico, infants under one year must be restrained in a rear-facing infant seat, children aged one to four or weighing less than 40lbs must use a car seat, and five- and six-year-olds and kids weighing less than 60lbs must use a booster. Utah law requires children under eight years old or shorter than 57in to sit in a car seat or booster; children who are not yet eight but are 57in or taller can use the car seat belt alone.
Most car-rental agencies rent rear-facing car seats (for infants under one), forward facing seats (from one to four years old or up to a certain height/weight) and boosters for $11 per day, but you must reserve these in advance. Clarify the type of seat when you make the reservation as each is suitable for specified ages and weights only.
#### Flying
Children under two fly free on most airlines when sitting on a parent's lap. Remember to bring a copy of your child's birth certificate – if the airline asks for it and you don't have it, you won't be able to board. Ask about children's fares, and reserve seats together in advance. Other passengers have no obli gation to switch seats and sometimes have no qualms about refusing to do so. Southwest Airlines' open seating policy helps avoid this.
### Planning
#### Planning Ahead
Perhaps the most difficult part of a family trip to this region will be deciding where to go and avoiding the temptation to squeeze in too much. Distances are deceptive and any one state could easily fill the standard two-week family vacation. Choose a handful of primary destinations, such as major cities, national parks and centers for outdoor recreation, to serve as the backbone of your trip. Then sit down with the map and connect these dots with a flexible driving plan.
### HELPFUL RESOURCES FOR FAMILIES
GrandCanyon.org (www.grandcanyon.org) Excellent listing of regionally focused children's books.
Kids in Vegas (www.kidsinvegas.com) A complete listing of kid friendly places in Las Vegas.
Family Travel Files (www.thefamilytravelfiles.com) Ready-made vacation ideas, destination profiles and travel tips.
Kids.gov (www.kids.gov) Eclectic, enormous national resource; download songs and activities, or even link to the CIA Kids' Page.
For all-around information and advice, check out Lonely Planet's _Travel with Children_. For outdoor advice, read _Kids in the Wild: A Family Guide to Outdoor Recreation_ by Cindy Ross and Todd Gladfelter, and Alice Cary's _Parents' Guide to Hiking & Camping_.
Book rooms at the major destinations and make advance reservations for horseback rides, rafting trips, scenic train rides and educational programs or camps, but allow a couple of days between each to follow your fancy.
Throughout this book, we've used the child-friendly icon ( ) to indicate attractions and sleeping and eating options that are geared toward families. This helps make planning your trip a cinch.
#### What to Bring
If you plan on hiking, you'll want a front baby carrier or a backpack with a built-in shade top. These can be purchased or rented from outfitters throughout the region (see listings in regional chapters). Older kids need sturdy shoes and, for playing in streams, water sandals.
Other things you'll want to include are towels, rain gear, a snuggly fleece or heavy sweater (even in summer, desert nights can be cold – if you're camping, bring hats) and bug repellent. To avoid children's angst at sleeping in new places and to minimize concerns about bed configurations, bring a Pack N Play – or a similar travel playpen/bed – for infants and sleeping bags for older children.
# regions at a glance
Top of section
Scenic as a road trip may be, we don't advise spending the whole trip in the car. Las Vegas is decidedly offbeat and works best for travelers interested in nightlife, dining and adult-oriented fun. Arizona offers nightlife and culture in Phoenix, but the state earns bragging rights at the Grand Canyon. Its mining towns and Native American sites are also a draw, attracting cultural explorers to the deserts and mountains. New Mexico unfurls the red carpet for artists, but its chile-infused cuisine and Pueblo culture lure crowds too. Peak baggers and cyclists love Colorado's lofty San Juan Mountains, while Mesa Verde wins praise from history buffs. Utah closes the book with swooping red-rock style and delicate natural grace.
### Las Vegas & Nevada
Nightlife
Dining
Off beat
###### CASINOS
The flashy casinos on the Las Vegas Strip are self contained party caves where you can hold 'em, fold 'em, sip cocktails, shake your booty and watch contortionists and comedians.
###### CORNUCOPIAS
In Vegas, food is about both quantity and quality. Stretch your budget and your waistline at the ubiquitous buffets or dine like royalty at a chef-driven sanctuary.
###### OUT THERE
From Hwy 50 (the Loneliest Rd) to Hwy 375 (the Extraterrestrial Hwy), Nevada is wild and wacky. Caravan to the Black Rock Desert in September for Burning Man, a conflagration of self-expression.
Click here
### Arizona
Culture
Adventure
Scenery
###### NATIVE AMERICANS
The history and art of the Native American tribes make Arizona unique. From craftwork to cliff dwellings to sprawling reservations, tribal traditions flourish across the state.
###### HIKING & RAFTING
Want to take it easy? Hike a desert interpretative trail or kayak a manmade lake. To ramp it up, head to canyon country to clamber over red rocks or swoosh over white-capped rapids.
###### CANYONS & ARCHES
After the continents collided, Mother Nature got involved with the decorating. Crumbly hoodoos, swooping spans, glowing buttes and crimson ridges –got batteries for the camera?
Click here
### New Mexico
Art
Culture
Food.
###### SANTA FE
Vendors on the Plaza. The galleries of Canyon Rd. Studio tours. The Georgia O'Keeffe Museum. The city itself is a living work of art, framed by mountains and crisp blue skies.
###### PUEBLOS
Nineteen Native American pueblos are clustered in the western and northcentral regions of the state. They share similarities, but their histories, customs and craftwork are distinctly fascinating.
###### RED & GREEN
New Mexican food comes with a chileinfused twist. Red, green – they're not just for salsas but are an integral part of the whole. Pinto beans. Posole. Carne adobada (marinated pork chunks). Isn't this why you're here?
Click here
### Southwestern Colorado
Adventure
Scenery
History
###### TRACKS & RACKS
You got stuff? Skis, snowboards, bikes, fishing poles? Then start unpacking. The San Juan Mountains are a primo place to empty your stuff racks and dirty up your gear
###### PEAKS & PONDEROSAS
When it comes to alpine scenery in the US, few places are more sublime than the San Juan Skyway: craggy peaks, steep canyons and glorious meadows. Just don't drive off the road.
###### HOLES IN THE ROCK
The Mesa Verde cliff dwellings offer a fascinating glimpse into the lives of the ancient Puebloans. Up in the San Juan Mountains, the mining past is recalled in Victorian homes and the abandoned claims.
Click here
### Utah
Outdoors
Ancient Sites
History
###### ROMPING ROOM
When it comes to all-natural playgrounds, Utah takes the lead. From tightly run national parks to empty Bureau of Land Management (BLM) expanses, the place is ready-made for adventure – usually with a sandstone backdrop.
###### ROCK ON
Dinosaurs roamed the earth and trilobites swam the seas, leaving footprints and fossils as calling cards. Elsewhere, cliffdwellings and rock art remind us we weren't the first inhabitants
###### MORMONS
The Mormons arrived in the 1840s, building temples, streets, farms and communities. Get some background at Temple Square in Salt Lake City, then explore.
Click here
### On the Road
###
**LAS VEGAS & NEVADA**
LAS VEGAS
AROUND LAS VEGAS
Red Rock Canyon
Lake Mead & Hoover Dam
Mt Charleston
GREAT BASIN
Along Hwy 95
Along Hwy 93
Along Hwy 50
Along I-80
RENO-TAHOE AREA
Reno
Carson City
Virginia City
Genoa
Black Rock Desert
Lake Tahoe
**ARIZONA**
GREATER PHOENIX
CENTRAL ARIZONA
Verde Valley & Around
Hwy 87: Payson & Mogollon Rim
Wickenburg
Prescott
Jerome
Cottonwood
Sedona
Oak Creek Canyon
Flagstaff
GRAND CANYON REGION
Grand Canyon National Park – South Rim
Tusayan
Williams
Havasupai Reservation
Hualapai Reservation & Skywalk
Grand Canyon National Park – North Rim
Arizona Strip
Page & Glen Canyon National Recreation Area
NAVAJO RESERVATION
Tuba City & Moenkopi
Kayenta
Monument Valley Navajo Tribal Park
Canyon de Chelly National Monument
HOPI RESERVATION
WESTERN ARIZONA
Bullhead City & Laughlin
Route 66: Topock to Kingman
Route 66: Kingman to Williams
Lake Havasu City
Parker
Yuma
SOUTHERN ARIZONA
Tucson
Tucson to Phoenix
Patagonia & the Mountain Empire
Sierra Vista & Around
Tombstone
Bisbee
Chiricahua National Monument
Benson & Around
EASTERN ARIZONA
Winslow
Holbrook to New Mexico
**NEW MEXICO**
ALBUQUERQUE
ALBUQUERQUE TO SANTA FE
Along I-25
Turquoise Trail
SANTA FE
AROUND SANTA FE
Los Alamos
Bandelier National Monument
Española
Abiquiú
TAOS
AROUND TAOS
Taos Ski Valley
Enchanted Circle
MORA VALLEY & NORTHEASTERN NEW MEXICO
Raton & Around
Las Vegas & Around
CHACO CANYON & NORTHWESTERN NEW MEXICO
Chama
Navajo Dam
Farmington & Around
Gallup
Scenic Route 53
Grants
SILVER CITY & SOUTHWESTERN NEW MEXICO
Socorro
Truth or Consequences & Around
Silver City & Around
Gila National Forest
Deming & Around
Las Cruces & Around
CARLSBAD CAVERNS & SOUTHEASTERN NEW MEXICO
White Sands National Monument
Alamogordo & Around
Cloudcroft & Around
Ruidoso & Around
Lincoln
Roswell
Carlsbad
Carlsbad Caverns National Park
I-40 EAST TO TEXAS
Santa Rosa
Tucumcari
Fort Sumner
**SOUTHWESTERN COLORADO**
Pagosa Springs & Around
Durango
Mancos
Mesa Verde National Park
Cortez
Dolores
Telluride
Ridgway
Ouray & the Million Dollar Hwy
Silverton
Black Canyon of the Gunnison National Park
Crested Butte
**UTAH**
MOAB & SOUTHEASTERN UTAH
Bluff
Monument Valley
Natural Bridges National Monument
Monticello
Canyonlands National Park
Moab
Arches National Park
Green River
Glen Canyon National Recreation Area & Lake Powell
ZION & SOUTHWESTERN UTAH
Capitol Reef National Park
Torrey
Boulder
Escalante
Grand Staircase-Escalante National Monument
Bryce Canyon National Park & Around
Panguitch
Hwy 89 – Panguitch to Kanab
Kanab
Zion National Park
Springdale
Cedar City
St George
SALT LAKE REGION
Salt Lake City
Brigham City & Around
Logan & Around
WASATCH MOUNTAINS
Salt Lake City Resorts
Park City
Ogden & Around
Heber City & Midway
Sundance Resort
Provo
NORTHEASTERN UTAH
Vernal & Around
Dinosaur National Monument
Flaming Gorge National Recreation Area
Price & San Rafael Swell
Top of section
# Las Vegas & Nevada
**Includes »**
Las Vegas
Red Rock Canyon
Lake Mead & Hoover Dam
Mt Charleston
Great Basin
Along Hwy 50
Along I-80
Reno
Carson City
Virginia City
Lake Tahoe
### Why Go?
Ski boots, high heels, flip flops, golf cleats, cowboy boots: when you come to Nevada, none of these would look out of place. Mysterious and misunderstood, Nevada's a paradox, which makes packing tricky. Expect thrills aplenty, whether you're a nightclub aficionado, an adventure junkie, a kitsch connoisseur or a conspiracy theorist.
If you're in the mood for extremes, you're in the right place. Rural brothels and hole-in-the wall casinos sit side-by-side with Mormon churches and Basque cowboy culture. The Wild West lives on in old silver mining towns, while Vegas offers up its own brand of modern day lawlessness. Piercing blue lakes and snowy mountains in the Reno–Tahoe area seem a world away from the open vistas of Great Basin and the lonely curves of Highway 50, where fighter jets whiz overhead at the speed of light...or was that an alien ship?
Whether Nevada delights, excites, intrigues or confounds you (and possibly all at once!) you just can't say it's not interesting.
### When to Go?
Apr–MaySouthern parts of the state are balmy by day and pleasantly cool at night.
Dec Las Vegas deals in excess, and they don't go more buck wild than at Christmas.
Jun–Aug Yes, it's hot. Yet low season in Vegas means awesome hotel deals.
### Best Places to Eat
»Wicked Spoon Buffet (Click here)
»DOCG Enoteca (Click here)
»L'Atelier de Joël Robuchon (Click here)
»Firefly (Click here)
»Old Granite Street Eatery (Click here)
### Best Places to Stay
»Encore (Click here)
»Hard Rock (Click here)
»Golden Nugget (Click here)
»Peppermill (Click here)
»Tropicana (Click here)
### Vegas Planning
Planning a Vegas trip can be strangely counterintuitive, because Vegas refuses to play by the rules of most cities. First off: though parking is widely free, it's not time or cost-effective to rent a car unless you'll be doing a lot of day trips. Stick to taxis, walking and the good bus/monorail system while you're exploring the city. Dinner reservations are often necessary; note that many high-end restaurants, bars and nightclubs enforce a dress code.
### DON'T MISS
Even if late nights, gambling and neon aren't your style, cut loose and cruise Las Vegas' infamous Strip for at least a day or two: chill out poolside at a 4-star resort, hit the clubs, and splurge on steak and martinis in Rat Pack style. While you're there, don't miss a Cirque du Soleil show.
In a state known for lovably bizarre small towns, the prize for the most unique is a toss-up between Virginia City, where the gold rush and the Wild West live on, or spirited Elko, with its Basque restaurants and cowboy poetry festival.
For unmatched outdoor bliss, Lake Tahoe offers fairytale ski slopes come winter and pristine summer beaches. If untamed wilderness strikes your fancy, you'll want to get lost in the vast Great Basin National Park or brave the eerily deserted US Hwy 50, nicknamed the 'Loneliest Road in America.'
Finally, the hottest place in Nevada is also home to one of the Southwest's most unique yearly events: the Burning Man festival, where iconoclasts, rebels, artists, soul-seekers and the irrepressibly curious celebrate and create in the shimmering heat of the Black Rock Desert.
### Tips for Drivers
»Most drivers speed across Nevada on interstate highways I-80 or I-15.
»It takes less than two hours to drive 125 miles from Primm, on the California state line, to Mesquite near the Utah border via I-15; the best overnight stop along this route is Las Vegas.
»When driving across the state on I-80, Winnemucca and Elko are the most interesting places to pull off for a night's sleep.
»Note that US Hwy 95 may be the quickest route between Las Vegas and Reno, but it's still a full day's drive without much to see or do along the way.
»For road conditions, call 877-687-6237 or visit www.nvroads.com.
### TIME ZONE
Nevada is in the Pacific Time Zone.
### Fast Facts
»Nevada population: 2.7 million
»Area: 109,800 sq miles
»Sales tax: 6.85%
»Las Vegas to Grand Canyon, AZ: 275 miles, 4½ hours
### Resources
»Nevada Commission on Tourism ( 800-638-2328; www.travelnevada.com)
»Las Vegas Convention & Visitors Authority (www.visitlasvegas.com)
»VEGAS.com (www.vegas.com)
»Cheapo Vegas (www.cheapovegas.com)
### Las Vegas & Nevada Highlights
Kicking back in Hollywood languor at one of Vegas' infamous pool parties (Click here)
Wandering the hipster playground Cosmopolitan (Click here) and its shopaholic neighbor, the sparkling CityCenter (Click here)
Discovering vintage downtown Vegas (Click here), where the original spirit of Sin City is alive and kicking
Admiring the American cando spirit (and killer views of Lake Mead) from Nevada's greatest engineering marvel, the Hoover Dam (Click here)
Hiking, biking or climbing your way through dramatic Red Rock Canyon (Click here)
Taking in the inspiring spires at the windswept Cathedral Gorge State Park (Click here)
Blissing out in South Lake Tahoe (Click here), home to four seasons of pristine beauty and adrenalineboosting adventures
###### History
What history, you ask. Looking around, you are to be forgiven. Unlike the rest of the ruin-laden Southwest, traces of early history are scarce in the Silver State.
Contrary to Hollywood legend, there was much more at the dusty crossroads than a gambling parlor and some tumbleweeds the day mobster Ben 'Bugsy' Siegel rolled in and erected a glamorous tropical-themed casino, the Flamingo, under the searing sun.
In 1855, Mormon missionaries built and then abandoned a fort in the Las Vegas valley, where a natural-springs oasis flowed. In 1859, the richest vein of silver ever discovered in the USA, the Comstock Lode, was struck at Virginia City, which became the most notorious boomtown in the West. President Abraham Lincoln ratified Nevada as a state in 1864.
After the completion of the railroad, Las Vegas finally boomed in the 1920s. Gambling dens, brothels and saloons soon sprang up beside the tracks, especially in Las Vegas' infamous Block 16 red-light district, which survived Nevada's bans on gambling and the supposedly 'dry' years of Prohibition.
The legalization of gambling in 1931, and the sudden lessening of the divorce residency requirement to six weeks, guaranteed an influx of jet-setting divorcees and taxable tourist dollars that carried Vegas through the Great Depression. WWII brought a huge air-force base and big aerospace bucks, plus a paved highway to Los Angeles. Soon after, the Cold War justified the Nevada Test Site. Monthly aboveground atomic blasts shattered casino windows in Las Vegas, while the city's official 'Miss Atomic Bomb' beauty queen graced tourism campaigns.
A building spree sparked by the Flamingo in 1946 led to mob-backed tycoons upping the glitz ante at every turn. Big-name entertainers, like Frank Sinatra, Liberace and Sammy Davis Jr, arrived on stage at the same time as topless French showgirls in the 'Fabulous Fifties.'
Since then, Sin City continues to exist chiefly to satisfy the desires of visitors. Once North America's fastest-growing metropolitan area, the recent housing crisis hit residents here especially hard. Now among the glittering lights of the Strip, you'll spot unlit, vacant condominium towers that speak to a need for economic revival. Yet Vegas has always been a boom or bust kind of place, and if history is any judge, the city will double-down and resume its winning streak in no time.
###### Nevada Scenic Routes
For those who love wild and lonely places, almost all of Nevada's back roads are scenic routes. Nicknamed the 'Loneliest Road in America,' famous Hwy 50 bisects the state. Request the _Hwy 50 Survival Guide_ from the Nevada Commission on Tourism ( 800-638-2328; www.travelnevada.com) to find out how to get a free souvenir pin and a signed certificate from the governor.
Plenty of shorter scenic routes abound in Nevada. The Las Vegas Strip is the USA's only nighttime scenic byway. Around Las Vegas, Red Rock Canyon, the Valley of Fire, Lake Mead and the Spring Mountains all have scenic drives, too. Lesser-known routes around Nevada include the Ruby Mountains outside Elko; stairway-to-heaven Angel Lake Rd via Wells; and, near Reno, the Pyramid Lake Scenic Byway and the Mt Rose Hwy, which winds down to Lake Tahoe.
## LAS VEGAS
It's three in the morning in a smoky casino when you spot an Elvis lookalike sauntering by arm-in-arm with a glittering showgirl just as a bride in a long white dress shrieks 'Blackjack!'
Vegas, baby: it's the only place in the world where you can spend the night partying in Ancient Rome, wake up in Paris and brunch under the Eiffel Tower, bump into Superman on the way to dinner in New York, watch an erupting volcano at sunset and get married in a Pink Cadillac at midnight. Take a free craps lesson or double down with the high rollers, browse couture or tacky souvenirs, sip a neon 3ft-high margarita or a frozen vodka martini set on a bar made of ice. Vegas' landscape is a constantly shifting paradox, a volatile cocktail of dueling forces: sophistication and smut, risk and reward, boom and bust. Sound schizophrenic? That's all part of its charm.
Head downtown to explore Vegas' nostalgic beginnings and its cultural renaissance of vintage shops and cocktail bars where local culture thrives. Explore east and west of the Strip to find intriguing museums celebrating Vegas' neon, atomic-fueled past, and discover local restaurants that give celebrity chefs a run for their money.
Despite the city's recent economic downturn, this spirited city never stops. If you can imagine the kind of vacation – or life – you want, it's already a reality here. Welcome to the dream factory: just don't expect to get much sleep.
To get your bearings: the Strip, aka Las Vegas Blvd, is the center of gravity in Sin City. Roughly four miles long, Circus Circus Las Vegas caps the north end of the Strip and Mandalay Bay is on the south end near the airport. Whether walking or driving, distances on the Strip are deceiving.
Downtown, the original town center at the north end of Las Vegas Blvd, is incredibly compact and can be explored with a minimum of fuss. Its main drag is fun-loving Fremont St.
McCarran International Airport is southeast of the Strip, off I-215. For local transportation, see Click here.
#### Sights
The action in Vegas centers on casinos, but there are some unique museums along with thrill rides and amusements guaranteed to get your adrenaline pumping.
The Strip
Top Sights
Atomic Testing Museum F5
Cosmopolitan C6
Encore D3
Hard Rock E6
Sights
1Adventuredome D2
2Bellagio C6
Bellagio Gallery of Fine Art (see 2)
3Caesars Palace C5
4Circus Circus D2
Circus Circus Midway (see 4)
5CityCenter C6
Coney Island Emporium (see 15)
6Cue Club F1
Eiffel Tower Experience (see 18)
7Excalibur C7
8Flamingo C5
9Imperial Palace C5
10Luxor C8
11Mandalay Bay C8
12Mandalay Place C8
13MGM Grand C7
MGM Grand Lion Habitat (see 13)
14Mirage C5
15New York–New York C7
16Palazzo D4
17Palms A5
18Paris–Las Vegas C6
19Planet Hollywood C6
Shark Reef (see 11)
20Slots A' Fun D2
21Stratosphere E1
Stratosphere Tower (see 21)
Stripper 101 (see 19)
22TI (Treasure Island) C4
23Tropicana C7
24Venetian C4
25Wynn Las Vegas D4
Activities, Courses & Tours
26Haunted Vegas Tours E3
27Papillon Grand Canyon Helicopters E5
Qua Baths & Spa (see 3)
Spa & Salon at Encore (see 31)
THEbathhouse (see 11)
Vegas Mob Tour (see 26)
Sleeping
28Artisan Hotel C1
Bellagio (see 2)
29Bill's Gamblin' Hall & Saloon C5
Caesars Palace (see 3)
30Cosmopolitan C6
31Encore D3
32Gold Coast A5
33Hard Rock E6
Mandalay Bay (see 11)
MGM Grand (see 13)
Mirage (see 14)
New York–New York (see 15)
Palms (see 17)
Paris–Las Vegas (see 18)
Planet Hollywood (see 19)
34Platinum Hotel & Spa D5
35Rumor E6
THEhotel at Mandalay Bay (see 11)
TI (Treasure Island) (see 22)
Tropicana (see 23)
Venetian (see 24)
Wynn Las Vegas (see 25)
Eating
Alizé (see 17)
Bouchon (see 24)
Buffet (see 2)
DOCG Enoteca (see 30)
36Ferraro's E6
Fiamma (see 13)
37Firefly E5
Golden Nugget (see 25)
38Golden Steer D1
39Harrie's Bagelmania F4
Hash House a Go Go (see 9)
Hofbraühaus (see 45)
Jean Philippe Patisserie (see 5)
Joël Robuchon (see 13)
Le Village Buffet (see 18)
40Lotus of Siam F1
Mesa Grill (see 3)
Mon Ami Gabi (see 18)
Mr Lucky's (see 33)
N9NE (see 17)
Olives (see 2)
Payard Bistro (see 3)
41Paymon's Mediterranean Café G5
Peppermill (see 44)
Pink Taco (see 33)
Sage (see 5)
SeaBlue (see 13)
Social House (see 5)
Society Café (see 31)
Spice Market Buffet (see 19)
STK (see 30)
Stripburger (see 55)
Stripsteak (see 11)
Sunday Gospel Brunch (see 11)
Todd English PUB (see 5)
42Veggie Delight A4
Victorian Room (see 29)
Village Eateries (see 15)
'wichcraft (see 13)
Wicked Spoon Buffet (see 30)
Wolfgang Puck Pizzeria & Cucina (see 5)
Drinking
Café Nikki (see 23)
Chandelier Bar (see 30)
43Double Down Saloon F6
44Fireside Lounge D3
ghostbar (see 17)
Gold Lounge (see 5)
45Hofbraühaus F6
La Cave (see 25)
LAVO (see 16)
Mandarin Bar & Tea Lounge (see 5)
Mix (see 11)
Napoleon's (see 18)
O'Sheas (see 9)
Parasol Up-Parasol Down (see 25)
Red Square (see 11)
Entertainment
Crazy Horse Paris (see 13)
Drai's (see 29)
House of Blues (see 11)
46Improv C5
Joint (see 33)
Kà (see 13)
47Krƒve C6
LOVE (see 14)
Marquee (see 30)
MGM Grand Garden (see 13)
Moon (see 17)
O (see 2)
Pearl (see 17)
Phantom (see 24)
48Sand Dollar Blues Lounge B4
49Spearmint Rhino C3
Surrender (see 31)
Tao (see 24)
50Thomas & Mack Center F6
51Tickets 2Nite C7
52Treasures C2
Tryst (see 25)
XS (see 31)
Zumanity (see 15)
Shopping
53Bonanza Gifts E1
54Buffalo Exchange G5
Crystals (see 5)
55Fashion Show Mall C4
Forum Shops (see 3)
Fred Leighton: Rare Collectible Jewels (see 2)
56Grand Canal Shoppes D4
Houdini's Magic Shop (see 3)
Miracle Mile Shops (see 19)
Shoppes at Palazzo (see 16)
Wynn Esplanade (see 25)
##### THE STRIP
Ever more spectacular, the world-famous (or rather, infamous) Strip is constantly reinventing itself. As the cliché goes, it's an adult Disneyland, dealing nonstop excitement. Every megaresort is an attraction in its own right, with plenty on offer besides gambling. Open for business 24/7/365 is the unwritten rule at casino hotels.
Major tourist areas are safe. However, Las Vegas Blvd between downtown and the Strip gets shabby, along with a desolate area along Las Vegas Blvd known as the 'Naked City'.
Cosmopolitan CASINO
(www.cosmopolitanlasvegas.com; 3708 Las Vegas Blvd S) Hipsters who have long thought they were too cool for Vegas finally have a place to go where they don't need irony to endure – much less enjoy – the aesthetics. Like the new Hollywood 'IT' girl, the Cosmo looks good at all times. Expect a steady stream of ingénues and entourages, plus regular folks who enjoy contemporary design. With a focus on pure fun, it avoids utter pretension, despite the constant wink-wink, retro moments: the Art-o-Matics (vintage cigarette machines hawking local art rather than nicotine), and possibly the best buffet in town, the Wicked Spoon. The va-va-va-voom casino lives up to the hotel's name, and the hotel bars – from a James Bond-esque lounge to a live music joint where soul singers belt it out on a stage that's practically on top of the bar – are some of the best in town.
Encore CASINO
(www.encorelasvegas.com; 3121 Las Vegas Blvd S) A slice of the French Riviera in Las Vegas – and classy enough to entice any of the Riviera's regulars – Steve Wynn has upped the wow factor, and the skyline, yet again with the Encore. Filled with indoor flower gardens, a butterfly motif and a dramatically luxe casino with scarlet chandeliers, it's an oasis of bright beauty. Botero, the restaurant headed by Mark LoRusso, is centered on a large sculpture by Fernando Botero himself. Don't miss the elegant Baccarat room with its jeweled peacocks, or the stunning casino bar. Come summertime, the Encore Beach Club (www.encorebeachclub.com) throws one of the hottest pool parties in town.
Bellagio CASINO
(www.bellagio.com; 3600 Las Vegas Blvd S) Fans of eye-popping luxury, along with movie buffs who liked _Ocean's Eleven_ (several key scenes were shot here) won't want to miss Steve Wynn's Vegas' original opulent pleasure _palazzo._ Inspired by a lakeside Italian village, the Bellagio is now a classic fixture of the strip, perhaps best known for its dazzling choreographed dancing fountain show that takes place every 15 to 30 minutes during the afternoon and evening. Other highlights include the dreamy pool area, a swish shopping concourse, a European-style casino and the Bellagio Gallery of Fine Art (adult/student $17/12; 10am-6pm Sun-Tue & Thu, to 7pm Wed, Fri & Sat). Don't miss the hotel lobby's showpiece: a Dale Chihuly sculpture composed of 2000 hand-blown glass flowers in vibrant colors. Check out the Bellagio Conservatory & Botanical Gardens (admission free; daily) which features gorgeously ostentatious floral designs that change seasonally.
CityCenter SHOPPING CENTER
(www.citycenter.com; 3780 Las Vegas Blvd S) Just when you thought you'd seen it all on the Strip, where themed hotels compete to outdo each other, comes the CityCenter, which beats the competition by not competing at all. We've seen this symbiotic relationship before (think giant hotel anchored by a mall 'concept') but the way this LEED-certified complex places a small galaxy of hyper-modern, chichi hotels in orbit around the glitzy Crystals (www.crystalslasvegas.com; 3750 Las Vegas Blvd S) shopping center is a first.
The uber-upscale spread includes the subdued, stylish Vdara (www.vdara.com; 2600 W Harmon Ave), the hush-hush opulent Mandarin Oriental (www.mandarinoriental.com; 3752 Las Vegas Blvd) and the dramatic architectural showpiece Aria (www.arialasvegas.com; 3730 Las Vegas Blvd), whose sophisticated wood and chrome casino provides a fitting backdrop for its visually stunning restaurants.
Venetian CASINO
(www.venetian.com; 3355 Las Vegas Blvd S) In a city filled with spectacles, the Venetian is surely one of the most spectacular. This facsimile of a doge's palace, inspired by the splendor of Italy's most romantic city, features roaming mimes and minstrels in period costume, hand-painted ceiling frescoes and full-scale reproductions of the Italian port's famous landmarks. Flowing canals, vibrant piazzas and stone walkways attempt to capture the spirit of La Serenissima Repubblica, reputedly the home of the world's first casino. Take a gondola ride (adult/private $16/64) outdoors or stroll through the atmospheric Grand Canal Shoppes.
Palazzo CASINO
(www.palazzo.com; 3325 Las Vegas Blvd S) The Venetian's pretty but less interesting kid sister, the Palazzo may be younger but she's hardly the scintillating life of the party. The decor exploits a variation on the Italian theme to a somewhat predictable effect, and despite the caliber of the Shops at Palazzo and the star-studded dining – including exhilarating ventures by culinary heavyweights Charlie Trotter, Emeril Legasse and Wolfgang Puck – the luxurious casino area somehow exudes a lackluster brand of excitement.
Caesars Palace CASINO
(www.caesars.com; 3570 Las Vegas Blvd S) If you want to glimpse a vision of the pre-Bellagio version of quintessential four-star Las Vegas, Caesar's is your first stop. When it debuted in 1966, this Greco-Roman fantasyland captured the world's attention with its full-size marble reproductions of classical statuary and its cocktail waitresses clothed as goddesses. Bar girls continue to roam the gaming areas in skimpy togas, and faux-ancient Muses guard the high-roller rooms. The Colosseum showroom hosts mega-concerts featuring international icons like chanteuse Celine Dion. Don't skip a stroll through the curious mix of haute couture and cheesy Roman spectacle at the Forum Shops.
Mirage CASINO
(www.mirage.com; 3400 Las Vegas Blvd S) With a tropical setting replete with a huge atrium filled with jungle foliage and soothing cascades, the Mirage captures the imagination. Circling the atrium is a vast Polynesian-themed casino, which places gaming areas under separate roofs to evoke intimacy, including a popular high-limit poker room. Don't miss the 20,000-gallon saltwater aquarium, with 60 species of critters hailing from Fiji to the Red Sea (including puffer fish, tangs and pygmy sharks), in the hotel registration area. Out front in the lagoon, a fiery faux volcano erupts hourly after dark until midnight.
New York-New York CASINO
(www.nynyhotelcasino.com; 3790 Las Vegas Blvd S) Give me your tired, huddled (over a Wheel of Fortune slot machine) masses. The frenetic mini-megapolis New York-New York features scaled-down replicas of the Brooklyn Bridge and the Statue of Liberty, with a Coney Island-style roller coaster wrapped around the exterior. Claustrophobes beware: this Disneyfied version of the Big Apple can get even more crowded than the real deal. Eateries and a handful of fun bars – from dueling pianos to perfectly poured Irish pints – hide behind colorful facades from Greenwich Village and Times Sq. Upstairs, kids dig the Coney Island Emporium arcade.
Paris-Las Vegas CASINO
(www.parislv.com; 3655 Las Vegas Blvd S) Adorned with fake Francophone signs like 'Le Buffet,' Paris-Las Vegas is a Gallic caricature that strives – with admirable effort – to capture the essence of the grande dame by re-creating her landmarks. Cut-rate likenesses of the Hotel de Ville, Opéra, Arc de Triomphe, Champs-Élysées and even the River Seine frame the property. Check out the new Chateau Beer Gardens, where a mediocre beer list is redeemed by gorgeous views from the terrace.
Of course, the signature attraction is the Eiffel Tower Experience ( 702-946-7000; adult/child from $10.50/7.50; 10am-1am, weather permitting). Ascend in a glass elevator to the observation deck for panoramic views of the Strip, notably the Bellagio's dancing fountains.
Circus Circus CASINO
(www.circuscircus.com; 2880 Las Vegas Blvd S) From the outside, Circus Circus looks bedraggled and pretty cheesy – and it _is_. Yet let's be honest: kids go crazy for this stuff. Suspended above the casino is the Circus Circus Midway, where acrobats, contortionists and trapeze artists freely perform daily every 30 minutes until midnight. The revolving carousel of the Horse-a-Round Bar, made infamous by gonzo journalist Hunter S Thompson's _Fear and Loathing in Las Vegas,_ has views of the stage and can feel hallucinogenic even to those who are completely sober. Cheap beers, cheap eats and cheap thrills like 24-hour beer pong rule Slots A' Fun, just a drunken stumble away. Out back of the casino hotel, kids will dig the indoor amusement park, Adventuredome (www.adventuredome.com; day pass over/under 48in tall $27/17, per ride $5-8; hr vary).
Excalibur CASINO
(www.excalibur.com; 3850 Las Vegas Blvd S) Faux drawbridges and Arthurian legends aside, the medieval caricature castle known as Excalibur epitomizes gaudy Vegas. Down on the Fantasy Faire Midway are buried ye-olde carnival games, with joystick joys and motion-simulator ridefilms hiding in the Wizard's Arcade. The dinner show, Tournament of Kings, is more of a demolition derby with more hooves than a flashy Vegas production.
Flamingo CASINO
(www.flamingolasvegas.com; 3555 Las Vegas Blvd S) Back in 1946, the Flamingo was the talk of the town. Its original owners – all members of the New York mafia – shelled out millions to build this unprecedented tropical gaming oasis in the desert. Today, it isn't quite what it was back when its janitorial staff wore tuxedos; think more _Miami Vice_ , less _Bugsy_. Drop by during the madhouse afternoon happy hours to sling back massive margaritas. Out back is a wildlife habitat with magnificent gardens where Chilean flamingos and African penguins wander, and 15 acres of meandering pools and waterfalls filled with swans and exotic birds.
Luxor CASINO
(www.luxor.com; 3900 Las Vegas Blvd S) Only a faint echo of Egypt's splendid ancient city, the landmark Luxor has a 40-billion-candlepower beacon visible to astronauts in outer space that shoots up out of its jet-black pyramid. Out front are a 10-story crouching sphinx and a sandstone obelisk etched with hieroglyphics. The interior is adorned with huge Egyptian statues and an audacious replica of the Great Temple of Ramses II. The confusingly laid out casino has a sub-par spread of table games and slot machines.
Mandalay Bay CASINO
(www.mandalaybay.com; 3950 Las Vegas Blvd S) Almost everything at 'M-Bay' is a spectacle, if you know where to look. There's a constellation of star chefs' restaurants, the sky-high Mix lounge atop THEhotel, where couples escape to THEbathhouse spa. High-stakes gamblers will appreciate the classy casino and cutthroat poker room, while those who prefer observing the survival of the fittest in nature will appreciate Bay's Shark Reef ( 702-632-4555; adult/child $18/12; 10am-8pm Sun-Thu, 10am-10pm Fri & Sat), a walk-through aquarium that's home to thousands of submarine beasties. M-Bay is connected to Luxor by the eclectic Mandalay Place shopping mall.
Wynn Las Vegas CASINO
(www.wynnlasvegas.com; 3131 Las Vegas Blvd S) Steve Wynn's signature (literally, his name is written in script across the top, punctuated by a period) casino hotel stands on the site of the imploded 1950s-era Desert Inn. The curvaceous, copper-toned 50-story tower exudes secrecy – the entrance is obscured from the Strip by an artificial mountain of greenery. Inside, the resort comes alive with vibrant colors, inlaid flower mosaics, natural-light windows, lush foliage and waterfalls. The sprawling casino is always crowded, especially the cutthroat poker room. Acclaimed director Franco Dragone created Wynn's dreamy production show, _La Rêve_ , in a specially constructed theater-in-the-round, where a million-gallon pool doubles as the stage.
MGM Grand CASINO
(www.mgmgrand.com; 3799 Las Vegas Blvd S) With a sprawling 5000 rooms, gaming areas equal in size to four football fields and a slew of fancy restaurants, the MGM is easy to get lost in. Owned by movie mogul Metro Goldwyn Mayer, the shimmering emerald-green 'City of Entertainment' co-opts themes from classic Hollywood movies. The casino consists of one gigantic circular room with an ornate domed ceiling and replicated 1930s glamour. Out front, it's hard to miss the USA's largest bronze statue, a 100,000lb lion. Popular attractions include a lion habitat.
TI (Treasure Island) CASINO
(www.treasureisland.com; 3300 Las Vegas Blvd S) Yo, ho, whoa: although traces of the original swashbuckling skull-and-crossbones theme linger at this casino hotel, TI's shift from family-friendly to bawdy and oh-so naughty epitomizes Vegas' efforts to put the 'sin' back in 'casino.' One-armed Playboy bandits have replaced the playful pirates, plastic doubloons and chests full o'booty. Several times nightly, the spiced-up and totally cheesy Sirens of TI show stages a mock sea battle between sultry temptresses and renegade freebooters.
Tropicana CASINO
(www.troplv.com; 3801 Las Vegas Blvd S) As once-celebrated retro properties go under, the Tropicana –keeping the Strip tropical vibe going since 1953 – just got (surprise!) cool again. The massive renovation shows, from the airy casino to the lush, relaxing gardens and pool area with its with their newly unveiled Nikki Beach Club. Nope, this isn't your father's Tropicana – although he'll probably enjoy it too. The happy hour under illuminated palm trees on Café Nikki (www.nikkibeachlasvegas.com/cafe-nikki) wooden deck is one of our favorite sunset secrets.
### VEGAS ON FILM
» _Casino_ , Martin Scorsese
» _Ocean's Eleven_ , Steven Soderbergh
» _Leaving Las Vegas_ , Mike Figgis
» _Fear and Loathing in Las Vegas_ , Terry Gilliam
» _The Hangover_ , Todd Phillips
Stratosphere CASINO
(www.stratospherehotel.com; 2000 Las Vegas Blvd S) Standing over 100 stories, the three-legged Stratosphere is the tallest observation tower in the US. While the casino recently received a much-needed remodel, skip it and head straight to the elevators. Atop the tapered tower (adult/child $16/10; 10am-1am Sun-Thu, to 2am Fri & Sat) is a revolving restaurant, a circular bar and indoor and outdoor viewing decks offering the most spectacular 360-degree panoramas in town. To get there, ride the USA's fastest elevators, which ascend 108 floors in 37 ear-popping seconds. Up top, queue for adrenaline-pumping thrill rides (per ride $12-13, all rides incl elevator $28-34; 10am-1am Sun-Thu, to 2am Fri & Sat).
Planet Hollywood CASINO
(www.planethollywoodresort.com; 3667 Las Vegas Blvd S) Lest you mistake that Planet Hollywood is to Hollywood what the Hard Rock is to rock and roll, two steps into the casino will instantly clear up the difference. We're not sure what the inordinate number of scantily clad women gyrating on poles above the table games have to do with the movies, but if that's your thing, plunk down your cash on blackjack in the Pleasure Pit. The coolest movie stuff actually hangs in some of the most inconspicuous places, like by the elevators or in the hallways: go figure.
Imperial Palace CASINO
( 702-731-3311; www.imperialpalace.com; 3535 Las Vegas Blvd S; admission free; 24hr) The blue neon-roofed pagoda facade and faux-Far East theme are unbelievably hokey, but the zany atmosphere inside the casino is quite all right. Elvis fans, rejoice: the King never leaves the building.
### LAS VEGAS IN...
#### One Day
Cruise the Strip, then hit the megaresorts like the Venetian and the Encore for a taste of high-roller action. Ride the double-decker Deuce bus or the monorail between casinos, with stops for noshing and shopping. Head to the Bellagio at sunset to watch the fountain show. After dinner at a star chef's restaurant, catch a late Cirque Du Soleil show, then party till dawn at Tryst or Marquee.
#### Two Days
Shake off the Rabelaisian fête of the night before at a brunch buffet. Indulge at a spa or chill poolside at your hotel before rolling west to Red Rock Canyon for sunset. On the way back to town, enjoy a casual dinner at local faves Firefly or Ferraro's, then head for cocktails at Mix to admire the skyline views before hitting a hot new ultralounge like the Gold Lounge.
#### Three Days
Spend the morning shopping and the afternoon at one of Vegas' quirky attractions, such as the Pinball Hall of Fame and the Atomic Testing Museum. Head downtown after dark to see where it all began. Visit the trippy Fremont Street Experience and the al-fresco Neon Museum, before testing your blackjack luck at the Golden Nugget. After midnight, let it ride on the Strip one last time, grabbing a bite or a nightcap at the Peppermill's Fireside Lounge before sunrise. Still have energy? The after-hours party at Drai's rages till past dawn.
#### Four Days
Better not push your luck.
##### DOWNTOWN
Think Vegas doesn't have real grit or soul? Come downtown and think again. The original spirit of Las Vegas looms large here Serious gamblers, colorful locals and rowdy tourists come to play $5 blackjack and drink giant daiquiris amid the swirling neon and open air shows on Fremont St. Expect a retro feel, cheaper drinks and lower table limits.
Note that the areas between downtown and the Strip and Fremont St east of downtown can be rather unsavory.
Neon MuseumMUSEUM
( 702-387-6366; www.neonmuseum.org; 821 Las Vegas Blvd N; displays free, guided tours $15; displays 24hr, guided tours noon & 2pm Tue-Sat) Experience the outdoor displays through a fascinating walking tour ($15) of the newly unveiled Neon Boneyard Park, where irreplaceable vintage neon signs – the original art form of Las Vegas – spend their retirement. At press time, the museum was expanding their digs and hoped to add a self-guided component in 2012; until then, be sure to reserve your tour at least one to two weeks in advance.
Stroll around downtown come evening (when the neon comes out to play) to discover the free, self-guided component of the 'museum.' You'll find delightful al-fresco galleries of restored vintage neon signs, including sparkling genie lamps, glowing martini glasses and 1940s motel marquees. The biggest assemblages are found at the on the 3rd St cul-de-sac just north of Fremont St.
Downtown Arts DistrictARTS
On the First Friday (www.firstfriday-lasvegas.org) of each month, a carnival of 10,000 art lovers, hipsters, indie musicians and hangers- on descend on Las Vegas' downtown arts district. These giant monthly block parties feature gallery openings, performance art, live bands and tattoo artists. The action revolves around the Arts Factory ( 702-676-1111; 101-109 E Charleston Blvd), Commerce Street Studios (1551 S Commerce St) and the Funk House (1228 S Casino Center Blvd). Check the website for shuttle bus info.
Fremont Street ExperiencePLAZA
(www.vegasexperience.com; Fremont St, btwn Main St & Las Vegas Blvd; hourly 7pm- midnight) Streaking down the center of Vegas' historic Glitter Gulch gambling district, this five-block pedestrian mall is topped by an arched steel canopy. Hourly from dusk until midnight, the 1400ft-long canopy turns on a six-minute light-and-sound show enhanced by 550,000 watts of wraparound sound and 12.5 million synchronized LEDs. The shows are ridiculously cheesy, but mesmerizing enough to stop passersby in their tracks, especially drunks.
El CortezCASINO
(www.elcortezhotelcasino.com; 600 Fremont St) Downtown and in the mood for blackjack? Head to the deliciously retro El Cortez, Vegas' oldest continuously operating casino. Going strong since 1941, it's one of the only joints in town where the slots are the real thing. If you hit the jackpot, you'll enjoy the clatter of actual coins – none of that newfangled paper ticket nonsense. For an all-out retro evening, duck into the Flame Steakhouse (www.elcortez.com; 1 E Fremont St; mains $10-26; dinner) and you'll swear Bugsy Siegel himself might wander in. The coral dining room is the color of a Hollywood starlet's handbag and the menu (Steak Diane, wedge salad) is straight out of 1941.
### GAMBLER'S SURVIVAL GUIDE
»The house always wins – eventually. Except for poker, all casino games pit the player against the house, which always has a statistical edge. Think of gambling only as entertainment – for which you do pay a fee.
»Always sign up for free player clubs at the casinos – they're located at the information desk on the casino floor.
»On a budget? Drink free cocktails while you're gambling, and hit the buffets at lunch – you'll probably not need to eat much the rest of the day.
»Take advantage of the introductory lessons in poker, blackjack and craps offered at some casinos.
»Don't be afraid to ask the dealer for advice on strategy or odds.
»If you're winning, it's polite to give your dealer a 'toke' (tip).
»As for the famous saying, 'what happens in Vegas stays in Vegas,' it's often true – especially in regard to your cash.
Golden Nugget CASINO
(www.goldennugget.com; 129 E Fremont St) Downtown's royal jewel has serious panache, thanks in part to gorgeous Dale Chihuly-inspired glasswork everywhere you look. No brass or cut glass was spared inside the swanky (and lively) casino, known for its nonsmoking poker room; the RUSH Lounge, where live local bands play; and some of downtowns' best restaurants. Don't miss the gigantic 61lb Hand of Faith, the world's largest gold nugget, around the corner from the hotel lobby.
Downtown Las Vegas
Top Sights
Fremont Street Experience C2
Sights
1Arts Factory B4
2Binion's C2
3Blue Sky Yoga B4
4El Cortez D2
5Golden Gate C2
6Golden Nugget C2
7Main Street Station C1
8Neon Museum Outdoor Galleries C2
Sleeping
9California C1
10El Cortez Cabana Suites D2
Golden Nugget (see 6)
Main Street Station (see 7)
Eating
Aloha Specialties (see 9)
Golden Gate (see 5)
Golden Nugget Buffet (see 6)
Grotto (see 6)
Lillie's Asian Cuisine (see 6)
11Second Street Grill C2
The Flame Steakhouse (see 4)
12Triple George Grill C1
Drinking
13Beauty Bar D2
Burlesque Hall of Fame (see 14)
14Emergency Arts D2
The Beat Coffeehouse (see 14)
Triple 7 Restaurant & Microbrewery (see 7)
Shopping
15Attic B4
16Gamblers General Store B3
17Las Vegas Premium Outlets A3
Main Street Station CASINO
(www.mainstreetcasino.com; 200 N Main St) This surprisingly elegant neo-Victorian casino hotel is adorned throughout with notable _objets d'histoire_ under its pressed tin ceilings and elegant ceiling fans. Pick up a free _Guide to Artifacts, Antiques & Artworks_ pamphlet from the hotel registration desk, then look for the art-nouveau chandelier from a Parisian opera house and a graffiti-covered chunk of the Berlin Wall.
Binion's CASINO
(www.binions.com; 128 E Fremont St) This old-school casino hotel is best known for its 'zero limit' betting policy and for being the birthplace of the World Series of Poker. While its heyday is over, it's a perfect place for beginners to learn blackjack at the low-limit ($2 and up) tables.
Viva Las Vegas Wedding Chapel CHAPEL
( 702-384-0771, 800-574-4450; www.vivalasvegasweddings.com; 1205 Las Vegas Blvd S; wedding packages from $201; hr vary) Even if you're not contemplating tying the knot, it's worth a peek inside this little assembly-line wedding chapel of loooovvvee to see if anyone is getting married. The public is welcome to attend the themed weddings: kitschy as all get-out, too, they range from Elvis' 'Blue Hawaii' and 'Pink Caddy' to James Bond,' 'Gangster' and 'Dracula's Tomb' themes.
##### OFF THE STRIP
Atomic Testing Museum MUSEUM
(www.atomictestingmuseum.org; 755 E Flamingo Rd; adult/child $14/11; 10am-5pm Mon-Sat, noon-5pm Sun) Recalling an era when the word 'atomic' conjured modernity and mystery, the Smithsonian-run Atomic Testing Museum remains an intriguing testament to the period when the fantastical – and destructive – power of nuclear energy was tested just outside of Las Vegas. After visiting the museum, it's almost possible to imagine that during the atomic heyday of the 1950s, gamblers and tourists picnicked on downtown casino rooftops while mushroom clouds rose on the horizon. Don't skip the deafening Ground Zero Theater, which mimics a concrete test bunker.
Hard Rock CASINO
(www.hardrockhotel.com; 4455 Paradise Rd) Beloved by SoCal visitors, this trés-hip casino hotel is home to one of the world's most impressive collections of rock and roll memorabilia, including Jim Morrison's handwritten lyrics to one of the Door's greatest hits, Madonna's cone bra and leather jackets from a who's who of famous rock stars. The Joint concert hall, Vanity Nightclub and Rehab summer pool parties attract a pimped-out, sex-charged crowd flush with celebrities.
Springs Preserve NATURE PRESERVE
(www.springspreserve.org; 333 S Valley View Blvd; adult/child $19/11, admission to gardens & trails by donation; 10am-6pm, trails close at dusk; ) On the site of the natural springs (which ran dry in 1962) that fed _las vegas_ ('the meadows'), where southern Paiutes and Spanish Trail traders camped, and later Mormon missionaries and Western pioneers settled the valley, this educational complex is an incredible trip through historical, cultural and biological time. The touchstone is the Desert Living Center, demonstrating sustainable architectural design and everyday eco-conscious living.
Palms CASINO
(www.palms.com; 4321 W Flamingo Rd) Equal parts sexy and downright sleazy, the Palms attracts notorious celebrities and gossip standbys (think Britney Spears) as well as a younger, mostly local crowd. While critics claim the Palms' glory days are waning, others rave that its restaurants and nightclubs remain some of the hottest in town. Highlights at the Palms include a 14-screen movie theater with IMAX capabilities and a 1200-seat showroom, the Pearl. PS: Don't take the elevator to the Playboy Club expecting debauchery à la Hef's mansion: while a few bunny-eared, surgically enhanced ladies deal blackjack in a stylishly appointed lounge full of mostly men, the sexiest thing about it is the stunning skyline view.
#### Activities
Cue Club POOL
(www.lvcueclub.com; Commercial Center, 953 E Sahara Ave; per hr $10.50; 24hr) Swim with the pool sharks at Vegas' largest billiard hall.
Pole Position Raceway SPORTS
(www.polepositionraceway.com; 4175 S Arville St, off W Flamingo Rd; membership $5, race from $20; 11am-10pm Sun-Thu; 11am-midnight Fri & Sat) Dreamed up by Nascar and Supercross champs and modeled on Formula 1 road courses, this European-style raceway boasts the USA's fastest indoor go-karts (up to 45mph).
Richard Petty Driving Experience SPORTS
(www.1800bepetty.com; Las Vegas Motor Speedway, 7000 Las Vegas Blvd N, off I-15 exit 54; rides from $149; hr vary) If you've got a need for speed, this driving experience is your chance to ride shotgun during a Nascar-style qualifying run.
Royal Links GOLF
( 888-427-6688; www.royallinksgolfclub.com; 5995 E Vegas Valley Dr; green fees $75-275) Inspired by the British Open's famous greens. Tiger Woods set the record here, scoring 67.
Tournament Players Clubs Las Vegas GOLF
( 702-256-2500; www.tpc.com; 9851 Canyon Run Dr; green fees $119-235) A PGA tour stop, the naturalistic, minimal-irrigation Canyons course is also an Audubon-certified cooperative sanctuary.
###### Spas & Gyms
The Strip's spas are perfect for pampering. Day-use fees ($20 to $45) are usually waived with a treatment (minimum $75). Most spas have fitness centers; workout attire and gym shoes are required.
Qua Baths & Spa SPA
( 866-782-0655; www.harrahs.com/qua; Caesars Palace, 3570 Las Vegas Blvd S; 6am-8pm) Social spa going is encouraged in the tea lounge, herbal steam room and arctic ice room, where dry-ice snowflakes fall. Among the many over-the-top spas in Vegas, this one remains a favorite for its unique atmosphere and ability to provide a blissful state of calm that's a rarity anywhere on the Strip.
THEbathhouse SPA
( 877-632-9636; www.mandalaybay.com; THEhotel at Mandalay Bay, 3950 Las Vegas Blvd S; 6am-9:30pm) A multimillion-dollar minimalist temple, it offers 'aromapothecary' massage oils, ayurvedic herbal baths and plunge pools.
The Spa & Salon at Encore SPA
( 702-770-3900; www.wynnlasvegas.com; Encore Las Vegas, 3131 Las Vegas Blvd S; 5:30am-10pm) One of the newest spas in town, with an already legendary reputation among spa addicts.
#### Courses
Blue Sky Yoga YOGA
(www.blueskyyogalv.com; 101 E Charleston Blvd; suggested donation $12; hr vary) Drop-in classes for all levels in Jivamukti, Vinyasa and Kundalini styles.
Stripper 101 DANCE
( 702-260-7200; www.stripper101.com; Planet Hollywood, 3667 Las Vegas Blvd S; tickets from $40; hr vary) In a cabaret setting complete with strobe lights, cocktails and feather boas, these (non-nude) pole-dancing classes are popular with bachelorettes.
#### Tours
It's easy enough to tour the Strip on your own via monorail or bus or on foot, but these companies offer more unique experiences. Check online for frequent promotions.
Haunted Vegas Tours TOUR
( 702-339-8744; www.hauntedvegastours.com; Royal Resort, 99 Convention Center Dr; 2½hr show & tour $66) A campy sideshow begins a tell-all bus tour visiting Bugsy at the Flamingo casino hotel, creepy Liberace's cafe, the 'Motel of Death' and more.
Papillon Grand Canyon Helicopters TOUR
( 702-736-7243, 888-635-7272; www.papillon.com; McCarran Executive Terminal, 275 E Tropicana Ave) Flightseeing tour operator offers luxury Grand Canyon tours. Its 10-minute 'Neon Nights Express' jetcopter flyover of the Strip (adult/child from $69/49) is popular.
Vegas Mob Tour TOUR
( 702-339-8744; www.vegasmobtour.com; Royal Resort, 99 Convention Center Dr; 2½hr tour & film $66) Nighttime bus tour delves into the mafia underworld of Sin City's past, including celebrity scandals, mobster assassinations and other dirty laundry.
### LAS VEGAS FOR CHILDREN
Few places in Vegas actually bill themselves as family-friendly. State law prohibits anyone under 21 from loitering in gaming areas. The only casino hotels on the Strip that cater to children are Circus Circus and Excalibur. That said, there are still plenty of things to see and do with youngsters. Don't miss Mandalay Bay's Shark Reef. Teenagers may be most entranced by sassy pool scenes.
Coney Island Emporium (www.coneyislandemporium.com; New York-New York, 3790 Las Vegas Blvd S; games from 50¢, roller coaster $14, all-day pass $25; 11am-11pm Sun-Thu, 10:30am-midnight Fri & Sat; ) The highlight of NY-NY's gargantuan video arcade and amusement center is the roller coaster, a four-minute high-octane ride with stomach-dropping dipsy-dos and stellar Strip views.
MGM Grand Lion Habitat (www.mgmgrand.com; MGM Grand, 3799 Las Vegas Blvd S; admission free; 11am-7pm; ) Inside the casino, this glass-walled habitat showcases up to six magnificent felines daily, all descendants of the movie company's original mascot. The kid-friendly, tropical-themed Rainforest Cafe is nearby.
Pinball Hall of Fame (www.pinballmuseum.org; 1610 E Tropicana Ave; admission free, games 25-50¢; 11am-11pm Sun-Thu, to midnight Fri & Sat; ) Next to a discount cinema east of the Strip, this interactive museum is more fun than any slot machines. Picture 200-plus vintage pinball, video-arcade and carnival-sideshow games dating from the 1950s to the '90s.
College of Southern Nevada Planetarium ( 702-651-4759; www.csn.edu/planetarium; 3200 E Cheyenne Ave, east of I-15 exit 46; adult/child $6/4; shows usually 6pm & 7:30pm Fri, 3:30pm, 6pm & 7:30pm Sat; ) Young scientists will love the multimedia shows and 'skywatch' astronomy programs at this small planetarium. Show up early to get a seat (no latecomers allowed). Weather permitting, the observatory telescopes open for public viewing after the late show.
#### Festivals & Events
For more information about special events, contact the LVCVA (Click here).
Chinese New Year CULTURAL
(www.lvchinatown.com) Lunar new year celebrations in January/February.
Nascar Weekend EXTREME SPORTS
(www.nascar.com) Rabid race fans descend on the Las Vegas Motor Speedway in early March.
St Patrick's Day CULTURAL
Fremont St throws a party and parade every March 17.
UNLVino FOOD & DRINK
(www.unlvino.com) Not-for-profit wine tasting extravaganza in mid-April.
Viva Las Vegas MUSIC
(www.vivalasvegas.net) Ultimate rockabilly weekend downtown in mid-April.
Helldorado Days CULTURAL
(www.elkshelldorado.com) Historic Old West hoedown, rodeo and barbecue near Fremont St in May.
World Series of Golf GOLF
(www.worldseriesofgolf.com) Ingeniously combines golf with high-stakes poker in mid-May.
World Series of Poker CASINO
(www.worldseriesofpoker.com) High rollers, casino dealers, Hollywood celebs and internet stars vie for millions from early June to mid-July.
National Finals Rodeo RODEO
(www.nfrexperience.com) Ten days of cowboys at the Thomas & Mack Center in December.
New Year's Eve CULTURAL
The Strip sees the biggest crush of humanity this side of Times Sq.
#### Sleeping
Pricewise, Vegas hotels are feast or famine: the awesome deal you got yesterday? It might triple for Friday's Lady Gaga concert. Then again, bargains in summer, midweek, and _after_ holidays can be shockingly good – even at luxe properties. If you arrive midweek, rooms go for up to 50% less than on weekends. Note that the best deals are often found via hotel websites – which usually feature calendars listing day-by-day room rates – rather than through discount travel websites. Travelzoo.com is a good website to find current deals.
Don't be surprised when you find a 'resort' fee of $5 up to $25 per night on your bill. Valet (tip at least $2) and self-parking are free.
### TOP POKER HOTSPOTS
With the rules of Texas Hold 'em a frequent conversation starter these days, it's obvious poker is the hottest game in town.
»Wynn Las Vegas (Click here) Vegas' most posh poker room
»Bellagio (Click here) World Poker Tour stop
»Golden Nugget (Click here) Classy carpet joint with nonsmoking tables
»Hard Rock (Click here) Poker Lounge with bottle service, iPod docking stations and free lessons lure in the young and the hip
##### THE STRIP
While few places on the Strip offer rock-bottom budget accommodations, you can still snag surprisingly reasonable deals, especially at some of the older properties. Families on a budget are in luck: the cheapest tend to be the most child-friendly.
Encore CASINO HOTEL $$$
( 702-770-8000; www.encorelasvegas.com; 3121 Las Vegas Blvd S; r $199-850; ) Classy and playful more than overblown and opulent – even people cheering at the roulette table clap with a little more elegance. The rooms are studies in subdued luxury.
Tropicana CASINO HOTEL $
( 702-739-2222; www.troplv.com; 3801 Las Vegas Blvd S; r from $40, ste from $140; ) A recent multi-million dollar renovation has made 'the Trop' one of our new faves on the Strip. We like how the 1950s spirit lingers in the casino, while the amenities and design are utterly contemporary. The earth-toned, breezily tropical rooms and bi-level Jacuzzi suites are steals, and the pool area is a hidden delight.
Venetian CASINO HOTEL $$$
( 702-414-1000, 877-883-6423; www.venetian.com; 3355 Las Vegas Blvd S; ste $199-1000; ) The 700-sq-ft 'standard' suites are anything but. In fact, they're among the Strip's largest and most luxurious, with oversized Italian marble baths and sunken living rooms.
Mandalay Bay CASINO HOTEL $$$
( 702-632-7777, 877-632-7800; www.mandalaybay.com; 3950 Las Vegas Blvd S; r $100-380; ) The ornately appointed rooms have a South Seas theme, and amenities include floor-to-ceiling windows and luxurious bathrooms. Swimmers will swoon over the sprawling pool complex, with a sand-and-surf beach. Or check into THEhotel ( 702-632-7777; www.mandalaybay.com; Mandalay Bay, 3950 Las Vegas Blvd S; ste $120-540; ), Mandalay's all-suite hotel, decked out with wet bars, plasma-screen TVs and deep soaking tubs.
Bellagio CASINO HOTEL $$$
( 702-693-7111, 888-987-6667; www.bellagio.com; 3600 Las Vegas Blvd S; r $169-570; ) Once the belle of the ball, the nouveau-riche Bellagio is still lavishly and artistically designed. Do rooms look small? That's because bathrooms are oversized. Luxurious lake-view suites front the resort's dancing fountains.
Caesars Palace CASINO HOTEL $$
( 866-227-5938; www.caesarspalace.com; 3570 Las Vegas Blvd S; r from $99; ) Send away the centurions and decamp in style – Caesars' standard rooms are some of the most luxurious you will find in town.
Wynn Las Vegas CASINO HOTEL $$$
( 702-770-7100, 877-321-9966; www.wynnlasvegas.com; 3131 Las Vegas Blvd S; r $199-515, ste from $289; ) Deluxe five-diamond resort rooms are bigger than some studio apartments, with high-thread-count linens, flat-screen high-definition TVs, Turkish towels and lots of little luxuries. Salon suites enjoy floor-to-ceiling windows and VIP check-in.
Bill's Gamblin' Hall & Saloon CASINO HOTEL $$
( 702-737-2100, 866-245-5745; www.billslasvegas.com; 3595 Las Vegas Blvd S; r $70-200; ) The mid-Strip's worst-kept budget secret sports plasma TVs, Victorian decor and a rollicking fun casino with low-limit blackjack tables for beginners. Guests may use the pool next door at the Flamingo without charge.
Cosmopolitan CASINO HOTEL $$$
( 702-698-7000; www.cosmopolitanlasvegas.com; 3708 Las Vegas Blvd S; r 200-400; ) Are the too-cool-for-school, hip rooms worth the price tag, especially when the service falls short of flawless? The indie set seems to think so. The rooms are impressive exercises in mod design, but the real delight of staying here is to stumble out of your room at 1am to play some pool in the upper lobbies before going on a mission to find the 'secret' pizza joint.
Mirage CASINO HOTEL $$
( 702-791-7111, 800-374-9000; www.mirage.com; 3400 Las Vegas Blvd S; r $80-699; ) Don't expect your room to evoke an erupting volcano: gone is the four-star hotel's original tropical theme, replaced by chic, contemporary rooms. Expect bold color palettes, plush patterned rugs, plasma-screen TVs and stereos with iPod docks.
New York-New York CASINO HOTEL $$
( 702-740-6969, 866-815-4365; www.nynyhotelcasino.com; 3790 Las Vegas Blvd S; r $70-480; ) The cheapest digs are rather tiny (just what one would expect in NYC), but pay more for a stylish Park Ave Deluxe and you'll have plenty of legroom. Avoid noisy lower-level rooms facing the roller coaster.
Paris-Las Vegas CASINO HOTEL $$
( 702-946-7000, 877-603-4386; www.parislasvegas.com; 3655 Las Vegas Blvd S; r from $80; ) Nice rooms with a nod to classic French design; the newer Red Rooms are a study in sumptuous class.
MGM Grand CASINO HOTEL $$
( 702-891-7777, 800-929-1111; www.mgmgrand.com; 3799 Las Vegas Blvd S; r $80-500, ste from $150; ) There's plenty to choose from at the world's largest hotel (5000-plus rooms), but is bigger better? That depends, but top-drawer restaurants, a sprawling pool complex and a monorail Station always make it a good bet – if you can find your room. Standard rooms have blah decor, so stay in the minimalist-modern West Wing instead.
Planet Hollywood CASINO HOTEL $$
( 702-785-5555, 866-919-7472; www.planethollywoodresort.com; 3667 Las Vegas Blvd S; r $69-369; ) Though not a standout in any category, Planet Hollywood remains one of the better midrange deals on the Strip. Skip the all-suite PH Towers Westgate and stay in the better value main tower instead. Each spacious, purple-accented room is themed after a specific movie (we spent the night with a 1990s Hugh Grant flop). Despite its sexy moniker, the 'Pleasure Pool' is fairly blah. Rooms with a view of the Bellagio fountain are a worthy splurge: the vantage point couldn't be better.
### COOL POOLS
»Hard Rock (Click here) Seasonal swim-up blackjack and Tahitian-style cabanas at the beautifully landscaped and uber-hip Beach Club, a constant throbbing (literally, there are underwater speakers!) meat-market party, especially during summer-only 'Rehab' pool parties.
»Mirage (Click here) Lush tropical pool is a sight to behold, with waterfalls tumbling off cliffs, deep grottos and palm-tree studded islands for sun bathing. Feeling flirty? Check out the topless Bare lounge.
»Mandalay Bay (Click here) Splash around an artificial sand-and-surf beach built from imported California sand and boasting a wave pool, lazy-river ride, casino and DJ-driven topless Moorea Beach Club.
»Caesars Palace (Click here) Corinthian columns, overflowing fountains, magnificent palms and marble-inlaid pools make the Garden of the Gods Oasis divine. Goddesses proffer frozen grapes in summer, including at the topless Venus pool lounge.
»Golden Nugget (Click here) Downtown's best pool offers lots of fun and zero attitude. Play poolside blackjack, or sip on a daiquiri in the Jacuzzi and watch the sharks frolic in the nearby aquarium.
TI (Treasure Island) CASINO HOTEL $$
( 702-894-7111, 800-288-7206; www.treasureisland.com; 3300 Las Vegas Blvd S; r $90-390; ) The micro rooms here feel deceptively expansive, thanks to floor-to-ceiling windows, airy earth tones, and soaking tubs. Rooms facing the strip overlook the cheesy-sexy pirate ship battle, an eye-rolling spectacle that best represents the way that TI has rebranded itself as towards grown up and cheeky rather than family-friendly.
##### DOWNTOWN
Avoid rent-by-the-hour fleapits by sticking close to the Fremont Street Experience.
El Cortez Cabana Suites BOUTIQUE HOTEL $$
( 800-634-6703; www.eccabana.com; 651 E Ogden Ave; ste $45-150; ) You probably won't recognize this sparkling little boutique hotel for its brief movie cameo in Scorcese's _Casino_ (hint: Sharon Stone was murdered here) and that's a good thing, because a massive makeover has transformed it into a vintage oasis downtown. Mod suites decked out in mint green include iPod docking stations, big flatscreen TVs and fab retro tiled bathrooms. There's a free fitness room and the funkiest old school casino in town – the El Cortez – is right across the street.
Golden Nugget CASINO HOTEL $$
( 702-385-7111, 800-846-5336; www.goldennugget.com; 129 E Fremont; r $59-229; ) Looking like a million bucks, this casino hotel has set the downtown benchmark for extravagance since opening in 1946. Ample standard rooms sport half-canopy beds and marble everywhere. Outside by the lavish pool area, a three-story water slide plunges through a 200,000-gallon shark tank.
Main Street Station CASINO HOTEL $$
( 702-387-1896, 800-713-8933; www.mainstreetcasino.com; 200 N Main St; r $40-120; ) For a more intimate experience, try this 17-floor hotel tower with marble-tile foyers and Victorian sconces in the hallways. Bright, cheery hotel rooms with plantation shutters and comfy beds are as handsome as the casino.
California CASINO HOTEL $$
( 702-385-1222, 800-634-6255; www.thecal.com; 12 E Ogden Ave; r $39-145, ste $139-239; ) Tropical flair and a rooftop pool make it popular with visitors from Hawaii. Airy rooms have white plantation shutters, mahogany furnishings and mini-fridges.
##### EAST OF THE STRIP
Don't get stuck at chain cheapies near the airport or the city's convention center.
Hard Rock CASINO HOTEL $$$
( 702-693-5000, 800-473-7625; www.hardrockhotel.com; 4455 Paradise Rd; r $69-450; ) Everything about this boutique hotel spells stardom. French doors reveal skyline and palm tree views, and brightly colored Euro-minimalist rooms feature souped-up stereos and plasma-screen TVs. While we dig the jukeboxes in the HRH All-Suite Tower, the standard rooms are nearly as cool. The hottest action revolves around the lush Beach Club.
Rumor BOUTIQUE HOTEL $
( 877-997-8667; www.rumorvegas.com; 455 E Harmon Ave; ste from $69; ) Across from the Hard Rock, Rumor features a carefree, Miami-cool atmosphere with fun happy hours and DJ nights in the lobby. Its airy suites overlook a palm-shaded courtyard pool area dotted with daybeds and hammocks perfect for lounging.
Platinum Hotel BOUTIQUE HOTEL $$
( 702-365-5000, 877-211-9211; www.theplatinumhotel.com; 211 E Flamingo Rd; r from $129; ) Just off the Strip, the coolly modern rooms at this spiffy, non-gaming property are comfortable and full of nice touches – many have fireplaces and they all have kitchens and Jacuzzi tubs.
##### WEST OF THE STRIP
Some off-strip hotels may provide free shuttles to the Strip.
Artisan Hotel BOUTIQUE HOTEL $$
( 800-554-4092; www.artisanhotel.com; 1501 W Sahara Ave; r $40-129; ) A Gothic baroque fantasy with a decadent dash of rock and roll, each suite is themed around the work of a different artist. Yet with one of Vegas' best after parties raging on weekend nights downstairs (a fave with the local alternative set), you may not spend much time in your room. The libidinous, mysterious vibe here isn't for everyone, but if you like it, you'll love it.
Orleans CASINO HOTEL $$
( 702-365-7111, 800-675-3267; www.orleanscasino.com; 4500 W Tropicana Ave; r $50-175; ) Tastefully appointed French-provincial rooms are good-value 'petite suites.' There's a free-access fitness center for guests in the spa, on-site childcare, a movie theater, a bowling alley and a live-music pub.
Palms CASINO HOTEL $$$
( 702-942-7777, 866-942-7770; www.palms.com; 4321 W Flamingo Rd; r $99-459, ste from $149; ) Britney Spears spent her _first_ wedding night here. Standard rooms are generous, as are tech-savvy amenities. Request an upper floor to score a Strip view. Playpen suites are tailored for bachelor and bachelorette parties, or escape to the high-rise Palms Place.
##### GREATER LAS VEGAS
Most of these hotels offer free Strip shuttles.
Sam's Town CASINO HOTELS $
( 702-456-7777, 800-897-8696; www.samstownlv.com; 5111 Boulder Hwy, east of I-515/US Hwy 93/US Hwy 95 exit 69; r $40-275; ) Ranchers, locals and RVers flock to this Wild West casino hotel, which neopunk band the Killers named their sophomore album after. Texas-sized rooms face a kitschy indoor garden or the city's neon lights.
South Point CASINO HOTELS $$$
( 702-796-7111, 866-791-7626; www.southpointcasino.com; 9777 Las Vegas Blvd S; r $70-300; ) Popular with cowboys for its equestrian center, this budget-deluxe casino hotel is a short drive south of the Strip, near the outlet mall. With rooms this big and beds this divine, who needs a suite? Perks include a spa, a cineplex and a bowling center.
Red Rock Resort RESORT $$$
( 702-797-7878; www.redrocklasvegas.com; 11011 W Charleston Blvd; r $110-625; ) Red Rock touts itself as the first off-Strip billion-dollar gaming resort, and most people who stay here eschew the Strip forever more. For adventurous types who want the best of Vegas' urban jungle and its vast outdoor desert playground, this stylish place rocks. There's free transportation between the Strip, and outings to the nearby Red Rocks State Park and beyond. Rooms are well appointed and comfy. Check out the PBA-tour bowling alley, with 72 lanes and VIP suites with bottle service.
#### Eating
Sin City is an unmatched culinary adventure. As celebrity chefs take up residence in nearly every casino, stakes are high, and there are many overhyped eating gambles.
Make reservations for more expensive restaurants as far in advance as possible, especially if you're here on a weekend. The dress code at most upscale eateries is business casual. At the most famous places, jackets and ties are preferred for men. For an unvarnished local view of the Vegas dining scene, check out the blog Eating Las Vegas (www.eatinglv.com).
##### THE STRIP
Strip casino restaurants alone could be fodder for an entire book; here are some favorites, but the choice seems nearly infinite. Look for the newest celebrity chefs' restaurants at the Palazzo resort, the CityCenter and the Cosmopolitan.
For a good range of budget options, head to New York-New York, where Greenwich Village bursts with tasty, budget-saving options.
Sage AMERICAN $$$
( 702-590-8690; Aria, www.arialasvegas.com; 3730 Las Vegas Blvd S; mains $25-42; 5pm-11pm Mon-Sat) Acclaimed Chicago chef Shawn McClain meditates on the seasonally sublime with global inspiration and artisanal, farm-to-table ingredients in one of Vegas' most drop-dead gorgeous dining rooms. Lounge at the eggplant velvet banquettes underneath the giant scrims of Impressionist paintings, or head to the stunning bar to sip on inspired seasonal cocktails doctored with housemade liqueurs.
Social House JAPANESE $$$
( 702-736-1122; www.socialhouselv.com; Crystals Mall, CityCenter, 3720 Las Vegas Blvd S; mains $24-44, tasting menu $95; 5pm-10pm Mon-Thu, noon-11pm Fri & Sat, noon-10pm Sun) Nibble on creative dishes inspired by Japanese street food in one of the Strip's most serene yet sultry dining rooms. Watermarked scrolls, wooden screens and loads of dramatic red and black conjure visions of Imperial Japan, while the sushi and steaks are totally contemporary.
DOCG Enoteca ITALIAN $$$
( 702-893-2001; Cosmopolitan, 3708 Las Vegas Blvd S; mains $15-27; 5:30pm-11pm) Among the Cosmopolitan's alluring dining options, this is one of the least glitzy – but most authentic – options. That's not to say it isn't loads of fun. Order up to-die-for fresh pasta or a wood-fired pizza in the stylish _enoteca_ (wine shop) inspired room that feels like you've joined a festive dinner party. Or head next door to sexy Scarpetta, which offers a more intimate, upscale experience by the same fantastic chef, Scott Conant.
Jean Philippe Patisserie FRENCH $$
(www.ariavegas.com; Aria; 3730 Las Vegas Blvd S; items $3-12; 6am-midnight; ) Step out of the Aria's mod casino buzz into this fantastical Alice in Wonderland land of sugar and spice (along with coffee, gelato and killer almond brioche). Indulge in creative takes on classic desserts like éclairs and Napoleons in flavors that promise to satisfy even the most hard-to-impress pastry connoisseur.
Hash House a Go Go AMERICAN $$$
(www.hashhouseagogo.com; Imperial Palace; 3535 Las Vegas Blvd; mains $12-29; 7am-11pm, to 2am Fri & Sat; ) Fill up on this SoCal import's 'twisted farm food,' which has to be seen to be believed. The pancakes are as big as tractor tires, while farm-egg scrambles and house-made hashes could knock over a cow.
Joël Robuchon FRENCH $$$
( 702-891-7925; MGM Grand, 3799 Las Vegas Blvd S; menu per person $120-420; 5:30-10pm Sun-Thu, to 10:30pm Fri & Sat) A once-in-a-lifetime culinary experience; block off a solid three hours and get ready to eat your way through the multicourse seasonal menu of traditional French fare. But we secretly dig next-door L'Atelier de Joël Robuchon even more, where you can belly up to the sexy scarlet and black lacquer bar for a slightly more economical but still wow-inducing meal.
Mesa Grill SOUTHWESTERN $$$
( 702-731-7731; www.mesagrill.com/las-vegas-restaurant; Caesar's Palace, 3750 Las Vegas Blvd S; mains $15-36; 5pm-11pm daily, 11am-2:30pm Mon-Fri, 10:30am-3pm Sat & Sun) While New York star chef Bobby Flay doesn't cook on the premises, his bold signature menu of Southwestern fusion fare lives up to the hype.
Mon Ami Gabi FRENCH $$$
( 702-944-4224; www.monamigabi.com; Paris-Las Vegas, 3655 Las Vegas Blvd S; mains $12-28; 7am-midnight) No, this charming French brasserie doesn't live up to culinary heavyweights like Bouchon, and it's not trying to. Come for solid classics like friendly service and alfresco brunches on one of the Strip's nicest outdoor patios.
'wichcraft SANDWICH SHOP $
(www.mgmgrand.com; MGM Grand, 3799 Las Vegas Blvd S; sandwiches $8-11; 10am-5pm; ) This designy little sandwich shop, the brainchild of celebrity chef Tom Colicchio, is one of the best places to taste gourmet on a budget. Think grilled cheddar with smoked ham and baked apples.
Olives MEDITERRANEAN $$$
( 702-693-8181; www.bellagio.com; Bellagio, 3600 Las Vegas Blvd S; mains $16-52; 11am-3pm, 5pm-10:30pm) Bostonian chef Todd English dishes up homage to the life-giving fruit. Flatbread pizzas, house-made pastas and flame-licked meats get top billing, and patio tables overlook Lake Como. Or try his rollicking new CityCenter venture, Todd English PUB (www.toddenglishpub.com; Crystals, 3720 Las Vegas Blvd S; mains $13-24; lunch & dinner) a strangely fun cross between a British pub and a frat party, with creative sliders, English pub classics and an interesting promotion: if you drink your beer in less than seven seconds, it's on the house.
Fiamma ITALIAN $$$
( 702-891-7600; www.mgmgrand.com; MGM Grand, 3799 Las Vegas Blvd S; meals $50-60; 5:30-10pm Sun & Mon, to 10:30pm Tue-Thu, to 11pm Fri & Sat) With its gorgeous woodwork and good happy hour, Fiamma is a top-tier dining experience you won't be paying off for the next decade. You haven't had spaghetti until you've had Fiamma's take on it, made with Kobe beef meatballs.
Seablue SEAFOOD $$$
( 702-891-3486; www.michaelmina.net; MGM Grand, 3799 Las Vegas Blvd S; mains $19-45; cafe lunch & dinner, restaurant dinner) Anything from Nantucket Bay scallops to Manila clams comes raw, fried, steamed or roasted out of two exhibition kitchens. Create your own farm fresh salads, or come for the shrimp and oyster happy hour from 5:30pm to 7:30pm.
Wolfgang Puck Pizzeria & Cucina MEDITERRANEAN, PIZZERIA $$$
(www.wolfgangpuck.com; Aria; 3720 Las Vegas Blvd S; mains $10-26; 11:30am-10pm, to 11pm Fri & Sat) Dig into crispy, creative pizzas and Cal-Italian classics on the primo terrace upstairs at the Crystals Mall.
### WORTHY INDULGENCES: BEST BUFFETS
The adage 'you get what you pay for' was never truer: most large casino hotels in Nevada lay on all-you-can-eat buffets, but look before you buy. Not all buffets are created equal. No host should stop you from perusing the offerings before putting down your money.
On the Strip, expect to pay $8 to $20 for a breakfast buffet, $15 to $25 for lunch and $20 to $40 or more for dinner or weekend champagne brunch. If you're insanely hungry, go for broke and try the 24-hour Buffet of Buffets (www.caesars.com/buffets; $49.99, or $44.99 if you sign up for the Total Rewards Players Club) pass, which gives you 24-hour access to seven buffets.
Vegas' best buffets, all of which are open for three round meals a day (unless otherwise noted), include the following:
»Wicked Spoon Buffet (www.cosmopolitanlasvegas.com; The Cosmopolitan, 3655 Las Vegas Blvd S)
»Le Village Buffet (www.parislv.com; Paris-Las Vegas, 3655 Las Vegas Blvd S)
»Spice Market Buffet (Planet Hollywood, 3667 Las Vegas Blvd S)
»Golden Nugget (www.goldennugget.com; 129 E Fremont St)
»Sterling Brunch at Bally's ( 702-967-7999; Bally's, 3645 Las Vegas Blvd S; Sun)
»The Buffet ( 702-693-7111; www.bellagio.com; Bellagio, 3600 Las Vegas Blvd S)
»Sunday Gospel Brunch ( 702-632-7600; www.hob.com; House of Blues, Mandalay Bay, 3708 Las Vegas Blvd S)
Bouchon FRENCH $$$
(www.bouchonbistro.com; The Venetian, 3355 Las Vegas Blvd S; breakfast & lunch $12-25. dinner $19-37; 7am-10pm) Thomas Keller's rendition of a Lyonnaise bistro features French classics in a lovely poolside dining room. Come for the extensive raw bar and leisurely, decadent breakfasts.
Society Café CAFE $$$
(www.wynnlasvegas.com; Encore, 3121 Las Vegas Blvd S; mains $14-30; 7am-midnight Sun-Thu, 7am-1am Fri & Sat) A slice of reasonably priced culinary heaven in the midst of Encore's loveliness.
Payard Bistro FRENCH, DESSERTS $$$
( 702-731-7292; Caesars Palace, 3570 Las Vegas Blvd S; breakfast & lunch $16-25, prix-fixe dinner $45-60; 6:30am-11pm, dinner Wed-Sun) Operated by third-generation chocolatier Françoise Payard, this exquisite place offers fresh takes on bistro classics and outrageously indulgent dessert-only dinner menus. Take-out pastry and espresso bar.
Stripburger BURGERS $
(www.stripburger.com; Fashion Show, 3200 Las Vegas Blvd S; items $4-10; 11:30am-1am Sun-Thu, to 2am Fri & Sat; ) On a bustling (read: loud) corner outside the mall, a silver diner-in-the-round serves up all-natural beef, chicken, tuna and veggie burgers, with stupendous cheese fries, thick milkshakes and gigantic cocktails.
##### DOWNTOWN
Fremont St is the neon-illuminated land of cheap and bountiful buffets, retro cafes and authentic ethnic hideaways.
Lillie's Asian Cuisine ASIAN $$$
(www.goldennugget.com; Golden Nugget, 129 E Fremont St; mains $19-35; dinner Mon & Thu-Sun) For sheer fun, this is one of downtown's top eating experiences. Amid blood-red light sculptures and walls of water flowing over glass, hibachi chefs dazzle with flashing knife tricks. Sit around an illuminated marble table and take your pick from seafood, steak and veggies, lit aflame as you watch.
Florida Café CUBAN $$
(www.floridacafecuban.com; Howard Johnson's, 1401 Las Vegas Blvd S; mains $9-18; 7am-10pm) Among a spirited local scene with live music some nights, enjoy authentic shredded steak and seasoned chicken with yellow rice. _Café con leche,_ flan and _batidos_ (tropical shakes) are superb.
### CHEAP EATS FOR LOSERS
Lucky streak on the downswing? Seeking solace in the form of comfort food at 3am, but are down to the last roulette bet in your pocket? Join the club.
»24-hour omelets at the Peppermill
»$1.99 shrimp cocktail at Golden Gate
»Old fashioned cheeseburgers and malts at vintage diner Tiffany's Cafe
»$4.99 steak and eggs at Mr. Lucky's
»The cheap and tasty buffet at Main Street Station
»Everything on the menu is half price during happy hour (4pm to 8pm) at Blue Martini
»Locals are in on the tastiest late-night dining deal in Vegas: happy hour antipasti at Ferraro's from 10pm to 2am (and 4pm to 7pm) Monday to Friday
»Half off all food (and drinks!) on Tuesdays to 1am, plus other days between 5pm and 7pm at Paymon's Mediterranean Cafe
Triple George Grill SUPPER CLUB $$$
( 702-384-2761; www.triplegeorgegrill. com; 201 N 3rd St; lunch $10-27, dinner $13-37; 11am-10pm Mon-Fri, 4pm-10pm Sat) Inspired by San Francisco's legendary Tattage Grill, this art-decoish joint feels like Sinatra himself might have breezed in post-concert for a filet mignon. Against a swinging 1940s soundtrack, sip a stiff martini at the mile-long bar, or head next door to the vintage Sidebar for a cigar.
Aloha Specialties HAWAIIAN $
(Hotel California; mains $4-8, cash only; 9am-9pm, to 10pm Fri & Sat) The local secret that even Hawaii transplants crave: think fried mahi mahi, giant teriyaki rice bowls and creamy coconut pudding. Where else in Vegas can you get Spam for breakfast?
Second Street Grill STEAK $$$
( 702-385-3232; Fremont, 200 E Fremont St; mains $19-35; dinner Mon & Thu-Sun) At this unabashedly rococo gem, chef Rachel Bern flies in the seafood fresh from Hawaii. You can score a 16oz T-bone steak with all the trimmings for under 20 bucks, too.
Golden Gate SEAFOOD $
( 702-385-1906; 1 E Fremont St; 11am- 3am) Famous $1.99 shrimp cocktails (supersize 'em for $3.99).
Grotto ITALIAN $$$
( 702-385-7111; Golden Nugget, 129 E Fremont St; mains $13-30; 11:30am-10:30pm Sun-Thu, to 11:30pm Fri & Sat) A convivial spot to nosh on housemade pastas with a unique shark tank view. On a blackjack run and forgot dinner? Wood-fired pizzas and 200 wines are available at the bar until 1am.
##### EAST & WEST OF THE STRIP
Pan-Asian delights and several food trucks – part of Vegas' new craze – await around the Spring Mountain Rd strip malls of Chinatown.
Ferraro's ITALIAN $$$
(www.ferraroslasvegas.com, 4480 Paradise Rd; mains $10-39; 11:30am-2am weekdays, 4pm-2am Sat & Sun) The photos on the wall offer testimony to the fact that locals have been flocking to classy, family-owned Ferraro's for 85 years to devour savory Italian classics. These days, the fireplace patio and the amazing late night happy hour draw an eclectic crowd full of industry and foodie types at the friendly bar. To-die-for housemade pastas compete for attention with legendary osso buco, and a killer antipasti menu served till midnight.
Firefly TAPAS $$
(www.fireflylv.com; 3900 Paradise Rd; small dishes $4-10, large dishes $11-20; 11:30am- 2am Sun-Thu, to 3am Fri & Sat) Locals seem to agree on one thing about the Vegas food scene: a meal at Firefly can be twice as much fun as an overdone Strip restaurant, and half the price. Is that why it's always hopping? Nosh on traditional Spanish tapas, while the bartender pours sangria and flavor-infused mojitos.
Luv-It Frozen Custard ICE CREAM $
( 702-384-6452; 505 E Oakey Blvd; items $2.50- 6; 1-10pm Sun-Thu, 1-11pm Fri & Sat; ) A local mecca since 1973, Luv-It's handmade concoctions are creamier than ice cream. Flavors change daily, so you'll be tempted to go back. Try the Luv-It special (straw berries, salted pecans, cherry) or a double-thick milkshake. Cash only.
Pink Taco MEXICAN $$
(www.hardrockhotel.com; Hard Rock, 4455 Paradise Rd; mains $8-24; 7am-11am Mon-Thu, to 3am Fri & Sat) Whether it's the 99¢ taco and margarita happy hour, the leafy poolside patio or the friendly rock and roll clientele, Pink Taco always feels like a worthwhile party.
Paymon's Mediterranean Café MEDITERRANEAN $$
(www.paymons.com; 4147 S Maryland Pkwy; mains $8-20; 11am-1am Sun-Thu, to 3am Fri & Sat; ) One of the city's few veggie spots serves baked eggplant with fresh garlic, baba ganoush, tabbouleh and hummus. The adjacent Hookah Lounge is a tranquil by day, too-much-fun by night spot to chill with a water pipe and fig-flavored cocktail.
Lotus of Siam THAI $$$
(www.saipinchutima.com; 953 E Sahara Ave; mains $8.95-28.95; 11:30am-2pm Mon-Fri, 5:30-9:30pm Mon-Thu, 5:30-10pm Fr & Sat) The top Thai restaurant in the US? According to _Gourmet Magazine,_ this is it. One bite of simple pad Thai – or any of the exotic northern Thai dishes – nearly proves it.
Alizé FRENCH $$$
( 702-951-7000; Palms, 4321 WFlamingo Rd; mains $36-68; dinner) __ André Rochat's top-drawer gourmet room is named after a gentle Mediterranean trade wind. The panoramic floor-to-ceiling views (enjoyed by every table) are stunning, just like the haute French cuisine. A huge wine-bottle tower dominates the room.
Veggie Delight VEGETARIAN $
(www.veggiedelight.biz; 3504 Wynn Rd; items $3-10; 11am-9pm; ) Buddhist-owned, Vietnamese-flavored vegetarian/vegan kitchen mixing up chakra color-coded Chinese herbal tonics.
Harrie's Bagelmania BAKERY, DELI $
( 702-369-3322; 855 E Twain Ave; items from $1.50, mains $4-8; 6:30am-3pm; ) __ Best bagels in Vegas? Even New Yorkers swear by this Kosher deli and bakery, with fantastic breakfast sandwiches.
Mr. Lucky's AMERICAN $$
(www.hardrockhotel.com; Hard Rock, 4455 Paradise Rd; mains $5-16; 24hr; ) __ If curing your hangover with a 'Rehab breakfast' while a giant portrait of Jim Morrison stares down at you amid the glow of vintage motel signs appeals, this joint's for you.
#### Drinking
For those who want to mingle with the locals and drink for free, check out SpyOnVegas (www.spyonvegas.com).
### BLOODY GOOD STEAKS
Vegas caters to all kinds of steak lovers, whether you like it rare or well-done, celebrity or local, retro or mod, and your background music Frank Sinatra or Lady Gaga.
»STK ( 702-698-7990; www.stkhouse.com; Cosmopolitan, 3950 Las Vegas Blvd S; mains $22-69; dinner) Vegas' uber-stylish new 'Not Your Daddy's' steakhouse, flush with fashionistas, high rollers and hipsters, rocks a club vibe with DJs that you'll love or hate.
»Golden Steer ( 702-384-4470; www.goldensteersteakhouselasvegas.com; 308 W Sahara; mains $30-55; 11:30am-4:30pm Mon-Fri, 5pm-11pm daily) A fabulously retro steakhouse where the Rat Pack once dined. The steak and the tableside Caesar salad are perfectly good, but you're here to soak up the old Vegas vibe and your waiter's salty tales.
»Stripsteak ( 702-632-7414; www.mandalaybay.com; Mandalay Bay, 3950 Las Vegas Blvd S; mains $25-72; 5:30-11pm) Famed seafood chef Michael Mina has dived into the competitive world of Vegas steakhouses. An exceptional menu of Angus and Kobe beef delightfully detours from tradition.
»Victorian Room (www.billslasvegas.com; Bill's Gamblin' Hall & Saloon, 3595 Las Vegas Blvd S; mains $8-25; 24hr) A hokey old-fashioned San Francisco theme belies one of the best deals in sit-down restaurants in Las Vegas. The rib-eye or steak and eggs specials are delicious around the clock.
»N9NE ( 702-933-9900; Palms, 4321 W Flamingo Rd; mains $26-43; dinner) At this hip steakhouse heavy with celebs, a dramatic dining room centers on a champagne and caviar bar. Chicago-style aged steaks and chops keep coming, along with everything from oysters Rockefeller to Pacific sashimi.
##### THE STRIP
One of Vegas' dark secrets: the Strip is packed with over-the-top ultralounges where wannabe fashionistas sip overpriced mojitos and poseur DJs spin mediocre Top-40 mashups. Head to these places instead to avoid the deadly combination of alcohol and boredom.
La Cave WINE BAR
(www.wynnlasvegas.com; Wynn; 3131 Las Vegas Blvd S) This inspired wine and tapas bar is a hidden Strip gem that gets raves from regulars and newbies alike in every category: wine, food, service, value and ambiance.
Chandelier Bar BAR
(www.cosmopolitanlasvegas.com; Cosmopolitan, 3709 Las Vegas Blvd S) In a city full of lavish hotel lobby bars, this one pulls out the stops. Kick back with the cosmopolitan hipsters and enjoy the curiously thrilling feeling that you're tipsy inside a giant crystal chandelier.
Parasol Up – Parasol Down BAR, CAFE
(www.wynnlasvegas.com; Wynn, 3131 Las Vegas Blvd S) Unwind with a fresh fruit mojito by the soothing waterfall at the Wynn to experience one of Vegas' most successful versions of paradise.
Gold Lounge LOUNGE, NIGHTCLUB
(www.arialasvegas.com; Aria, 3930 Las Vegas Blvd S) A fitting homage to Elvis, you won't find watered-down Top 40 at this luxe ultralounge done up like a 1970s-era playboy's rec room, but you will find gold, gold and more gold. Make a toast in front of the giant portrait of the King himself.
Mix LOUNGE
(www.mandalaybay.com;64th fl, THEhotel at Mandalay Bay, 3950 Las Vegas Blvd S; cover after 10pm $20-25) THE place to grab sunset cocktails. The glassed-in elevator has amazing views, and that's before you even glimpse the mod interior design and soaring balcony. This is the best bathroom view we've seen – anywhere.
Red Square BAR
(www.mandalaybay.com; Mandalay Bay, 3950 Las Vegas Blvd S) Heaps of Russian caviar, a solid ice bar and over 200 frozen vodkas, infusions and cocktails. Don a Russian army coat to sip vodka in the subzero vault.
Mandarin Bar & Tea Lounge LOUNGE
(www.mandarianoriental.com; Mandarin Oriental, 3752 Las Vegas Blvd S) With panoramic Strip views from the hotel's 23rd floor lobby, this sophisticated lounge serves exotic teas by day and champagne by night.
LAVO LOUNGE, NIGHTCLUB
(www.palazzo.com; Palazzo, 3325 Las Vegas Blvd S) One of the sexiest new restaurant-lounge-nightclub combos for the see-and-be-seen set, LAVO's terrace is the place to be at happy hour. Sip a Bellini in the dramatically lit bar or stay to dance among reclining Renaissance nudes in the club upstairs.
Napoleon's THEME BAR
(Paris-Las Vegas, 3655 Las Vegas Blvd S; 4pm-2am) Be whisked away to a never-neverland of 19th-century France, with overstuffed sofas and over 100 types of bubbly, including vintage Dom Perignon.
O'Sheas BAR
(www.osheaslasvegas.com; 3555 Las Vegas Blvd S; drinks from $2; 24hr) Luckily for the thirsty among us, O'Sheas has a 24-hour happy hour and 'bottle service' that gets you a bottle of Jack Daniel's or Smirnoff vodka and a mixer for $45.
##### DOWNTOWN
Want to chill out with the locals? Head to one of these go-to favorites, and watch for new bastions of hipness as they open up along Fremont St.
Fireside Lounge COCKTAIL BAR
(www.peppermilllasvegas.com; Peppermill, 2985 Las Vegas Blvd S; 24hr) The Strip's most unlikely romantic hideaway is inside the Peppermill, a retro coffee shop serving giant omelets, pancakes and pie to the just married, the freshly divorced and the hungover. Courting couples flock here for the low lighting, sunken fire pit and cozy nooks built for supping on multi-strawed tiki drinks and for acting out your most inadvisable 'what happens in Vegas, stays in Vegas' moments.
Beauty Bar COCKTAIL BAR
(www.beautybar.com; 517 E Fremont St; cover $5-10; 10pm-4am) At the salvaged innards of a 1950s New Jersey beauty salon, swill a cocktail while you get a makeover demo or chill out with the hip DJs and live local bands. Then walk around the corner to the Downtown Cocktail Room, a low-lit speakeasy owned by the friendly young entrepreneurs who run the Beat Coffeehouse.
### EMERGENCY ARTS
A coffee shop, an art gallery, working studios and a de facto community center of sorts, all under one roof and right smack downtown? The Emergency Arts (www.emergencyartslv.com; 520 Fremont St) building, also home to the Beat Coffeehouse (www.thebeatlasvegas.com; sandwiches $6-7; 7am-midnight Mon-Fri, 9am-midnight Sat, 9am-3pm Sun) is a friendly bastion of laid-back cool, with strong coffee and fresh baguette sandwiches against a soundtrack of vintage vinyl spinning on old turntables. It's also home to the retro-fabulous Burlesque Hall of Fame (www.burlesquehall.com; admission free; noon-6pm Fri & Sat, to 3pm Sun). If you're aching to meet some savvy locals who know their way around town, this is your hangout spot. After 7pm they serve beer and wine, and the space transforms into a 21+ venue.
Triple 7 Restaurant & Microbrewery MICROBREWERY
(www.mainstcasino.com; Main St Station; 200 N Main St; cover $5-10; 24hr) Sports fans, tourists and a crusty crowd of gamblers flock to this gargantuan brewpub for excellent happy hour and graveyard specials including decent sushi and microbrews on tap.
##### OFF THE STRIP
Double Down Saloon BAR
(www.doubledownsaloon.com; 4640 Paradise Rd; no cover; 24hr) You can't get more punk rock than a dive whose tangy, blood-red house drink is named 'Ass Juice' and where happy hour means everything in the bar is two bucks. (Ass Juice and a Twinkie for $5; one of Vegas' bizarrely badass bargains.) Killer jukebox, cash only.
Blue Martini COCKTAIL BAR
(www.bluemartinilounge.com; Town Square; 6593 Las Vegas Blvd S) Want to meet an actual Vegas local? (Yes, they do exist.) This is Vegas' friendliest, best-deal happy hour and possibly the perfect antidote to the fear that you could while away your evenings drinking overpriced martinis with tourists.
Frankie's Tiki Room THEME BAR
(www.frankiestikiroom.com; 1712 W Charleston Blvd; average drinks $8; 24hr) At the only round-the-clock tiki bar in the US, the drinks are rated in strength by skulls and the top tiki sculptors and painters in the world have their work on display. After a couple of mai tais in the dim light you might be transported to the South Seas.
ghostbar ULTRA LOUNGE
(www.n9negroup.com; 55th fl, Palms, 4321 W Flamingo Rd; cover $10-25; 8pm-4am) Sure, these days the crowd is thicker with celeb wannabes rather than actual celebs, but this sky-high ultra lounge gets packed nonetheless (and who can tell the difference between the average B-lister and her lookalikes, anyway?) Join hoochie mamas and guys living out their _Entourage_ fantasies on the balcony to take in the admittedly stunning panoramic skyline views.
Hofbräuhaus BEER BAR
(www.hofbrauhauslasvegas.com; 4510 Paradise Rd; 11am-11pm Sun-Thu, to midnight Fri & Sat) This Bavarian beer hall and garden is a replica of the original in Munich. Celebrate Oktoberfest year-round with premium imported suds, trademark _gemütlichkeit_ (congeniality), fair _fräuleins_ and live oompah bands nightly.
#### Entertainment
Las Vegas has no shortage of entertainment on any given night, and Ticketmaster ( 702-474-4000; www.ticketmaster.com) sells tickets for pretty much everything except nightclubs.
###### Nightclubs
Little expense has been spared to bring clubs inside casino hotels on par with NYC and LA in the area of wildly extravagant hangouts. Most are open 10pm to 4am later in the week; cover charges average $20 to $40. For Clubbing FAQs, including how to get on the all-important 'list,' see Click here.
### VEGAS HAPPY HOURS
When the slots have eaten up all of your cash, you might not want to lay down 15 bucks for that pomegranate mojito, even if the ice is hand-crushed and served by a bronzed model in a satin corset. If that's the case, head to one of these happy hours, which feature half-price or discounted drinks, usually in the early evening hours. Contrary to what overpriced bars want you to believe, they do exist in Vegas. Here are a few of the best:
»Double Down Saloon (Click here)
»Blue Martini (Click here)
»Triple 7 Brewery (Click here)
»LAVO (Click here)
»Café Nikki (Click here)
»Firefly (Click here)
»Frankie's Tiki Room (Click here)
Tryst CLUB
(www.trystlasvegas.com; Wynn; 3131 Las Vegas Blvd S) All gimmicks aside, the flowing waterfall makes this place ridiculously (and literally) cool. Blood red booths, and plenty of space to dance ensure that you can have a killer time even without splurging for bottle service.
Marquee CLUB
(www.cosmopolitanlasvegas.com; Cosmopolitan, 3708 Las Vegas Blvd) When someone asks where the coolest club in Vegas is these days, Marquee is lately the undisputed answer. Celebrities (we spotted Macy Gray as we danced through the crowd), an outdoor beach club, hot DJs and that certain _je ne sais quoi_ that makes a club worth waiting in line for.
Surrender CLUB
(www.surrendernightclub.com; Encore; 3121 Las Vegas Blvd S) Even the club-averse admit that this is an audaciously gorgeous place to hang out for an evening, with its saffron-colored silk walls, mustard banquettes and a bright yellow patent leather entrance. Play blackjack by the pool at night or join one of the raging daytime pool parties. Surrender Your Wednesdays is one of the best club nights in town, with plenty of in-the-know locals.
XS CLUB
(Encore; www.xslasvegas.com; 3131 Las Vegas Blvd S) The only club where we've seen club goers jump in the pool to dance (and not be thrown out by the bouncers), XS is an up-and-coming Vegas favorite with a more diverse crowd (read: you won't feel outta place if you're over 30) than most. Dress up or you won't get in.
Drai's CLUB
(Bill's Gamblin' Hall & Saloon; www.drais.net; 3595 Las Vegas Blvd S; 1am-8am Thu-Mon) Feel ready for an after-hours scene straight outta Hollywood? Things don't really get going until 4am, when DJs spinning progressive discs keep the cool kids content. Critics say it's full of cooler-than-thou scenesters; fans say it's the best afterparty in town, especially on Industry Mondays. Dress to kill.
Krāve GAY CLUB
(www.kravelasvegas.com; Miracle Mile Shops, 3663 Las Vegas Blvd S; nightly) Drawing a mixed crowd, it's the hottest gay nightclub in town, and the only one on the Strip. A glam warehouse-sized dance space is packed wall-to-wall with hard bodies and VIP cabanas.
Stoney's Rockin' Country LIVE MUSIC
(www.stoneysrockincountry.com; 9151 Las Vegas Blvd S; cover after 8pm Fri & Sat $10; 7pm-5am Tue-Sat) An off-Strip place worth the trip. Friday and Saturday has all-you-can-drink draft beer specials and free line dancing lessons from 7:30pm to 8:30pm. Bikini bull-riding, anyone?
Moon CLUB
(www.n9negroup.com; 53rd fl, Fantasy Tower, Palms, 4321 W Flamingo Rd) Stylishly outfitted like a nightclub in outer space, the retractable roof opens for dancing under the stars. Admission includes entry to the only Playboy Club in the world, a surprisingly chic and intimate affair whose skyline views are decidedly more eye-popping and dramatic than the, ah, views offered by the surgically-enhanced, bunny-eared blackjack dealers.
Tao CLUB
(www.taolasvegas.co; Venetian, 3355 Las Vegas Blvd S) Some Vegas clubbing aficionados claim that Tao, like a Top 40 hit that's maxed out on radio play, has reached a been-there-done-that saturation point. Newbies however, still gush at the decadent details and libidinous vibe: from the giant gold Buddha to the near-naked go-go girls languidly caressing themselves in rose petal-strewn bathtubs.
###### Live Music
Contact these live-music venues directly for ticket prices and show times.
House of Blues LIVE MUSIC
( 702-632-7600; www.hob.com; Mandalay Bay, 3950 Las Vegas Blvd S) Blues is the tip of the hog at this Mississippi Delta juke joint, showcasing modern rock, pop and soul.
Joint LIVE MUSIC
( 702-693-5066; www.hardrockhotel.com; Hard Rock, 4455 Paradise Rd) Concerts at this intimate venue (capacity 1400) feel like private shows, even when the Killers or Coldplay are in town.
Pearl LIVE MUSIC
( 702-944-3200; www.palms.com; Palms, 4321 W Flamingo Rd) Modern rock acts like Gwen Stefani and Morrissey have burned up the stage at this 2500-seat concert hall with brilliant acoustics.
Sand Dollar Blues Lounge LIVE MUSIC
( 702-871-6651; 3355 Spring Mountain Rd, enter off Polaris Ave; cover $5-10) Dive bar with live blues nightly after 10pm.
###### Production Shows & Comedy
Some say it's a crime to leave town without seeing a show. But choose wisely: plenty of casino stage shows are fairly lame productions with jacked-up prices. The shows we've listed are all established and well-reviewed. In general, you can't go wrong with Cirque du Soleil: the production values, creativity, talent and sheer entertainment value justify the sometimes eye-popping prices.
If you're a comedy fan, check out who's headlining at the Hilton, Flamingo, Caesars Palace and Golden Nugget casino hotels.
You can buy same-day discount tickets for a variety of shows at Tix 4 Tonight ( 877-849-4868; www.tix4tonight.com; Fashion Show, 3200 Las Vegas Blvd S; 11am-8pm), with additional locations on the Strip and downtown, or from Tickets 2Nite ( 702-939-2222; www.tickets2nite.com; Showcase Mall, 3785 Las Vegas Blvd S; 11am-9pm).
LOVE PERFORMING ARTS
( 702-792-7777, 800-963-9634; www.cirquedusoleil.com; Mirage, 3400 Las Vegas Blvd S; tickets $99-150; 7pm & 9:30pm Thu-Mon; ) Another smash hit from Cirque du Soleil, which has a dizzying number of shows on the Strip, LOVE psychedelically fuses the musical legacy of the Beatles with the troupe's aerial acrobatics.
Steel Panther LIVE MUSIC
( 702-617-7777; www.greenvalleyranchresort.com; Green Valley Resort, 2300 Paseo Verde Pkwy, Henderson; admission free; 11pm-late Thu) A hair-metal tribute band makes fun of the audience, themselves and the 1980s with sight gags, one-liners and many a drug and sex reference.
Phantom PERFORMING ARTS
( 702-414-9000, 866-641-7469; www.venetian.com; Venetian, 3355 Las Vegas Blvd S; tickets $69-158; 7pm Mon-Sat, 9:30pm Mon & Sat; ) A $40-million, gorgeous theater mimics the 19th-century Parisian opera house where Andrew Lloyd Webber's musical story takes place. Expect pyrotechnics, an onstage lake and chandelier tricks to wow even musical haters. If the show isn't sold out, ask for a free seat upgrade.
Crazy Horse Paris CABARET
( 702-891-7777, 800-880-0880; www.mgmgrand.com; MGM Grand, 3799 Las Vegas Blvd S; tickets $51-61; 8pm & 10:30pm Wed-Mon) Za, za, zoom. The 100% red room's intimate bordello feel oozes sex appeal. Onstage, balletic dancers straight from Paris' Crazy Horse Saloon perform provocative cabaret numbers.
O PERFORMING ARTS
( 702-796-9999; www.cirquedusoleil.com; tickets $99-200) Still a favorite is Cirque du Soleil's aquatic show, O, performed at the Bellagio.
Zumanity PERFORMING ARTS
( 702-740-6815; www.cirquedusoleil.com; tickets $69-129) A sensual and sexy adult-only show at New York-New York.
Kà PERFORMING ARTS
( 702-891-7777, 877-880-0880; www.ka.com; MGM Grand, 3799 Las Vegas Blvd S; adult $69-150, child $35-75; 7pm & 9:30pm Tue-Sat; c) Cirque du Soleil's sensuous story of imperial twins takes place on moving platforms elevating a frenzy of martial arts-inspired performances.
Improv COMEDY
( 702-369-5223; www.harrahs.com; Harrah's, 3475 Las Vegas Blvd S; admission $29; 8:30pm & 10:30pm Tue-Sun) NYC's well-established showcase spotlights touring stand-up headliners _du jour_.
### VEGAS CLUBBING 101
Brave the velvet rope – or skip it altogether – with these nightlife survival tips culled from Vegas doormen, VIP hosts and concierges.
»Avoid waiting in that long line by booking ahead with the club VIP host. Most bigger clubs have someone working the door during the late afternoon and early evening hours. Stop by in the late afternoon or early evening to get on the list.
»Always be polite and friendly with club staff. Being 'assertive' (aka pushy) usually backfires, possibly leaving you at the back of the line...all night.
»Do dress well. Most clubs have a dress code, and will generally not let in men wearing sneakers, baggy clothes or athletic wear. What's acceptable for a Saturday night outing in the rest of the US may not pass muster here.
»Ask the concierge of your hotel for clubbing suggestions – he or she will almost always have free passes for clubs, or be able to make you reservations with the VIP host.
»Cover charges vary wildly depending on the night, if you have a reservation, and your gender (yep, it's sexist – clubs aim for more women than men). While men usually have to pay a cover charge of between $20 and $40 at the hotter clubs, men who have female friends in their company will have an easier time getting to the front of the line.
»If you hit blackjack at the high-roller table or just want to splurge, think about bottle service: yes, it's expensive (starting at around $300 to $400 and upwards for a bottle, including mixers, plus tax and tip) but it usually waives cover charge (and waiting in line) for your group, plus you get a table.
»Friday and Saturday nights invariably mean crowds and high cover charges, but don't overlook other less-crowded but equally cool weeknights where locals come for special themes, DJs or promotions. Remember, in Vegas it's a 24/7 party: why not go clubbing on Tuesday? (Check hours in advance, however: most clubs go dark between two to four nights a week).
###### Cinemas
Check Fandango ( 800-326-3264; www.fandango.com) for show times and more theater locations.
Las Vegas 5 Drive-In CINEMA
( 702-646-3565; 4150 W Carey Ave, off N Rancho Dr; adult/child $6/free; gates open 6:30pm or 7pm; ) Old-fashioned place screens up to five double-features daily.
Town Square 18 CINEMA
(www.mytownsquarevegas.com; Town Square, 6587 Las Vegas Blvd S; adult/child $10/6.25) Swanky off-Strip cineplex offers digital projection and XL stadium seating.
###### Sports
Although Vegas doesn't have any professional sports franchises, it's a sports-savvy town. You can wager on just about anything at most casinos' race and sports books.
For auto racing, including Nascar, Indy racing, drag and dirt-track races, check out the mega-popular Las Vegas Motor Speedway (www.lvms.com; 7000 Las Vegas Blvd N, off I-15 exit 54).
World-class boxing draws fans from all over the globe to Las Vegas. The biggest and most popular venues include the Mandalay Bay Events Center ( 877-632-7800; www.mandalaybay.com; Mandalay, 3950 Las Vegas Blvd S), MGM Grand Garden ( 877-880-0880; www.mgmgrand.com; MGM Grand, 3799 Las Vegas Blvd S) and the Thomas & Mack Center ( 702-739-3267, 866-388- 3267; www.unlvtickets.com; UNLV campus, S Swenson St at Tropicana Ave) among others.
###### Strip Clubs
Prostitution may be illegal, but plenty of places offer the illusion of sex on demand. R-rated lap dances cost from $20, while X-rated ones take place in the VIP rooms (bottle service required). Unescorted women are usually not welcome at popular strip clubs, including the following.
Spearmint Rhino STRIP CLUB
(www.spearmintrhinolv.com; 3344 S Highland Dr; cover $30; 24hr) Fall in love, if only for two minutes (the length of an average lap dance, that is). Strip club connoisseurs rave about the Rhino.
Treasures STRIP CLUB
(www.treasureslasvegas.com; 2801 Westwood Dr; cover $30; 24hr) Treasures gets raves as much for its four-star steaks as it does for its faux-baroque interior and glam dancers. Good happy hour from 4pm to 8pm with cheap beer and a free buffet.
#### Shopping
The Strip has the highest-octane shopping action, with the full gamut of both chain and designer stores. Downtown is the center of vintage and retro inspired cool. Cruise west of the Strip for XXX adult goods and trashy lingerie. East of the Strip, near UNLV, Maryland Parkway is chock-a-block with hip, bargain-basement shops catering to college students.
###### Shopping Malls & Arcades
Most casino shopping malls and arcades are open from 10am until 11pm Sunday through Thursday, until midnight Friday and Saturday.
Crystals MALL
(www.crystalsatcitycenter.com; 3720 Las Vegas Blvd S) If you're on a first name basis with Stella (McCartney), Donna (Karan), Gianni (Versace) or Nanette (Lepore), you'll feel right at home in Vegas' newest shopping extravaganza.
Forum Shops MALL
(www.caesarspalace.com; 3570 Las Vegas Blvd S) Franklins fly out of Fendi bags faster at Caesars' fancifully gaudy re-creation of an ancient Roman market, housing 160 catwalk designer emporia.
Grand Canal Shoppes MALL
(www.thegrandcanalshoppes.com; Venetian, 3355 Las Vegas Blvd S) Living statues and mezzo-sopranos stroll along the cobblestone walkways of this Italianate indoor mall, winding past 85 upscale shops like BCBG, Burberry, Godiva, Jimmy Choo and Sephora.
Shoppes at the Palazzo MALL
(www.theshoppesatthepalazzo.com; Palazzo, 3327 Las Vegas Blvd S). Next door to Grand Canal, Palazzo is anchored by Barneys New York. Over 80 international designers, from Tory Burch to Jimmy Choo, flaunt their goodies.
Wynn Esplanade MALL
(www.wynnlasvegas.com; 3131 Las Vegas Blvd S) Wynn has lured high-end retailers like Oscar de la Renta, Jean-Paul Gaultier, Chanel and Manolo Blahnik to a giant concourse of consumer bliss.
Miracle Mile Shops MALL
(www.miraclemileshopslv.com; Planet Hollywood, 3663 Las Vegas Blvd S) A staggering 1.5 miles long; get a tattoo, drink and rock star duds.
Fashion Show Mall MALL
(www.thefashionshow.com; 3200 Las Vegas Blvd S) Nevada's biggest and flashiest mall.
Las Vegas Premium Outlets MALL
(www.premiumoutlets.com; 875 S Grand Central Pkwy) Discount-shopping outlet mall features high-end names such as Armani Exchange, Calvin Klein, Dolce & Gabbana, Guess and Max Studio, alongside casual everyday brands like Levi's.
Not Just Antiques Mart ANTIQUES
(www.notjustantiquesmart.com; 1422 Western Ave; 10:30am-5:30pm Mon-Sat) It's a one-stop antique-shopping extravaganza in the downtown arts district. Look for art-deco estate jewelry, casino memorabilia and vintage tiki ware.
###### Clothing & Jewelry
Attic VINTAGE
(www.atticvintage.com; 1018 S Main St; 10am-6pm, closed Sun) Be mesmerized by fabulous hats and wigs, hippie-chic clubwear and lounge-lizard furnishings at Vegas' best vintage store.
Buffalo Exchange USED CLOTHING
(www.buffaloexchange.com; 4110 S Maryland Pkwy; 10am-8pm Mon-Sat, 11am-7pm Sun) Trade in your nearly new garb for cash or credit at this savvy secondhand chain. They've combed through dingy thrift- store stuff and culled only the best 1940s to '80s vintage fashions, clubwear and designer duds.
Fred Leighton: Rare
Collectible Jewels JEWELRY
(www.fredleighton.com; Via Bellagio, 3600 Las Vegas Blvd S; 10am-midnight) Many Academy Awards night adornments are on loan from the world's most prestigious collection of antique jewelry
### WANT MORE?
For in-depth information, reviews and recommendations at your fingertips, head to the Apple App Store to purchase Lonely Planet's _Las Vegas City Guide_ iPhone app.
###### Weird & Wonderful
Bonanza Gift ShopSOUVENIRS
(www.worldslargestgiftshop.com; 2460 Las Vegas Blvd S; 8am-midnight) If it's not the 'World's Largest Gift Shop,' it's damn close. The amazing kitsch selection of overpriced souvenirs includes entire aisles of dice clocks, snow globes, tacky T-shirts and shot glasses. If you're seeking R (or X) rated gifts, check out the adult-only annexe of the store, where grown adults can be spotted blushing and giggling as they peruse candy underwear and naughty games.
Gamblers General StoreSOUVENIRS
(www.gamblersgeneralstore.com; 800 S Main St; 9am-6pm) It boasts one of the largest inventories of slot machines in Nevada, with new models and beautiful vintage machines, plus loads of souvenir gambling paraphernalia.
Strings of Las VegasACCESSORIES
(www.stringsvegas.com; 4970 Arville St; noon- 8pm Mon-Sat) All those hard-working sexy women and beefy guys obviously don't have time to make their own G-strings and tasseled undies. This industrial strip-mall warehouse outfits them from head to toe, with almost nothing in between.
Houdini's Magic ShopQUIRKY
(www.houdini.com; Forum Shops, 3500 Las Vegas Blvd S) The legendary escape artist's legacy lives on at this shop packed with gags, pranks, magic tricks and authentic Houdini memorabilia. Magicians perform, and each purchase includes a free private lesson.
Zia RecordsMUSIC
(www.ziarecords.com; 4225 S Eastern Ave; 10am-midnight) You can dig up a demo by Vegas' next breakout band (who needs the Killers anyway?) at this shop, which calls itself the 'last real record store.' Live instore performances go off on a stage, with a warning sign: 'No moshing allowed.'
Bauman's Rare BooksBOOKS
(www.baumanrarebooks.com; Shoppes at the Palazzo, 3327 Las Vegas Blvd S; 10am-11pm) Book lovers won't want to miss browsing Bauman's, where rare first editions of books like _The Great Gatsby and Huckleberry Finn_ sit side-by-side with historical documents signed by US presidents and historic figures.
#### Information
###### Emergency
Gamblers Anonymous ( 702-385-7732; www.gamblersanonymous.com) Assistance with gambling concerns.
Police (www.lvmpd.com; 702-828-3111)
Rape Crisis Hotline ( 702-366-1640)
###### Internet Access
Wi-fi is available in most hotel rooms (about $10 to $25 per day, sometimes included in the 'resort fee') and there are internet kiosks with attached printers in most hotel lobbies. Free wi-fi hotspots are found at some chain coffee shops, casual restaurants and off -Strip at the airport and convention center. If you didn't bring your laptop, try:
FedEx Kinko's (www.fedexkinkos.com) Downtown ( 702-383-7022; 830 S 4th St; per min 10-30¢; 7am-9pm Mon-Fri, 9am-5pm Sat); East of the Strip ( 702-951-2400; 395 Hughes Center Dr; per min 10-30¢; 24hr)
###### Media
The conservative daily _Las Vegas Review-Journal_ (www.lvrj.com) is Nevada's largest newspaper, publishing Friday's _Neon_ entertainment guide. Free alternative tabloid weeklies include _Las Vegas Weekly_ (www.lasvegasweekly.com), with good restaurant and entertainment listings, and _Las Vegas CityLife_ (www.lasvegascitylife.com). Available in hotel rooms and at the airport, free tourist magazines like _Las Vegas Magazine + Showbiz Weekly_ and _What's On_ contain valuable discount coupons and listings of attractions, entertainment, nightlife, dining and more.
###### Medical Services
Harmon Medical Center ( 702-796-1116; www.harmonmedicalcenter.com; 150 E Harmon Ave; 24hr) Discounts for uninsured patients; limited translation services.
Sunrise Hospital & Medical Center ( 702-731-8000; www.sunrisehospital.com; 3186 S Maryland Pkwy)
University Medical Center ( 702-383-2000, emergency 702-383-2661; www.umcsn.com; 1800 W Charleston Blvd; 24hr) Nevada's most advanced trauma center.
Walgreens The Strip ( 702-739-9645; 3765 Las Vegas Blvd S; 24hr); Downtown ( 702-385-1284; 495 E Fremont St; 24hr) Call for prescription pharmacy hours.
###### Money
Every casino and bank and most convenience stores have ATMs. Fees imposed by casinos for foreign-currency exchange and ATM transactions (which usually carry a $5 fee) are much higher than at banks.
American Express ( 702-739-8474; Fashion Show, 3200 Las Vegas Blvd S; 10am-9pm Mon-Fri, to 8pm Sat, noon-6pm Sun) Changes currencies at competitive rates.
TIPPING Dealers expect to be tipped (or 'toked') only by winning players, typically with a side bet that the dealer collects if the bet wins. Buffet meals are self-serve, but leave a couple of dollars per person for the waitstaff who bring your drinks and clean your table. Valet parking is usually free, but tip at least $2 when the car keys are handed back to you.
###### Post
Post office Downtown (www.usps.com; 201 Las Vegas Blvd S 8:30am-5pm Mon-Fri); Strip Station (www.usps.com; 3100 S Industrial Rd; 8:30am-5pm Mon-Fri)
###### Tourist Information
Las Vegas Visitor Information Center OR Las Vegas Convention & Visitors Authority ( 702-892-0711, 877-847-4858; www.visitlasvegas.com; 3150 Paradise Rd; 8am-5pm) Helpful hotline (6am to 9pm), and an office with free local calls, internet access and maps galore.
###### Websites
Cheapo Vegas (www.cheapovegas.com) Good for a run-down of casinos with low table limits and their insider's guide to cheap eating.
Only Vegas (www.visitlasvegas.com) The city's official tourism site.
Raw Vegas (www.rawvegas.tv) Programing 24/7, from daily news to reality vlogs.
Las Vegas.com (www.lasvegas.com) Travel services.
Lasvegaskids.net (www.lasvegaskids.net) The lowdown on what's up for the wee ones.
Vegas.com (www.vegas.com) Travel information with booking service.
#### Getting There & Away
###### Air
Las Vegas has direct flights (including many cheap deals) from most US cities, as well as some Canadian, Mexican, European and Asian gateways. During peak periods (eg holidays, weekends), vacation packages including airfare and accommodations can be fair deals.
Near the South Strip, McCarran International Airport ( 702-261-5211; www.mccarran.com; 5757 Wayne Newton Blvd; ) offers free internet access; ATMs, currency-exchange booths and a bank; a post office; a 24-hour fitness center (day pass $10) and a kids' play area. Left-luggage lockers are unavailable post-September 11. Most domestic airlines use Terminal 1; international, charter and some domestic flights use Terminal 2. A free, wheelchair-accessible tram links outlying gates. Short-term metered parking costs 25¢ per 10 minutes.
###### Bus & Train
Long-distance Greyhound buses arrive at a downtown bus station ( 702-384-9561; Plaza, 200 S Main St). Amtrak's California Zephyr follows I-80 across northern Nevada, stopping in Reno, Winnemucca and Elko en route to Chicago from San Francisco Bay. The nearest Amtrak station to Las Vegas, however, is in Kingman, AZ. Greyhound may provide connecting Thruway motor coach service to Las Vegas ($27 to $34, 2¾ to four hours).
###### Car & Motorcycle
The main roads into and out of Las Vegas are I-15 and US Hwy 95. US Hwy 93 leads southeast from downtown to Hoover Dam; I-215 goes by McCarran International Airport. It's a 165-mile drive (2½ hours) to Utah's Zion National Park, 275 miles (4½ hours) to Arizona's Grand Canyon Village and 270 miles (four hours) to Los Angeles. Along the I-15 corridor to/from California, Highway Radio (98.1FM, 99.5FM) broadcasts traffic updates every 30 minutes.
For car rental companies and policies, see Click here.
#### Getting Around
Gridlock along the Strip makes navigating the city's core a chore. The best way to get around is on foot, along with the occasional air-con taxi, monorail or bus ride.
###### To/From the Airport
Shuttle service remains the fastest affordable option. Bell Trans ( 702-739-7990; www.bell-trans.com) operates shuttles ($7) between the airport and the Strip. Fares to downtown or off Strip destinations are slightly higher. At the airport, exit door 9 near baggage claim to find the Bell Trans booth.
Taxi fares to Strip hotels – 30 minutes in heavy traffic – run $10 to $15 (to downtown, average $20), cash only. Fare gouging ('long-hauling') through the airport connector tunnel is common; ask your driver to use surface streets instead. If you're traveling light, CAT bus No 109 ($2, 30 to 60 minutes) runs downtown 24/7. Between 5am and 2am, CAT bus 108 ($2, 40 to 55 minutes) also heads downtown, stopping at the Las Vegas Convention Center, Hilton and Sahara monorail stations.
###### Car & Motorcycle
RENTAL
Trying to decide whether to rent a car in Vegas? The biggest pro: all of the attractions in Vegas have free self-parking and valet parking available. The biggest cons: car rentals in Las Vegas are more expensive than elsewhere in the Southwest, and using a car to navigate the Strip (especially in the evening) will certainly transport you to Venice, Paris or New York– but not in the way you'd imagined.
Hertz ( 800-654-3131; www.hertz.com) rents cars at the McCarran International Airport. Booking ahead is essential on weekends, with the airport usually being cheaper than the Strip or downtown.
TRAFFIC
Traffic often snarls, especially during morning and afternoon rush hours and at night on weekends around the Strip. Work out in advance which cross street will bring you closest to your destination and try to utilize alternate routes like Industrial Rd and Paradise Rd. Tune to 970AM for traffic updates. If you're too drunk to drive, call Designated Drivers ( 702-456-7433; 24hr) to pick you up and drive your car back to your hotel; fees vary, depending on mileage.
###### Public Transportation
The fast, frequent monorail (www.lvmonorail.com; 1-/2-ride ticket $5/9, 24/72hr pass $12/28, child under 6 free; 7am-2am Mon-Thu, to 3am Fri-Sun) stops at the MGM Grand, Bally's/Paris-Las Vegas, Flamingo/Caesars Palace, Harrah's/Imperial Palace, Las Vegas Convention Center and Las Vegas Hilton stations. A discounted six-ride ticket ($20) can be used by multiple riders.
Citizens Area Transit (CAT; 702-228-7433, 800-228-3911; www.catride.com; 24hr pass $5; most routes 5am-2am) operates dozens of local bus lines (one-way fare $2) and double-decker the 'Deuce' buses (2-hour/24-hour pass $5/7), which run 24/7 along the Strip to and from downtown. Cash only (exact change required).
Many off-Strip hotels and resorts offer guests free shuttle buses or trams to/from and around the Strip: ask your concierge what your hotel offers.
###### Taxi
It's illegal to hail a cab on the street. Taxi stands are found at casino hotels and malls. A 4.5-mile lift from one end of the Strip to the other runs $12 to $16, plus tip. Fares (cash only) are metered: flagfall is $3.30, plus $2.60 per mile and 20¢ per minute while waiting. By law, the maximum number of passengers is five, and all companies must have at least one wheelchair-accessible van. Call Desert Cab ( 702-386-9102), Western Cab ( 702-736-8000) or Yellow/Checker/Star ( 702-873-2000).
## AROUND LAS VEGAS
You might be surprised to discover geologic treasures in Nevada's amazing wind- and water-carved landscape, all within a short drive of surreal facsimiles of Ancient Rome and belle-époque Paris. While Las Vegas may be the antithesis of a naturalist's vision of America, it's certainly close to some spectacular outdoor attractions. For iconic desert landscapes, Red Rock Canyon and Valley of Fire State Park are just outside the city limits. Straddling the Arizona–Nevada state line are Hoover Dam, just outside Boulder City, and the cool oasis of Lake Mead National Recreation Area.
#### Tours
Hoover Dam package deals can save ticketing and transportation headaches, while adventure outfitters ease logistical hassles for many outdoor excursions. Some tours include free pick-ups and drop-offs from Strip casino hotels. Check free Vegas magazines for deals.
Black Canyon River Adventures RAFTING
( 702-294-1414, 800-455-3490; www.blackcanyonadventures.com; Hacienda Hotel & Casino, off US Hwy 93, Boulder City; adult/child $88/54) Motor-assisted Colorado River raft floats launch beneath Hoover Dam, with stops for swimming and lunch.
Desert Adventures KAYAKING, HIKING
( 702-293-5026; www.kayaklasvegas.com; 1647 Nevada Hwy, Suite A, Boulder City; trips from $149) With Lake Mead and Hoover Dam just a few hours' drive away, would-be river rats should check out Desert Adventures for lots of half-, full- and multiday kayaking adventures. Hiking, horseback and mountain-bike trips, too.
### Red Rock Canyon
The startling contrast between Las Vegas' artificial neon glow and the awesome natural forces in this national conservation area (www.redrockcanyonlv.org; day-use per car/bicycle $7/3; scenic loop 6am-dusk) can't be exaggerated. Created about 65 million years ago, the canyon is more like a valley, with a steep, rugged red rock escarpment rising 3000ft on its western edge, dramatic evidence of tectonic-plate collisions.
### MOVING ON?
For tips, recommendations and reviews, head to shop.lonelyplanet.com to purchase a downloadable PDF of the Palm Springs and the Desert chapter from Lonely Planet's _California_ guide.
A 13-mile, one-way scenic drive passes some of the canyon's most striking features, where you can access hiking trails and rockclimbing routes, or simply be mesmerized by the vistas. Stop at the visitor center ( 702-515-5350; 8:30am-4:30pm), for its natural-history exhibits and information on hiking trails, rock-climbing routes and 4WD routes. Red Rock Canyon Interpretive Association ( 702-515-5361/5367; www.redrockcanyonlv.org) operates the nonprofit bookstore there and organizes activities, including birding and wildflower walks (advance reservations may be required).
Call ahead to reserve guided horseback tours led by Cowboy Trail Rides ( 702-387- 2457; www.cowboytrailrides.com; off Hwy 159; tours $69-339; ). Mountain biking is allowed only on paved roads, not dirt trails. Rent bikes at Las Vegas Cyclery ( 702-596-2953; www.lasvegascyclery.com; 8221 W Charleston Blvd; per day from $30; 10am-6pm Mon-Fri, 9am-6pm Sat, 10am-4pm Sun) in suburban Summerlin.
To get here from the Strip, take I-15 south, exit at Blue Diamond Rd (NV Hwy 160), and drive westward, veering right onto NV Hwy 159. On the return trip, keep driving east on Hwy 159, which becomes Charleston Blvd. About 2 miles east of the visitor center off NV Hwy 159 is a campground ( 702-515- 5350; tent & RV sites $15; Sep-May), offering first-come, first-served sites with water and vault toilets.
### Spring Mountain Ranch State Park
South of Red Rock Canyon's scenic loop drive, a side road leaves Hwy 159 and enters the petite Spring Mountain Ranch State Park ( 702-875-4141; entry $9; 8am-dusk, visitor center 10am-4pm), abutting the cliff s of the Wilson Range. The ranch was established in the 1860s and has had various owners including the eccentric billionaire Howard Hughes. Popular with picnicking families on weekends, today it's a verdant place, with white fences and an old red ranch house, which has historical exhibits. Call for schedules of guided ranch tours, moonlight canyon hikes and outdoor summer theater performances.
### Lake Mead & Hoover Dam
Even those who challenge, or at least question, the USA's commitment to damming the US West have to marvel at the engineering and architecture of the Hoover Dam. Set amid the almost unbearably dry Mohave Desert, the dam towers over Black Canyon and provides electricity for the entire region.
Hoover Dam created Lake Mead, which boasts 700 miles of shoreline, while Davis Dam created the much smaller Lake Mohave, which straddles the Arizona border. Black Canyon, the stretch of the Colorado River just below Hoover Dam, links the two lakes. All three bodies of water are included in the Lake Mead National Recreation Area, created in 1964.
#### Sights
Hoover DamHISTORIC SITE
( information 702-293-8321, reservations 702- 992-7990, 866-998-3427; www.usbr.gov/lc/hoover dam; US Hwy 93; admission $8, incl power-plant tour adult/child $11/9, all-inclusive tour $30; 9am- 5pm, to 6pm in summer, last ticket sold 45min before closing) A statue of bronze winged figures stands atop Hoover Dam, memorializing those who built the massive 726ft concrete structure, one of the world's tallest dams. Originally named Boulder Dam, this New Deal public works project, completed ahead of schedule and under budget in 1936, was the Colorado River's first major dam. Thousands of men and their families, eager for work in the height of the Depression, came to Black Canyon and worked in excruciating conditions – dangling hundreds of feet above the canyon in 120°F (about 50°C) desert heat. Hundreds lost their lives.
Today, guided tours begin at the visitor center, where a video screening features original footage of the construction. Then take an elevator ride 50 stories below to view the dam's massive power generators, each of which alone could power a city of 100,000 people. Parking at the site costs $7.
### VALLEY OF FIRE STATE PARK
A masterpiece of desert scenery filled with psychedelically shaped sandstone outcroppings, this park (www.parks.nv.gov/vf.htm; admission $10) on the north edge of Lake Mead wows. It's amazing that this fantasyland of wondrous shapes carved in psychedelic sandstone by the erosive forces of wind and water is also a relaxing escape that's only 55 miles from Vegas.
Hwy 169 runs right past the visitor center ( 702-397-2088; 8:30am-4:30pm), which offers information on hiking, and excellent desert-life exhibits. sells books and maps, and has information about ranger-led activities like guided hikes and stargazing.
Take the winding scenic side road out to White Domes, an 11-mile round-trip. En route you'll pass Rainbow Vista, followed by the turn-off to Fire Canyon and Silica Dome (incidentally, where Captain Kirk perished in _Star Trek: Generations_ ).
Spring and fall are the best times to visit; daytime summer temperatures typically exceed 100°F (more than 37°C). The valley is at its most fiery at dawn and dusk, so consider grabbing a first-come, first-served site in the campgrounds (tent/RV sites $20/30). The fastest way here from Las Vegas is to drive I-15 north to NV Hwy 169, taking about an hour.
Hoover Dam Museum MUSEUM
( 702-294-1988; www.bcmha.org; Boulder Dam Hotel, 1305 Arizona St, Boulder City; adult/child $2/1; 10am-5pm Mon-Sat; ) You'll enjoy the dam tour more if you stop at this small but engagingly hands-on museum first. It's upstairs at the historic Boulder Dam Hotel, where Bette Davis, FDR and Howard Hughes once slept. Exhibits focus on Depression-era America and the tough living conditions endured by the people who came to build the dam. A 20-minute film features historic footage of the project.
Mike O'Callaghan-Pat
Tillman Memorial Bridge BRIDGE
Featuring a pedestrian walkway with perfect views upstream of Hoover Dam, this bridge is definitely not recommended for anyone with vertigo. Mike O'Callaghan was governor of Nevada from 1971 to 1979. NFL star Pat Tillman was a safety for the Arizona Cardinals when he enlisted as a US Army Ranger in 2002. He was slain by friendly fire during a battle in Afghanistan in 2004, and top army commanders, who promoted the fabrication that he'd been killed by enemy forces, covered up the circumstances surrounding his death.
#### Activities
For motorized float trips and guided kayaking tours launching below Hoover Dam, see Click here. Popular year-round activities in Lake Mead National Recreation Area ( 702-293-8906; www.nps.gov/lame; 7-day entry pass individual/car $5/10; 24hr) include swimming, fishing, boating, waterskiing and kayaking. The splendid scenic drive winds north along Lakeshore Dr and Northshore Rd, passing viewpoints, hiking and birding trailheads, beaches and bays, and full-service marinas.
Don't overlook a simple stroll around charming, serene Boulder City, the only casino-free town in Nevada. Originally erected to house workers constructing the Hoover Dam, casinos were outlawed to prevent distractions from their monumental task.
Fish Vegas FISHING
( 702-293-6294; www.fishvegas.com; guided tours 1-2 people from $300) Chartered fishing trips on Lake Mead. Go online for Cap'n Mike's monthly fishing reports and news.
Lake Mead Cruises BOAT TOUR
( 702-293-6180; www.lakemeadcruises.com; 90min midday cruise per adult/child $24/12; noon & 2pm) Kid-friendly tours, along with lunch and brunch cruises, on triple-decker, air-con, Mississippi-style paddle wheelers depart from Hemenway Harbor.
###### Hiking
While most visitors come to Lake Mead for the water, there are a handful of hiking trails, too, most of which are short. At Grapevine Canyon near Lake Mohave, for instance, a quarter-mile jaunt takes you to a petroglyph panel, but if you want you can boulder-hop further up the gorge, which cups a ribbon-like stream trickling down from a spring. Longer routes include a 3.7-mile trail along a historic railway line with five tunnels that links the Alan Bible Visitor Center to Hoover Dam. The most challenging hike in the park follows a 3-mile trail down 800ft to a set of hot springs in a slot off Black Canyon. This one's not recommended in summer.
#### Sleeping
Cottonwood Cove Motel MOTEL $$
( 702-297-1464; www.cottonwoodcoveresort.com; r $65-115) On Lake Mohave, this motel has rooms with sliding glass doors overlooking a swimming beach.
NPS Campgrounds CAMPGROUNDS $
( 702-293-8906; tent & RV sites $10) It's first-come, first-served at these campgrounds found on Lake Mead at Boulder Beach, Callville Bay, Echo Bay and Las Vegas Bay.
Boulder Dam Hotel HOTEL $$
(www.boulderdamhotel.com; 702-293-3093; r $64-140; ) For a peaceful night's sleep worlds away from the madding crowds and neon of Vegas, this gracious Dutch Colonial-style hotel has welcomed illustrious guests since 1933. Relax with a cocktail at the art-deco jazz lounge onsite.
#### Eating
Milo's WINE BAR $$
(www.miloswinebar.com; 538 Nevada Way; dishes $4.50-13; 11am-10pm Sun-Thu, to midnight Fri & Sat) In downtown Boulder City, Milo's serves fresh sandwiches, salads and gourmet cheese plates at sidewalk tables outside the wine bar.
Le Bistro Café ITALIAN $$
( 702-293-7070; 1312 Nevada Hwy; mains $12-18; dinner) Order home-cooked classic Italian pasta dishes and meatier fare, with tiramisu afterward.
You'll find only basic restaurants at the Temple Bar, Boulder Beach and Echo Bay marinas on Lake Mead, and at Cottonwood Cove and Katherine Landing on Lake Mohave. Other lakeshore marinas have convenience stores for snacks and drinks.
#### Information
Boulder City ( 702-294-1252; 100 Nevada Hwy, off US Hwy 93; 8am-4:30pm) Near Hoover Dam.
Alan Bible Visitor Center ( 702-293-8990; Lakeshore Scenic Dr, off US Hwy 93; 8am-4:30pm) In Nevada, 5 miles west of Hoover Dam. Excellent source of information on area recreation and desert life.
Katherine Landing Ranger Station ( 928-754-3272; off AZ Hwy 68, Bullhead City; 8:30am-4pm) In Arizona, 3 miles north of Davis Dam.
#### Getting There & Away
From the Strip, take I-15 south to I-215 east to I-515/US 93 and 95 and continue over Railroad Pass, staying on US Hwy 93 past Boulder City. As you approach the dam, park in the multilevel parking lot ($7, cash only; open 8am to 6pm) before you reach the visitor center. Or continue over the Arizona state line and park for free on the roadside (if you can find a space), then walk back over the top of the dam to the visitor center.
### Mt Charleston
Up in the Humboldt-Toiyabe National Forest, the Spring Mountains form the western boundary of the Las Vegas valley, with higher rainfall, lower temperatures and fragrant pine, juniper and mahogany forests.
Just past the NV Hwy 158 turn-off and campground, the information station ( 702-872-5486; www.fs.fed.us/r4/htnf; Kyle Canyon Rd; hours vary) has free trail guides, brochures and outdoor activity information.
The village of Mt Charleston gives access to several hikes, including the demanding 16.6-mile round-trip South Loop Trail up Charleston Peak (elevation 11,918ft), starting from Cathedral Rock picnic area. The easier, 2.8-mile round-trip Cathedral Rock Trail offers canyon views.
Mt Charleston Lodge ( 702-872-5408, 800-955-1314; www.mtcharlestonlodge.com; 1200 Old Park Rd; cabins $108-295; ) has a chalet-style dining room (mains $11-24; 8am-9pm Sun-Thu, 8am-10pm Fri & Sat) and rustic, romantic log cabins with fireplaces, whirlpool tubs and private decks.
Heading back downhill, turn left onto Hwy 158, a curvy alpine road that passes even more trailheads and campgrounds ( reservations 518-885-3639, 877-444-6777; www.recreation.gov; tent & RV sites $15-25; mid-May–Oct, some year-round). At NV Hwy 156 (Lee Canyon Rd), turn either right to return to US Hwy 95 or left to reach Las Vegas Ski & Snowboard Resort ( 702-385-2754, snow report 702-593-9500; www.skilasvegas.com; half-day pass adult/child $50/30; usually mid-Nov–Apr; ), which has four lifts, 11 trails (longest run 3000ft) and a half-pipe and terrain park for snowboarding.
### PIONEER SALOON
Seven miles west of Jean, near the California border, have a mini Wild West adventure in the almost ghost town of Goodsprings where the tin-roofed Pioneer Saloon ( 702-874-9362; 11am-late) dates from 1913. Riddled with bullet holes, it still serves up cold beers atop an antique cherrywood bar. Admire the vintage poker table and movie-star memorabilia.
### Mesquite
Just over an hour's drive northeast of Las Vegas via I-15, Mesquite ( 877-637-7848; www.visitmesquite.com) is another Nevada border town stuffed full of casino hotels, all banking on slot machine-starved visitors from Utah and Arizona. Escape the casi nos by overnighting at the Falcon Ridge Hotel ( 702-346-2200; www.falconridgehotel.com; 1030 W Pioneer Blvd; d $70- 119; ), down the street from Sushi Masa ( 702-346-3434; 155 Pioneer Blvd; mains $6-18; 10am-10pm) where even Californians rave about the sushi lovingly crafted by the talented Japanese chef.
## GREAT BASIN
Geographically speaking, nearly all of Nevada lies in the Great Basin – a high desert characterized by rugged mountain ranges and broad valleys that extends into Utah and California. Far from Nevada's major cities, this land is largely empty, textured only by peaks covered by snow in winter. It's big country out here – wild, remote and quiet. Anyone seeking the 'Great American Road Trip' will savor the atmospheric small towns and quirky diver sions tucked away along these lonely highways. Each of the main routes used by drivers to cut across the state is described here, covering interesting places to stop along the way, plus some unusual detours.
### Along Hwy 95
US Hwy 95 runs vaguely north–south through western Nevada. Although it's hardly a direct route, it's the fastest way to get from Las Vegas to Reno – and still, it's a full day's drive of 450 miles, so get an early start. The highway zigzags to avoid mountain ranges and passes through old mining centers that are not much more than ghost towns today.
##### BEATTY
It's another hour's drive northwest to broken-down Beatty, the northeastern gateway to Death Valley National Park. The chamber of commerce ( 775-553-2424, 866-736-3716; www.beattynevada.org; 119 Main St; 9:30am-2:30pm Tue-Sat) is downtown. Four miles west of town, off NV Hwy 374, is the mining ghost town of Rhyolite (www.rhyolitesite.com; donation appreciated; 24hr), where you can see a 1906 'bottle house' and the skeletal remains of a three-story bank. Next door, the bizarre Goldwell Open Air Museum ( 702-870-9946; www.goldwellmuseum.org; admission free; 24hr) stars Belgian artist Albert Szukalski's spooky _The Last Supper_. Five miles north of town, past the sign for Angel's Ladies brothel, Bailey's Hot Springs ( 775-553-2395; entry $5, tent/RV sites $15/18; 8am-8pm) offers private mineral pools at a 1906 former railroad depot.
##### GOLDFIELD & TONOPAH
Another hour's drive further north, Goldfield became Nevada's biggest boomtown after gold was struck here in 1902. A few precious historic structures survive today, including the Goldfield Hotel; a restored firehouse, now a museum; and the county courthouse, with its Tiff any lamps. Another survivor, the rough-and-tumble Santa Fe Saloon ( 775-485-3431; 925 N 5th Ave; hours vary) is a hoary watering hole.
### WHAT THE...? NEVADA TEST SITE
About 65 miles northwest of Las Vegas, starkly scenic US Hwy 95 rounds the Spring Mountains and passes a side road signposted 'To Mercury.' Behind barbed wire lies the Nevada Test Site, where over 900 atmospheric and underground nuclear explosions were detonated between 1951 and 1992. Free public bus tours ( 702-295-0944; www.nv.doe.gov/nts/tours.htm) depart monthly, usually from Las Vegas' Atomic Testing Museum, but you must apply for reservations months in advance.
Almost 30 miles further north, huge mine headframes loom above Tonopah, a historic silver-mining town that clings to its remaining population in a bereft yet beautiful setting. The Central Nevada Museum ( 775-482-9676; 1900 Logan Field Rd; admission free; 9am-5pm Tue-Sat) has a good collection of Shoshone baskets, early photographs, mining relics and mortician's instruments. The Tonopah Historic Mining Park ( 775-482-9274; www.tonopahhistoricminingpark.com; 520 McCulloch Ave; admission free, walking tours adult/child $5/4; 9am-5pm daily Apr-Sep, 10am-4pm Wed-Sun Oct-Mar) lets you explore an underground tunnel and peer into old silver-mine shafts. At night, it's dark enough for stargazing (www.tonopahstartrails.com).
### AREA 51 & THE EXTRATERRESTRIAL HWY
Die-hard UFO fans and conspiracy theorists won't want to miss the way-out-there trip to Area 51, where some believe secret government research into reverse-engineering alien technology takes place.
Coming from Tonopah, drive east along US Hwy 6 for 50 miles, then follow NV Hwy 375, aka the 'Extraterrestrial Hwy,' for another hour to the roadside pit-stop of Rachel. Have burgers and beer at the Little A'le'Inn ( 775-729-2515; www.littlealeinn.com; 1 Old Mill Rd, Alamo; meals from $5, RV sites with hookups $12, r $50-140; 8am-10pm).
Sky-watchers gather further east at the 29-mile marker on the south side of Hwy 375.
##### HAWTHORNE
The desert surrounding Hawthorne is oddly dotted with concrete bunkers storing millions of tons of explosives from a WWII-era military ammunition depot bizarrely turned into a golf course. Hungry yet? Locals adore Maggie's Restaurant & Bakery ( 775-945-3908; 785 E St; meals $5-15; 7am-8:30pm).
Heading north, Hwy 95 traces the shrinking shoreline of Walker Lake State Recreation Area ( 775-867-3001; www.parks.travelnevada.com; admission free; 24hr), a popular picnicking, swimming, boating and fishing spot that's evaporating fast. Alt-US Hwy 95 is the scenic route to Reno, joining I-80 westbound at Fernley.
### Along Hwy 93
US Hwy 93 is the oft-deserted route from Las Vegas to Great Basin National Park, a 300-mile trip taking over five hours. Expect to pass by mining ghost towns and wide open rangeland populated by more head of cattle than humans.
##### PAHRANAGAT VALLEY
North of I-15, US Hwy 93 parallels the eastern edge of the Desert National Wildlife Range, where bighorn sheep can be spotted. About 90 miles outside of Las Vegas, the road runs by Pahranagat National Wildlife Refuge ( 775-725-3417; www.fws.gov/desertcomplex/pahranagat; admission free; 24hr), where spring-fed lakes surrounded by cottonwoods are a major stopover for migratory birds, and a public rest area provides a good stopover for a bathroom break and a shaded picnic lunch.
##### CALIENTE
Past Alamo and Ash Springs, US Hwy 93 leads to a junction, where you turn east through some desolate countryside to Caliente, a former railroad town with a Mission-style 1923 railway depot that makes for a cool photo op. Locals rave about Pioneer Pizza ( 775-726-3215; 127 N Spring St; mains $10-17; dinner). South of town via NV Hwy 317, Rainbow Canyon is known for its colorful cliffs and petroglyphs.
East of US Hwy 395, take a backcountry drive along NV Hwy 372 to Spring Valley State Park ( 775-962-5102;www.parks.travelnevada.com; entry $7, tent & RV sites $17) or Echo Canyon State Park ( 775-962-5103; www.parks.travelnevada.com; entry $7, tent & RV sites $17), both offering boating and fishing on artificial reservoirs.
##### NORTH TO HWY 50 & I-80
US Hwy 93 continues north for 80 miles to US Hwy 50, heading east to Great Basin National Park or west to Ely.
### Along Hwy 50
The nickname says it all: on the 'Loneliest Road in America' barren, brown desert hills collide with big blue skies. The highway goes on forever, crossing solitary terrain. Towns are few and far between, with the only sounds being the whisper of wind or the rattle-and-hum of a truck engine. Once part of the coast-to-coast Lincoln Hwy, US Hwy 50 follows the route of the Overland Stagecoach, the Pony Express and the first transcontinental telegraph line.
### CATHEDRAL GORGE STATE PARK
Awe, then _ahhh_ : this is one of our favorite state parks ( 775-728-4460; www.parks.nv.gov/cg.htm entry $4, tent & RV sites $10; visitor center 9am-4pm), not just in Nevada, but in the whole USA. Fifteen miles north of Caliente, just past the turn-off to Panaca, Cathedral Gorge State Park really does feel like you've stepped into a magnificent, many-spired cathedral, albeit one whose dome is a view of the sky. Miller Point Overlook has sweeping views, with several easy hikes into narrow side canyons. Sleep under the stars at the first-come, first-served campsites ($17) set amid badlands-style cliffs.
##### FALLON
Look up into the sky and you might spot an F-16 flying over Fallon, home of the US Navy's TOPGUN fighter-pilot school. Dragsters and classic hot rods compete at the Top Gun Raceway ( 775-423-0223; www.topgunraceway.com; tickets $8-65) between March and November.
Besides the usual pioneer relics, the Churchill County Museum & Archives ( 775-423-3677; www.ccmuseum.org; 1050 S Maine St; admission free; 10am-5pm Mon-Sat, closes 1hr earlier Dec-Feb) also displays an interesting replica of a Paiute hut and sponsors twice-monthly guided tours ($1) of Hidden Cave. The cave is near Grimes Point Archaeological Area ( 775-885-6000; www.blm.gov/nv; admission free; 24hr; ), about 10 miles east of Fallon, where a marked trail leads past boulders covered by Native American petroglyphs. Northeast of town, off Stillwater Rd (NV Hwy 166), Stillwater National Wildlife Refuge ( 775-428-6452; www.fws.gov/stillwater; admission free; 24hr) is a haven for over 280 species of birds, best seen during the Spring Wings Festival (www.springwings.org) in mid-May.
##### SAND MOUNTAIN RECREATION AREA
About 25 miles southeast of Fallon off US Hwy 50, this recreation area ( 775-885-6000; www.blm.gov/nv; admission free; 24hr) boasts sand dunes that 'sing,' occasionally producing a low-pitched boom. The best time to hear it is on a hot, dry evening when the dunes are not covered with screeching off-road vehicles and whooping sandboarders. Pony Express station ruins have been excavated at the small Sand Springs Desert Study Area. Designated campsites with vault toilets (no water) are free.
##### COLD SPRINGS
Midway between Fallon and Austin, there's a historical marker on the south side of the highway. There a windswept 1½-mile walking path leads to the haunting ruins of Cold Springs Pony Express Station, built in 1860 but quickly replaced by a stagecoach stop and then the transcontinental telegraph line. It's just about the best place on US Hwy 50 to be carried away by the romance of the Old West. In fact, the mountain vistas alone are worth stopping for, at least to stretch your legs.
##### AUSTIN
Although it looks pretty interesting after hours of uninterrupted basin-and-range driving, there's not much to this mid-19th-century boomtown – really, just a few frontier churches and atmospherically decrepit buildings along the short main street.
What most people come to Austin for is to play outdoors. Mountain biking is insanely popular; the chamber of commerce ( 775-964-2200; www.austinnevada.com; 122 Main St; 9am-noon Mon-Thu) can recommend routes. The USDA Forest Service Austin Ranger District office ( 775-964-2671; www.fs.fed.us/htnf; 100 Midas Canyon Rd, off US Hwy 50; 7:30am-4:30pm Mon-Fri) has info on camping, hiking trails and scenic drives, including the trip to Toquima Cave, where you can see rock art by ancient Shoshones.
Inside a former hotel moved here in pieces from Virginia City in 1863, the International Cafe & Saloon (www.internationalcafeandsaloon.com; 59 Main St; meals $4-11; h6am-8pm) is one of Nevada's oldest buildings. The Toiyabe Cafe ( 775-964-2301; 150 Main St; items $3-10; 6am-2pm Oct-Apr, 6am-9pm May-Sep) is known for its breakfasts.
North of US Hwy 50 at Hickison Summit, about 24 miles east of Austin, Hickison Petroglyph Recreation Area ( 775-635-4000; www.blm.gov/nv; admission & camping free; 24hr; ) has panoramic lookout points; a self-guided, ADA-accessible trail for viewing the petroglyphs; and a primitive campground (vault toilets, no water).
##### EUREKA
Eureka! In the late 19th century, $40 million worth of silver was extracted from the hills around Eureka. Pride of place goes to the county courthouse ( 775-237-5540; 10 S Main St; admission free; 8am-5pm Mon-Fri), with its handsome pressed-tin ceilings and walk-in vaults, and the beautifully restored opera house ( 775-237-6006; 31 S Main St), also dating from 1880, which hosts an art gallery and summer folk-music concerts. The Eureka Sentinel Museum ( 775-237-5010; 10 S Bateman St; admission free; 10am-6pm Tue-Sat Nov-Apr, 10am-6pm daily May-Oct) displays yesteryear newspaper technology and some colorful examples of period reportage. Budget motels and cafes line Main St.
##### ELY
The biggest town for miles around, Ely deserves an overnight stop. Its old downtown has beautiful regional history murals and awesome vintage neon signs.
East of downtown's gambling strip, marked by the 1929 Hotel Nevada and Jailhouse Casino, the White Pine County Tourism & Recreation Board ( 775-289-3720; www.elynevada.net; 150 Sixth St; 8am-5pm Mon-Fri) provides visitor information on zany town events like Cocktails and Cannons and the annual Bathtub Races. Ask about the mysterious Ghost Train and the Ely Renaissance Village (www.elyrenaissance.com; 150 Sixth St; 10am-4pm Sat, Jul-Sep) a collection of 1908 period homes built by settlers from France, Slovakia, China, Italy and Greece.
Ely was established as a mining town in the 1860s, but the railroad didn't arrive until 1907. The interesting East Ely Railroad Depot Museum (www.museums.nevadaculture.org; 1100 Ave A; adult/child $2/free; 8am-4:30pm, Wed-Sat) inhabits the historic depot. There the Nevada Northern Railway ( 775-289-2085, 866-407-8326; www.nevadanorthernrailway.net; adult/child from $24/15; Apr-Dec) offers excursion rides on trains pulled by historic steam engines.
Off US Hwy 93 south of town via signposted dirt roads, Ward Charcoal Ovens State Historic Park ( 775-728-4460; http://parks.nv.gov/ww.htm; entry $7, tent & RV sites $14, yurt $20) protects a half-dozen beehive-shaped structures dating from 1876 that were once used to make charcoal to supply the silver smelters.
Kitsch lovers will dig the Hotel Nevada ( 775-289-6665, 888-406-3055; www.hotelnevada.com; 501 Aultman St; r $35-125; aWi) with clean rooms above a funky old casino with a bar that defines the term 'local color.' In the morning, stop by the cafe (mains $6-20; 24 hr) for giant cinnamon rolls, steak and eggs, and Starbucks coffee.
Ely's casinos have mostly ho-hum eateries, some open 24 hours. The Silver State Restaurant ( 775-289-8866; 1204 Aultman St; meals from $6; 6am-9pm) is an authentic diner-style coffee shop, where the waitresses call you 'hun' and comfort food is the only thing on the menu (cash only). La Fiesta ( 775-289-4114; 700 Ave H; mains $9-20; 11am-9pm; ) serves up deliciously cheesy enchiladas and good frozen margaritas.
##### GREAT BASIN NATIONAL PARK
Near the Nevada–Utah border, this uncrowded national park ( 775-234-7331; www.nps.gov/grba; admission free; 24hr) encompasses 13,063ft Wheeler Peak, rising abruptly from the desert, creating an awesome range of life zones and landscapes within a very compact area. The peak's narrow, twisting scenic drive is open only during summer, usually from June through October. Hiking trails near the summit take in superb country made up of glacial lakes, groves of ancient bristlecone pines (some over 5000 years old) and even a permanent ice field. The summit trail is an 8.2-mile round-trip trek, with a vertical ascent of nearly 3000ft.
Back below, the main park visitor center ( 8am-4:30pm, extended hr summer) sells tickets for guided tours ($4 to $10) of Lehman Caves, which are brimming with limestone formations. The temperature inside is a constant 50°F (10°C), so bring a sweater.
The park's four developed campgrounds (tent & RV sites $12) are open during summer; only Lower Lehman Creek is available year-round. Next to the visitor center, a simple cafe stays open from May through October. The nearby village of Baker has a gas station, a basic restaurant and sparse accommodations.
### Along I-80
I-80 is the old fur trappers' route, following the Humboldt River from northeast Nevada to Lovelock, near Reno. It's also one of the earliest emigrant trails to California. Transcontinental railroad tracks reached Reno in 1868 and crossed the state within a year. By the 1920s, the Victory Hwy traveled the same route, which later became the interstate. Although not always the most direct route across Nevada, I-80 skirts many of the Great Basin's steep mountain ranges. Overnight stops in the Basque-flavored country around Elko or Winnemucca will give you a true taste of cowboy life.
##### LOVELOCK
Couples in love who want to leave a piece of their romance in Nevada would be advised to stop by the quiet small town of Lovelock, a 90-minute drive northeast of Reno. Behind the Pershing County Courthouse ( 775-273-7213; 400 S Main St; 8am-5pm Mon-Fri), inspired by Rome's pantheon, you can symbolically lock your passion on a chain for all eternity in Love Lock Plaza (www.loverslock.com). At the 1874 Marzen House ( 775-273-4949; 25 Marzen Lane; admission free; 1:30-4pm May-Oct), a small historical museum displays mementos of local sweetheart Edna Purviance, Charlie Chaplin's leading lady. A country-style diner, the Cowpoke Cafe ( 775-273-2444; 995 Cornell Ave; meals from $5; 6am-8pm Mon, Wed & Thu, to 8pm Tue & Fri, 7am-3pm Sat, 8am-3pm Sun) serves from-scratch buffalo burgers, brisket sandwiches and homemade desserts like red velvet cake.
##### UNIONVILLE & AROUND
This rural late-19th-century ghost town's big claim to fame is that Mark Twain tried his hand (albeit unsuccessfully) at silver mining here. Take a stroll by the writer's old cabin and the Buena Vista schoolhouse, pioneer cemetery and old-fashioned covered bridge. Further west along I-80, Rye Patch State Recreation Area ( 775-538-7321; www.parks.nov.gov; entry $7, tent & RV sites $14) offers swimming, fishing and boating.
##### WINNEMUCCA
Winnemucca has been a travelers' stop since the days of the Emigrant Trail. Even Butch Cassidy dropped by to rob a bank. Named after a Paiute chief, the biggest town on this stretch of I-80 is also a center for the state's Basque community, descended from 19th-century immigrant shepherds.
Unassuming Winnemucca boasts a vintage downtown full of antique shops and a number of Basque restaurants, in keeping with the town's fascinating Basque heritage. Get information on the town's annual June Basque Festival at the Winnemucca Visitors Center & Chamber of Commerce ( 775-623-5071; www.winnemucca.nv.us; 50 W Winnemucca Blvd; 8am-noon, 1-5pm Mon-Fri, 9am-noon Sat, 11am-4pm Sun), along with a self- guided downtown walking tour brochure and information on horseback riding at local ranches. Wannabe cowboys and cowgirls should check out the Buckaroo Hall of Fame – full of cowboy art and folklore – while taxidermy fans will want to check out the big game museum in the lobby.
North of the river in a former church, the Humboldt County Museum (www.humboldtmuseum.com; cnr Jungo Rd & Maple Ave; admission free; 10am-noon Mon-Fri, 1-4pm Mon-Sat) shows off antique cars, farming implements and beautiful Paiute baskets.
East of town, off Highland Dr at the end of Kluncy Canyon Rd, the Bloody Shins Trails are part of a burgeoning mountain biking trail system. Stop by the BLM Winnemucca Field Office ( 775-623-1500; www.blm.nv.gov; 5100 E Winnemucca Blvd; 7:30am-4:30pm Mon-Fri) for more information.
Winnemucca's main drag has abundant motels and a few casino hotels with 24-hour restaurants. Family-owned Town House Motel ( 775-623-3620, 800-243-3620; www.townhouse-motel.com; 375 Monroe St; r $70-80; ) has tidy budget rooms equipped with microwaves and mini-fridges, while the Winnemucca Inn ( 775-623-2565; www.winnemuccainn.com; 741 W Winnemucca Blvd; r from $80; ) offers spacious, well-equipped rooms with a bustling casino, 24 hour restaurant and children's arcade.
Don't miss a stop at the Griddle (www.thegriddle.com; 460 W Winnemucca Blvd; mains $4-12; breakfast & lunch daily, dinner Thu-Sat) one of Nevada's best retro cafes, serving up fantastic breakfasts, diner classics and homemade desserts since 1948. Locals also adore the Third Street Bistro ( 775-623-0800; 45 E Winnemucca Blvd; mains $7-10; 7am-2pm Mon-Sat) for its homebaked goods, tasty soups and excellent Philly cheesesteaks in a genteel atmosphere. Those making Winnemucca a full overnight trip should seriously plan their evening around dinner at the Martin Hotel (www..themartinhotel.com; 94 W Railroad St; multi-course dinner $17-32; 11:30am-2pm Mon-Fri, 4-9pm nightly; ), where ranchers, locals and weary travelers have come since 1898 to enjoy family-style Basque meals under pressed-tin ceilings.
To fuel up for what will likely be a long drive in any direction, delightful Delizioso Global Coffee ( 775-625-1000; 508a W Winnemucca Blvd; items $2-5; 5am-5pm Mon-Fri, 6am-1pm Sat; ) offers creative espresso drinks like the 'Winnemocha' and fresh scones amid a fanciful forest-like interior.
About 50 miles north of town, the Santa Rosa Mountains offer rugged scenery, hiking trails and camping in the Humboldt-Toiyabe National Forest.
### WHAT THE...? THE MINESHAFT
While sultry – or, more often, seedy – establishments employing scantily clad women are practically as commonplace across Nevada as casinos themselves, there's one consolation that even the flesh-wary can count on: that it's the employees, not thecustomers, who you might vie in various states of undress. Not so at Winnemucca's The Mineshaft Bar (www.themineshaftbar.com; 44 W Railroad St; 24hr) which bills itself as 'Nevada's only clothes-optional bar.' You know it's a serious dive when its website features the competing slogans 'Hard Rock Music for Hard Rock Miners,' and 'Where T and A is A-OK.' Weekend nights aren't for the faint of heart or the easily offended: think metal bands, wet t-shirt contests and girl-on-girl kissing contests.
##### ELKO
Though small, Elko is the largest town in rural Nevada and a center of cowboy culture, with a calendar of Western cultural events and a museum big on buckaroos, stagecoaches and the Pony Express. The other cultural influence is Basque; in fact, Basque shepherds and Old West cattlemen had some violent conflicts over grazing rights in the late 19th century. The visitor center ( 775-738-4091, 800-248-3556; www.elkocva.com; 1405 Idaho St; hr vary) is inside a historic ranch house.
The Northeastern Nevada Museum ( 775-738-3418; www.museumelko.org; 1515 Idaho Ave; adult/child $5/1; 9am-5pm Mon-Sat, 1-5pm Sun) has excellent displays on pioneer life, Pony Express riders, Basque settlers and modern mining techniques. Free monthly tours of the nearby Newmont gold mine usually start here; call 775-778-4068 for reservations. Aspiring cowboys and cowgirls should visit the Western Folklife Center & Wiegland Gallery (www.westernfolklife.org; 501 Railroad St; admission free; 10:30am-5:30pm Tue-Fri), which hosts the remarkably popular Cowboy Poetry Gathering in January. The National Basque Festival (www.elkobasque.com) is held around July 4, with games, traditional dancing and even Elko's own 'Running of the Bulls.'.
South of Elko, the Ruby Mountains (www.rubymountains.org) are a superbly rugged range, nicknamed Nevada's alps for their prominent peaks, glacial lakes and alpine vegetation. The village of Lamoille has basic food and lodging, and one of the most photographed rural churches in the USA. Just before the village, Lamoille Canyon Rd branches south, following the forested canyon for 12 miles past cliffs, waterfalls and other glacial sculptures to the Ruby Crest trailhead at 8800ft.
A popular overnight stop for truckers and travelers, Elko has over 2000 rooms that fill up fast, especially on weekends. Chain motels and hotels line Idaho St, particularly east of downtown. Of the chains, we like the comfy Hilton Garden Inn ( 775-777-1200; www.hiltongardeninn.com; 736 Idaho St; r $90-160; ), while the best budget choice is the locally run Thunderbird Motel ( 775-738-7115; www.thunderbirdmotelelko.com; 345 Idaho St; r incl breakfast $59-69; ).
For decent pizza and local Nevada beer, sidle up to the bar at the Stray Dog Pub & Café ( 775-753-4888; 374 5th St; mains $7-12; dinner 3-9pm Mon-Sat, bar open late, closed Sun), decked out with old bikes and surfboards. If you've never sampled Basque food, the best place in town for your inaugural experience is the Star Hotel (www.elkostarhotel.com; 246 Silver St; mains $15-32; lunch Mon-Fri, dinner Mon-Sat), a family-style supper club located in a 1910 boardinghouse for Basque sheepherders. The irrepressibly curious will not want to miss a peek behind the restaurant, where Elko's small 'red light' district of legal brothels sits, including 'Inez's Dancing and Diddling,' perhaps the most bizarrely-named business – tawdry or not – in the state.
### MOVING ON?
For tips, recommendations and reviews, head to shop.lonelyplanet.com to purchase a downloadable PDF of the California chapter from Lonely Planet's _USA_ guide.
Serving up strong espresso from the crack of dawn through the afternoon, Cowboy Joe ( 775-753-5612; 376 5th St; items $2-6; 6am-5pm Mon-Fri, 5:30am-3pm Sat, 7am-noon Sun; ) is a great little small-town coffeehouse with an eponymous signature drink that will keep you going till Reno.
##### WELLS
Sports fans should know that heavyweight boxer Jack Dempsey started his career here, as a bouncer in the local bars. After strolling around the rough-edged Front Street historic district today, you can imagine how tough that job must've been. The Trail of the '49ers Interpretive Center ( 775-752-3540; www.wellsnevada.com; 395 S 6th St; hr vary) tells the story of mid-19th-century pioneers on the Emigrant Trail to California.
Southwest of town, scenic byway NV Hwy 231 heads into the mountains, climbing alongside sagebrush, piñon pine and aspen trees past two campgrounds ( 877-444-6777; www.recreation.gov; tent sites $12-22; Jun-Oct). After 12 miles, the road stops at cobalt-blue Angel Lake (8378ft), a glacial cirque beautifully embedded in the East Humboldt Range. Along NV Hwy 232, further south of Wells, a large natural window near the top of Hole in the Mountain Peak (11,306ft) is visible from the road.
##### WEST WENDOVER
If you just can't make it to Salt Lake City tonight, stop in West Wendover, where ginormous casino hotels ( 800-537-0207; www.wendoverfun.com; r $55-140) with 24-hour restaurants line Wendover Blvd. Over on the Utah side, Historic Wendover Airfield (www.wendoverairbase.com; 345 Airport Apron, Wendover; admission by donation; 8am-6pm) is a top-secret WWII-era USAF base, where the Enola Gay crew trained for dropping the atomic bomb on Japan. The Bonneville Speed Museum ( 775-664-3138; 1000 E Wendover Blvd, Wendover; adult/child $2/1; 10am-6pm Jun-Nov) documents attempts to set land speed records on the nearby Bonneville Salt Flats, where 'Speed Week' time trials in the third full week of August draw huge crowds every year.
## RENO-TAHOE AREA
A vast sagebrush steppe, the western corner of the state is carved by mountain ranges and parched valleys. It's also the place where modern Nevada began. It was the site of the state's first trading post, pioneer farms and the famous Comstock silver lode, which spawned Virginia City, financed the Union during the Civil War and earned Nevada its statehood. Today, Reno and the state capital, Carson City, have little of the Wild West rawness still extant in the Black Rock Desert, reached via Pyramid Lake. For pampering all-seasons getaways, it's a short drive up to emerald Lake Tahoe, right on the California border.
### Reno
A soothingly schizophrenic city of big-time gambling and top-notch outdoor adventures, Reno resists pigeonholing. the 'Biggest Little City in the World' has something to raise the pulse of adrenaline junkies, hardcore gamblers and city people craving easy access to wide open spaces.
#### Sights
National Automobile Museum MUSEUM
( 775-333-9300; www.automuseum.org; 10 S Lake St; adult/child $10/4; 9:30am-5:30pm Mon-Sat, 10am-4pm Sun; ) Stylized street scenes illustrate a century's worth of automobile history at this engaging car museum. The collection is enormous and impressive, with one-of-a-kind vehicles including James Dean's 1949 Mercury from _Rebel Without a Cause,_ a 1938 Phantom Corsair and a 24-karat gold-plated DeLorean, and rotating exhibits bringing in all kinds of souped-up or fabulously retro rides.
Nevada Museum of Art MUSEUM
( 775-329-3333; www.nevadaart.org; 160 W Liberty St; adult/child $10/1; 10am-5pm Wed-Sun, 10am-8pm Thu) In a sparkling building inspired by the geologic formations of the Black Rock Desert north of town, a floating staircase leads to galleries showcasing temporary exhibits and images related to the American West. Great cafe for postcultural refueling.
University of Nevada, Reno UNIVERSITY
Pop into the flying saucer-shaped Fleischmann Planetarium & Science Center ( 775-784-4811; http://planetarium.unr.nevada.edu; 1650 N Virginia St; admission free; noon-5pm Mon & Tue, noon-9pm Fri, 10am-9pm Sat, 10am-5pm Sun) for a window on the universe during star shows and feature presentations (adult/child $6/4). Nearby is the Nevada Historical Society Museum ( 775-688-1190; www.museums.nevadaculture.org; 1650 N Virginia St; adult/child $4/free; 10am-5pm Wed-Sat), which includes permanent exhibits on neon signs, local Native American culture and the presence of the federal government.
##### VIRGINIA ST
Wedged between the I-80 and the Truckee River, downtown's N Virginia St is casino central. South of the river it continues as S Virginia St. All of the following hotel casinos are open 24 hours.
Circus Circus CASINO
(www.circusreno.com; 500 N Sierra St; ) The most family-friendly of the bunch, it has free circus acts to entertain kids beneath a giant, candy-striped big top, which also harbors a gazillion carnival and video games that look awfully similar to slot machines.
Silver Legacy CASINO
(www.silverlegacyreno.com; 407 N Virginia St) A Victorian-themed place, it's easily recognized by its white landmark dome, where a giant mock mining rig periodically erupts into a fairly tame sound-and-light spectacle.
Eldorado CASINO
(www.eldoradoreno.com; 345 N Virginia St) The Eldorado has a kitschy Fountain of Fortune that probably has Italian sculptor Bernini spinning in his grave.
Harrah's CASINO
(www.harrahsreno.com; 219 N Center St) Founded by Nevada gambling pioneer William Harrah in 1946, it's still one of the biggest and most popular casinos in town.
Peppermill CASINO
(www.peppermillreno.com; 2707 S Virginia St) About 2 miles south of downtown, this place dazzles with a 17-story Tuscan-style tower.
Atlantis CASINO
(www.atlantiscasino.com; 3800 S Virginia St) Now more classy than zany, with an extensive spa, the remodeled casino retains a few tropical flourishes like indoor waterfalls and palm trees.
#### Activities
Reno is a 30- to 60-minute drive from Tahoe ski resorts, and many hotels and casinos offer special stay and ski packages.
Truckee River Whitewater Park WATER SPORTS
Mere steps from the casinos, the park's Class II and III rapids are gentle enough for kids riding inner tubes, yet sufficiently challenging for professional freestyle kayakers. Two courses wrap around Wingfield Park, a small river island that hosts free concerts in summertime. Tahoe Whitewater Tours ( 775-787-5000; www.gowhitewater.com) and Wild Sierra Adventures ( 866-323-8928; www.wildsierra.com) offer kayak trips and lessons.
Historic Reno Preservation Society WALKING TOUR
( 775-747-4478; www.historicreno.org; tours $10) Dig deeper with a walking or biking tour highlighting subjects including architecture, politics and literary history.
#### Festivals & Events
Reno River Festival SPORTS
(www.renoriverfestival.com) The world's top freestyle kayakers compete in a mad paddling dash through Whitewater Park in mid-May. Free music concerts as well.
### PYRAMID LAKE
A piercingly blue expanse in an otherwise barren landscape 25 miles north of Reno on the Paiute Indian Reservation, Pyramid Lake is a stunning standalone sight, with shores lined with beaches and eye-catching tufa formations. Nearer its east side, iconic pyramidlike Anaho Island is a bird sanctuary for American white pelicans. Popular for camping and fishing, the area offers permits for camping (primitive campsites per vehicle per night $9) and fishing (per person $9) at outdoor suppliers and CVS drugstore locations in Reno, as well as at the ranger station ( 775-476-1155; www.pyramidlake.us; 8am-6pm) on SR 445 in Sutcliffe.
Tour de Nez SPORTS
(www.tourdenez.com) Called the 'coolest bike race in America,' the Tour de Nez brings together pros and amateurs for five days of races and partying in July.
Hot August Nights CULTURAL
(www.hotaugustnights.net) Catch the _American Graffiti_ vibe during this seven-day celebration of hot rods and rock and roll in early August. Hotel rates skyrocket to their peak.
### RENO AREA TRAILS
For extensive information on regional hiking and biking trails, including the Mt Rose summit trail and the Tahoe-Pyramid Bikeway, download the Truckee Meadows Trails guide (www.reno.gov/Index.aspx?page=291).
#### Sleeping
Lodging rates vary widely depending on the day of the week and local events. Sunday through Thursday are generally the best; Friday is somewhat more expensive and Saturday can be as much as triple the midweek rate.
In the summer months, there's gorgeous high altitude camping at Mt Rose ( 877-444-6777; www.recreation.gov; Hwy 431; RV & tent sites $16).
Peppermill CASINO HOTEL $$
( 775-826-2121, 866-821-9996; www.peppermillreno.com; 2707 S Virginia St; r Sun-Thu $50-140; Fri & Sat $70-200; ) Now awash in Vegas-style opulence, the popular Peppermill boasts Tuscan-themed rooms in its newest 600-room tower, and has almost completed a plush remodel of its older rooms. The three sparkling pools (one indoor) are dreamy, with a full spa on hand. Geothermal energy powers the resort's hot water and heat.
Sands Regency CASINO HOTEL $
( 775-348-2200, 866-386-7829; www.sandsregency.com; 345 N Arlington Ave; r Sun-Thu/Fri & Sat from $29/89; ) With some of the largest standard digs in town, rooms here are decked out in a cheerful tropical palette of upbeat blues, reds and greens – a visual relief from standard-issue motel decor. The 17th-floor gym and Jacuzzi are perfectly positioned to capture your eyes with drop-dead panoramic mountain views. Empress Tower rooms are best.
Wildflower Village MOTEL $$
( 775-747-8848; www.wildflowervillage.com; 4395 W 4th St; r $50-75, B&B $100-125; ) Perhaps more of a state of mind than a motel, this artists colony on the west edge of town has a tumbledown yet creative vibe. Individual murals decorate the facade of each room, and you can hear the freight trains rumble on by.
#### Eating
Reno's dining scene goes far beyond the casino buffets.
Old Granite Street Eatery AMERICAN $$
( 775-622-3222; 243 S Sierra St; dishes $9-24; 11am-10pm Mon-Thu, 11am-midnight Fri, 10am-midnight Sat, 10am-4pm Sun) A lovely well-lighted place for organic and local comfort food, old-school artisanal cocktails and seasonal craft beers, this antique-strewn hotspot enchants diners with its stately wooden bar, water served in old liquor bottles and its lengthy seasonal menu. Forgot to make a reservation? Check out the iconic rooster and pig murals and wait for seats at a community table fashioned from a barn door.
Pneumatic Diner VEGETARIAN $
(501 W 1st St, 2nd fl; dishes $6-9; noon-10pm Mon, 11am-10pm Tue-Thu, 11am-11pm Fri & Sat, 8am-10pm Sun; ) Consume a garden of vegetarian delights under salvaged neon lights. This groovy little place near the river has meatless and vegan comfort food and desserts to tickle your inner two-year-old, like the ice-cream laden Cookie Bomb. It's attached to the Truckee River Terrace apartment complex; use the Ralston St entrance.
Silver Peak Restaurant & Brewery PUB $$
(124 Wonder St; mains lunch $8-10, dinner $9-21; 11am-midnight) Casual and pretense-free, this place hums with the chatter of happy locals settling in for a night of microbrews and great eats, from pizza with roasted chicken to shrimp pasta and filet mignon.
Peg's Glorified Ham & Eggs DINER $
(420 S Sierra St; dishes $7-10; 6:30am-2pm; ) Locally regarded as the best breakfast in town, Peg's offers tasty grill food that's not too greasy.
#### Drinking
Jungle Java & Jungle Vino CAFE, WINE BAR
(www.javajunglevino.com; 246 W 1st St; 6am-midnight; ) A side-by-side coffee shop and wine bar with a cool mosaic floor and an internet cafe all rolled into one. The wine bar has weekly tastings, while the cafe serves breakfast bagels and lunchtime sandwiches ($8) and puts on diverse music shows.
Imperial Bar & Lounge BAR
(150 N Arlington Ave; 11am-2am Thu-Sat, to midnight Sun-Wed) A classy bar inhabiting a relic of the past, this building was once an old bank, and in the middle of the wood floor you can see cement where the vault once stood. Sandwiches and pizzas go with 16 beers on tap and a buzzing weekend scene.
St James Infirmary BAR
(445 California Ave) With an eclectic menu of 120 bottled varieties and 18 on tap, beer aficionados will short circuit with delight. Red lights blush over black-and-white retro banquettes and a wall of movie and music stills, and it hosts sporadic events including jazz and bluegrass performances.
#### Entertainment
The free weekly _Reno News & Review_ (www.newsreview.com) is your best source for listings.
Edge CLUB
(www.edgeofreno.com; Peppermill, 2707 S Virginia St; admission $10-20; Thu-Sun) The Peppermill reels in the nighthounds with a big glitzy dance club, where go-go dancers, smoke machines and laser lights may cause sensory overload. If so, step outside to the view lounge patio and relax in front of cozy fire pits.
Knitting Factory LIVE MUSIC
( 775-323-5648; http://re.knittingfactory.com; 211 N Virginia St) This mid-sized venue opened in 2010, filling a gap in Reno's music scene with mainstream and indie favorites.
#### Information
An information center sits near the baggage claim at Reno-Tahoe Airport, which also has free wi-fi.
Java Jungle (246 W 1st St; per hr $2; 6am-midnight; ) Great riverfront cafe with a few computers and free wi-fi.
Reno-Sparks Convention & Visitors Authority ( 800-367-7366; www.visitrenotahoe.com; 2nd fl, Reno Town Mall, 4001 S Virginia St; 8am-5pm Mon-Fri)
#### Getting There & Away
About 5 miles southeast of downtown, the Reno-Tahoe International Airport (RNO; www.renoairport.com; ) is served by most major airlines.
The North Lake Tahoe Express ( 866-216-5222; www.northlaketahoeexpress.com) operates a shuttle ($40, six to eight daily, 3:30am to midnight) to and from the airport to multiple North Shore Lake Tahoe locations including Truckee, Squaw Valley and Incline Village. Reserve in advance.
To reach South Lake Tahoe (weekdays only), take the wi-fi-equipped RTC Intercity bus (www.rtcwashoe.com) to the Nevada DOT stop in Carson City ($4, five per weekday, one hour) and then the BlueGo (www.bluego.org) 21X bus ($2 with RTC Intercity transfer, seven to eight daily, one hour) to the Stateline Transit Center.
Greyhound ( 775-322-2970; www.greyhound.com; 155 Stevenson St) buses run daily service to Truckee, Sacramento and San Francisco ($34, five to seven hours), as does the once daily westbound California Zephyr route operated by Amtrak ( 775-329-8638, 800-872-7245; 280 N Center St). The train is slower and more expensive, but also more scenic and comfortable, with a bus connection from Emeryville for passengers to San Francisco ($46, 7½ hours).
#### Getting Around
The casino hotels offer frequent free airport shuttles for their guests (and don't ask to see reservations).
The local RTC Ride buses ( 775-348-7433; www.rtcwashoe.com; per ride/all day $2/4) blanket the city, and most routes converge at the RTC 4th St Station downtown. Useful routes include the RTC Rapid line for S Virginia St, 11 for Sparks and 19 for the airport. The free Sierra Spirit bus loops around all major downtown landmarks – including the casinos and the university – every 15 minutes from 7am to 7pm.
### DOWN & DIRTY NEVADA
Prostitution is illegal only in Clark and Washoe Counties (including Las Vegas and Reno), yet illegal prostitution runs rampant ( _especially_ in Las Vegas) under the guise of strip clubs, escort services and massage parlors. Remember that not only is paying for sex through these seemingly innocuous channels illegal and punishable by law, but anyone who does so may be contributing to Nevada's sex trafficking problem. The human trafficking of women and girls is an international epidemic that is unfortunately growing in the United States.
Legalized, heavily regulated brothels are found in Nevada's more rural counties. Don't expect a romantic Old West bordello, though; most are just a few doublewide trailers behind a scary barbed-wire fence on the side of a lonesome highway.
### Carson City
Is this the most underrated town in Nevada? We're going to double down and say that it is. An easy drive from Reno or Lake Tahoe, it's a perfect stop for lunch and a stroll around the quiet, old-fashioned downtown. Expect handsome antique buildings and pleasant tree-lined streets centered around the 1870 Nevada State Capitol (cnr Musser & Carson; admission free) where the governor's door is always open – you'll just have to charm your way past his assistant. Note the silver dome, which fittingly symbolizes Nevada's 'Silver State' status.
US Hwy 395 from Reno becomes the town's main drag, called Carson St. Look for the Cactus Jack neon sign letting you know you've reached downtown. About a mile further south, the Carson City Convention & Visitors Bureau ( 775-687-7410, 800-638-2321; www.visitcarsoncity.com; 1900 S Carson St; 9am-4pm Mon-Fri, to 3pm Sat & Sun) has information about mountain-biking trails and hands out a historical walking-tour map of the Kit Carson Trail, with interesting podcasts that you can download online.
Several historic attractions and museums are worth visiting. Housed inside the 1869 US Mint building, the Nevada State Museum (www.nevadaculture.org; 600 N Carson St; adult/child $8/free; 8:30am-4:30pm Wed-Sat) puts on rotating exhibits of Native American, frontier and mining history. Train buffs shouldn't miss the Nevada State Railroad Museum ( 775-687-6953; 2180 S Carson St; adult/child $6/free; 8:30am-4:30pm), displaying some 65 train cars and locomotives, most pre-dating 1900. For made-in-Nevada artisan crafts, shop at the Brewery Arts Center ( 775-883-1976; www.breweryarts.org; 449 W King St; 10am-4pm Mon-Sat).
Lunch, sip and linger at fetching, art-filled Comma Coffee (www.commacoffee.com; 312 S Carson St; dishes $5-9; 7am-6pm Mon & Wed-Thu, to 10pm Tue & Fri & Sat; ) where eavesdropping is always interesting: the next table over might be Nevada lobbyists discussing a new bill over lattes or wine. Nosh on English pub classics in red velvet booths at the Firkin and Fox (www.thefirkinandfox.com; 310 S Carson St; mains $10-19; 11am-midnight Sun-Thu, to 2am Fri & Sat) downtown in the historic St Charles Hotel. Or spend the evening at the town's friendly, locally owned microbrewery, High Sierra Brewing Company (www.highsierrabrewco.com; 302 N Carson St; mains $8-20; 11am-midnight Sun-Thu, to 2am Fri & Sat), for great local beer and eclectic international dishes on the patio or near the stage, where nationally touring musicians perform some nights.
### WHET YOUR WHISTLE
Drink like an old-time miner at one of the many Victorian-era watering holes that line C street. We like the longtime family-run Bucket of Blood Saloon (www.bucketofbloodsaloonvc.com; 1 S C St; 2-7pm) which serves up beer and 'bar rules' at its antique wooden bar ('If the bartender doesn't laugh, you are not funny') and the Palace Restaurant & Saloon (www.palacerestaurant1875.com; 1 S C St; mains $6-10; hr vary) which is full of town memorabilia and serves up tasty breakfasts and lunches.
### Virginia City
Twenty-five miles south of Reno, this national historic landmark is the site where the legendary Comstock Lode was struck, sparking a silver bonanza that began in 1859 and stands as one of the world's richest strikes. During the 1860s gold rush, Virginia City was a high-flying, rip-roaring Wild West boomtown. Newspaperman Samuel Clemens, alias Mark Twain, spent some time in this raucous place during its heyday and vividly captured the Wild West shenanigans in a book called _Roughing It_.
Sure, Virginia City can feel a bit like a high-elevation theme park, but it's still fun to visit. The high-elevation town is a bona fide National Historic Landmark, with a main street of Victorian buildings, wooden sidewalks and historic saloons. The main drag is C St; check out the visitor center ( 775-847-4386, 800-718-7587; www.virginiacity-nv.org; 86 S C St; 10am-4pm) inside the historic Crystal Bar. Nearby is the Mark Twain Bookstore (www.marktwainbooks.com; 111 S C St; hours vary).
### GREAT BALLS OF FIRE!
For one week at the end of August, Burning Man (www.burningman.com; admission $210-320) explodes onto the sunbaked Black Rock Desert, and Nevada sprouts a third major population center – Black Rock City. An experiential art party (and alternative universe) that climaxes in the immolation of a towering stick figure, Burning Man is a whirlwind of outlandish theme camps, dust-caked bicycles, bizarre bartering, costume-enhanced nudity and a general relinquishment of inhibitions.
The cheesy, old-fashioned Way It Was Museum ( 775-847-0766; 113 N C St; adult/child $3/free; 10am-6pm) offers historical background on mining the lode. Stop by the Mackay Mansion ( 775-847-0173; 129 D St; admission $3; 10am-6pm) to see how the mining elite once lived.
From May through October, the Virginia & Truckee Railroad ( 775-847-0380; www.virginiatruckee.com; F & Washington Sts; 35min narrated tour adult/child $9/5; ) offers vintage steam-train excursions.
A mile south of town via NV Hwy 342, the Gold Hill Hotel & Saloon ( 775-847-0111; www.goldhillhotel.net; 1540 Main St; r $55-225; ) claims to be Nevada's oldest hotel, and feels like it, with a breezy, old-fashioned charm and atmospheric bar boasting a great wine and spirits selection. Some rooms have fireplaces and views of the Sierras.
Inside a 1870s boarding house, Sugarloaf Mountain Motel ( 775-847-0551; 430 S C St; r $60-100) is cozily historical and gets raves for hosts Jim and Michelle's friendly hospitality. The renovated rooms at Silverland Inn & Suites (; 775-847-4484; www.silverlandusa.com; 100 N E St; r $89-169; ) will appeal to those who prefer more modern (if nondescript) digs along with a sunny pool and hot tub area with mountain views.
Locals agree that the best food in Virginia City is probably at Cafe del Rio (www.cafedelriovc.com; 394 S C St; mains $9-15; 4:30-8pm Wed & Thu, 11:30-8pm Fri & Sat, 10am-2pm Sun), serving a nice blend of _nuevo_ Mexican and Southwest cuisine, including brunch. For gorgeous 100-mile views of the surrounding valleys, sip a strong coffee or have an ice-cream cone on the back porch of the Comstock Creamery ( 775-847-7744; 171 S C St; mains $4-8) where the friendly owners also serve up eight different kinds of burgers.
### Genoa
This pretty village at the edge of Carson Valley, beneath the Sierra Nevada mountains, was the first European settlement at the western edge of the former Utah Territory. The Genoa Saloon claims to be the oldest bar in the state (since 1863), and it certainly looks the part. The Genoa Courthouse Museum ( 775-782-4325; 2304 Main St; adult/child $3/2; 10am-4:30pm May-Oct) contains the original jail and a collection of woven Washo baskets. It's free to wander through the early settlement of Mormon Station State Historic Park ( 775-782-2590; museum $1; 10am-4pm Wed-Sun). About 2 miles south of town, off NV Hwy 206, David Walley's Hot Springs & Spa ( 775-782-8155; www.davidwalleys-resort.com; 2001 Foothill Rd; pools, sauna & work-out room day pass $20; 7am-10pm) offers a respite from traveling Nevada's dusty roads.
### Black Rock Desert
North of Pyramid Lake, NV Hwy 447 continues straight as an arrow for about 60 miles to the dusty railway town of Gerlach, with a gas station, a motel, a cafe and a few bars. Its motto is 'Where the pavement ends, the West begins.' Bruno's Country Club ( 775-557-2220; 445 Main St; meals $6-15; hr vary) is famous for its meaty ravioli in cheese sauce. Outside Gerlach, world land-speed records have been set on the dry, mud-cracked _playas_ of the Black Rock Desert ( 775-557-2900; www.blackrockfriends.org). Although most people only visit during the Burning Man festival, this vast wilderness is primed for outdoor adventures year-round.
### Lake Tahoe
Shimmering in myriad blues and greens, Lake Tahoe is the nation's second-deepest lake. Driving around its spellbinding 72-mile scenic shoreline gives you quite a workout behind the wheel. The north shore is quiet and upscale; the west shore, rugged and old-timey; the east shore, undeveloped; and the south shore, busy and tacky with aging motels and flashy casinos. The horned peaks surrounding the lake, which straddles the California–Nevada state line, are four-seasons playgrounds.
Tahoe gets packed in summer, on winter weekends and holidays, when reservations are essential. Lake Tahoe Visitors Authority ( 800-288-2463; www.tahoesouth.com) and North Lake Tahoe Visitors' Bureaus ( 888-434-1262; www.gotahoenorth.com) can help with accommodations and tourist information. There's camping in state parks ( reservations 800-444-7275; www.reserveamerica.com) and on USFS lands ( reservations 877-444-6777; www.recreation.gov).
##### SOUTH LAKE TAHOE & WEST SHORE
With retro motels and eateries lining busy Hwy 50, South Lake Tahoe gets crowded. Gambling at Stateline's casino hotels, just across the Nevada border, attracts thousands, as does the world-class ski resort of Heavenly ( 775-586-7000; www.skiheavenly.com; 3860 Saddle Rd; ). In summer, a trip up Heavenly's gondola (adult/child $32/20) guarantees fabulous views of the lake and Desolation Wilderness (www.fs.fed.us/r5/ltbmu). This starkly beautiful landscape of raw granite peaks, glacier-carved valleys and alpine lakes is a favorite with hikers. Get maps, information and overnight wilderness permits (per adult $5-10; www.recreation.gov) from the USFS Taylor Creek Visitor Center ( 530-543-2674; Hwy 89; daily May-Oct, hr vary). It's 3 miles north of the 'Y' intersection of Hwys 50/89, at Tallac Historic Site (tour $5; 10am-4:30pm mid-Jun-Sep, Fri & Sat only late May–mid-Jun), which preserves early 20th-century vacation estates. Lake Tahoe Cruises ( 800-238-2463; www.zephyrcove.com; adult/child from $39/15) ply the 'Big Blue' year-round. Back on shore, vegetarian-friendly Sprouts (3123 Harrison Ave; mains $6-10; 8am-9pm; ) is a delish natural-foods cafe.
Hwy 89 threads northwest along the thickly forested west shore to Emerald Bay State Park (www.parks.ca.gov; per car $8, campsites $35; late May-Sep), where granite cliffs and pine trees frame a fjordlike inlet, truly sparkling green. A steep 1-mile trail leads down to Vikingsholm Castle (tours adult/child $5/3; 10:30am-4:30pm). From this 1920s Scandinavian-style mansion, the 4.5-mile Rubicon Trail ribbons north along the lakeshore past an old lighthouse and petite coves to DL Bliss State Park (www.parks.ca.gov; entry per car $8, campsites $35-45; late May-Sep), offering sandy beaches. Further north, Tahoma Meadows B&B Cottages ( 530-525-1553, 866-525-1533; www.tahomameadows.com; 6821 W Lake Blvd, Tahoma; d incl breakfast $109-269) rents darling country cabins (pet fee $20).
##### NORTH & EAST SHORES
The north shore's commercial hub, Tahoe City is great for grabbing supplies and renting outdoor gear. It's not far from Squaw Valley USA ( 530-583-6985; www.squaw.com; off Hwy 89; ), a megasized ski resort that hosted the 1960 Winter Olympics. Après-ski crowds gather for beer 'n' burgers at woodsy Bridgetender Tavern (www.tahoebridgetender.com; 65 W Lake Blvd; mains $8-12; 11am-12am, to midnight Fri & Sat) back in town, or fuel up on French toast and eggs Benedict at down-home Fire Sign Cafe (1785 W Lake Blvd; dishes $6-12; 7am-3pm).
In summer, swim or kayak at Tahoe Vista or Kings Beach. Spend a night at Franciscan Lakeside Lodge ( 530-546-6300, 800-564-6754; www.franciscanlodge.com; 6944 N Lake Blvd, Tahoe Vista; d $80-265; Wsc), where simple cabins, cottages and suites have kitchenettes. East of Kings Beach, which has cheap, filling lakeshore eateries, Hwy 28 barrels into Nevada. Try your luck at the gambling tables or catch a live-music show at the Crystal Bay Club Casino ( 775-831-0512; www.crystalbaycasino.com; 14 Hwy 28). But for more happening bars and bistros, drive further to Incline Village.
With pristine beaches, lakes and miles of multiuse trails, Lake Tahoe-Nevada State Park (http://parks.nv.gov/lt.htm; per car $7-12) is the east shore's biggest draw. Summer crowds splash in the turquoise waters of Sand Harbor. The 15-mile Flume Trail ( 775-749-5349; www.theflumetrail.com; trailhead bike rental $45-65, shuttle $5-10), a mountain biker's holy grail, starts further south at Spooner Lake.
### WANT MORE?
For further information head to shop.lonelyplanet.com to purchase a downloadable PDF of the Lake Tahoe chapter from Lonely Planet's _California_ guide.
##### TRUCKEE & AROUND
North of Lake Tahoe off I-80, Truckee is not in fact a truck stop but a thriving mountain town, with organic-coffee shops, trendy boutiques and dining in downtown's historical district. Ski bunnies have several area resorts to pick from, including glam Northstar-at-Tahoe ( 800-466-6784; www.northstarattahoe.com; off Hwy 267; ); kid-friendly Sugar Bowl ( 530-426-9000; www.sugarbowl.com; off Hwy 40; ), cofounded by Walt Disney; and Royal Gorge ( 530-426-3871; www.royalgorge.com; off I-80; ), paradise for cross-country skiers.
West of Hwy 89, Donner Summit is where the infamous Donner Party became trapped during the fierce winter of 1846–47. Led astray by their guidebook, less than half survived – by cannibalizing their dead friends. The grisly tale is chronicled at the museum inside Donner Memorial State Park (www.parks.ca.gov; Donner Pass Rd; entry per car $8, campsites $35; museum 9am-4pm daily year-round, campground mid-May–mid-Sep), where Donner Lake is popular with swimmers and windsurfers.
Eco-conscious Cedar House Sport Hotel ( 530-582-5655, 866-582-5655; www.cedarhousesporthotel.com; 10918 Brockway Rd; r incl breakfast $170-270; W) is green building-certified, and has an outdoor hot tub and stylishly modern boutique rooms (pet fee $50). For live jazz and wine, Moody's Bistro & Lounge ( 530-587-8688; www.moodysbistro.com; 10007 Bridge St; dinner mains $18-40; 11:30am-9:30pm Sun-Thu, to 10pm Fri & Sat) sources locally ranched meats and seasonal produce. Down pints of 'Donner Party Porter' at Fifty Fifty Brewing Co (www.fiftyfiftybrewing.com; 11197 Brockway Rd) across the tracks.
#### Getting There & Around
###### To/From the Airport
South Tahoe Express ( 866-898-2463; www.southtahoeexpress.com) runs frequent shuttles from Nevada's Reno-Tahoe International Airport to Stateline (adult/child one way $27/15). North Lake Tahoe Express ( 866-216-5222; www.northlaketahoeexpress.com) connects Reno's airport with Truckee, Squaw Valley and north-shore towns (one way/round-trip $40/75).
###### Bus & Train
Truckee's Amtrak depot (10065 Donner Pass Rd) has daily trains to Sacramento ($37, 4½ hours) and Reno ($15, 1½ hours) and twice-daily Greyhound buses to Reno ($18, one hour), Sacramento ($42, 2½ hours) and San Francisco ($40, six hours). Amtrak Thruway buses connect Sacramento with South Lake Tahoe ($34, three hours).
Tahoe Area Regional Transit (TART; 800-736-6365; www.laketahoetransit.com; s-ride/24hr pass $1.75/3.50) runs local buses to Truckee and around the north and west shores. South Lake Tahoe is served by BlueGO ( 530-541-7149; www.bluego.org; s-ride/day pass $2/6), which operates a summer-only trolley up the west shore to Tahoma, connecting with TART.
###### Car
Tire chains are often required in winter on I-80, US 50, Hwy 89 and Mt Rose Hwy, any or all of which may close during and after snowstorms.
Top of section
# Arizona
928 / POP 69,500
**Includes »**
Greater Phoenix
Central Arizona
Sedona
Flagstaff
Grand Canyon Region
Havasupai Reservation
Navajo Reservation
Monument Valley Navajo Tribal Park
Hopi Reservation
Western Arizona
Lake Havasu City
Tucson
Bisbee
Eastern Arizona
### Why Go?
Arizona makes you wish your life was set to music. Cowboy songs in Monument Valley. The Eagles in Winslow. Anything produced by T Bone Burnett on a dusty mining road. And for the Grand Canyon? A fist-pumping 'We Will Rock You,' of course. Arizona, you see, is made for road trips. It has its gorgeous, iconic sites, but it's the road that breathes life into a trip. Take Route 66 into Flagstaff for a dose of mom-and-pop friendliness. Channel the state's mining past on a twisting drive through rugged Jerome. Reflect on Native American history as you drive below a mesa-top Hopi village.
Political controversies – such as immigration reform and budget slashing – have grabbed headlines recently, but these hot-button issues need perspective. Politicians are temporary. But the sunset beauty of the Grand Canyon, the saguaro-dotted deserts of Tucson and the red rocks of Sedona... they're here for the duration and hoping you'll stop by, regardless of the politics.
### When to Go
Jan–Mar Visit spas in southern Arizona. Cross-country ski in Kaibab National Forest.
Jun–Aug High season for exploring the Grand Canyon, Monument Valley and Sedona.
Sep & Oct Hike down to Phantom Ranch from the Grand Canyon's South Rim.
### Best Places to Eat
»El Tovar (Click here)
»Grand Canyon Lodge (Click here)
»Motor Lodge (Click here)
»Boulders (Click here)
»View Hotel (Click here)
### Best Places to Eat
»Elote Cafe (Click here)
»Poco (Click here)
»15.Quince Grill & Cantina (Click here)
»El Tovar Dining Room (Click here)
»Cafe Poca Cosa (Click here)
### Arizona Planning
Although the summer months (June to early September) are a popular time to visit Grand Canyon National Park, it's the opposite in the southern part of the state where the heat can be unbearable at that time of year. Save trips to Phoenix and southern Arizona for the spring. A good rule of thumb is to gauge the climate by the altitude. The lower you are, the hotter and drier it will be.
For Grand Canyon trips, make reservations for lodging, overnight mule rides and white-water rafting a year in advance, particularly if you plan to visit in summer.
### DON'T MISS
Grand Canyon Visitor Center on the South Rim has been revamped. Read the interpretive exhibits for background then stroll to Mather Point on the new, pedestrian-friendly plaza. You'll also find bike rentals and the introductory film _Grand Canyon: A Journey of Wonder_. On the Rim Trail, just west of the Yavapai Geology Museum & Observation Station, look for the new Trail of Time display.
In summer, save time and gas by prepurchasing your ticket and hopping on the new Tusayan shuttle, which runs from the National Geographic Visitor Center in Tusayan to the Grand Canyon Visitor Center in the park.
The California condor isn't new, but the gnarly bird with the 9ft wingspan remains a popular topic of conversation at the park. To learn more about this prehistoric scavenger, attend a ranger-led Condor Talk, held daily on both rims during the busy seasons (March to October South Rim, mid-May to mid-October North Rim).
### Tips for Drivers
»The main east–west highway across northern Arizona is the 400-mile stretch of I-40, which roughly follows the path of Historic Route 66. It's the interstate to take if you're headed for the Grand Canyon or the Navajo Reservation. I-10 enters western Arizona at Blythe and travels about 400 miles to New Mexico via Phoenix and Tucson.
»South of Phoenix, the I-8 coming west from Yuma joins the I-10. The I-8 is the most southerly approach from California, and it's a lonely highway indeed.
»Cell phone reception, FM radio, lodging and gas are almost nonexistent along I-8 between Yuma and Gila Bend.
»Phoenix Sky Harbor International Airport (Click here) and Las Vegas' McCarran International Airport (Click here) are major gateways, but Tucson also receives its share of flights.
»Greyhound and Amtrak do not typically stop at national parks in Arizona, nor do city buses and trains.
»For more information on transportation throughout the Southwest, see Click here.
### TIME ZONE
Arizona is on Mountain Time (seven hours behind GMT) but is the only Western state not to observe daylight saving time from spring to fall. The exception is the Navajo Reservation, which – in keeping with those parts of the reservation located in Utah and New Mexico – does observe daylight saving time. The small Hopi Reservation, which it surrounds, follows Arizona.
### Fast Facts
»Population: 6.39 million
»Area: 113,635 sq miles
»Sales tax: 6.6%
»Phoenix to Grand Canyon Village: 235 miles, 3½ hours
»Phoenix to Tucson: 116 miles, 1¾ hours
»Kingman to Holbrook: 240 miles, 3¼ hours
### Resources
»Arizona Department of Transportation: www.az511.gov
»Arizona Heritage Traveler: www.arizonaheritagetraveler.org
»Arizona Office of Tourism: www.arizonaguide.com
### Arizona Highlights
Wander past towering formations at Chiricahua National Monument (Click here)
Swoop in for birdwatching and wine tasting in Patagonia (Click here)
Pamper yourself with spa treatments, upscale shopping and patio dining in Scottsdale (Click here)
Cowboy up for a dude ranch ride in Wickenburg (Click here)
Commune beside a vortex in Sedona (Click here)
Bike the Greenway and the road to Hermit's Rest at Grand Canyon National Park (Click here)
Walk in beauty at Canyon de Chelly National Monument (Click here)
Revel in the surreal beauty of the towering buttes in Monument Valley Navajo Tribal Park (Click here)
Hide your Chihuahua; California condors with 9ft wingspans nest in the Vermilion Cliffs (Click here)
###### History
Native American tribes inhabited Arizona for centuries before Spanish explorer Francisco Vásquez de Coronado led an expedition from Mexico City in 1540. Settlers and missionaries followed in his wake, and by the mid-19th century the US controlled Arizona. The Indian Wars, in which the US Army battled Native Americans to protect settlers and claim land for the government, officially ended in 1886 with the surrender of Apache warrior Geronimo.
Railroad and mining expansion grew and people started arriving in ever larger numbers. After President Theodore Roosevelt visited Arizona in 1903 he supported the damming of its rivers to provide year-round water for irrigation and drinking, thus paving the way to statehood: in 1912 Arizona became the last of the 48 contiguous US states to be admitted to the Union.
The state shares a 250-mile border with Mexico and an estimated 250,000 immigrants crossed it illegally in 2009. After the mysterious murder of a popular rancher near the border in 2010, the legislature passed a law requiring police officers to ask for identification from anyone they suspect of being in the country illegally. This controversial law, known as SB 1070, is winding its way through the federal court system.
###### Arizona Scenic Routes
Dozens of scenic roads crisscross the state. Some of Arizona's best drives are included in monthly magazine _Arizona Highways_ (www.arizhwys.com), created in 1925 to cover them all and still going strong. For additional ideas, see www.byways.org and www.arizonascenicroads.com.
Grand Canyon North Rim Parkway (Hwy 67) Runs from Jacob Lake south to the North Rim via the pine, fir and aspen of Kaibab National Forest (Click here).
Historic Route 66 from Topock to Seligman The longest uninterrupted remaining stretch of original Mother Road (Click here).
Wickenburg to Sedona (Hwy 89A) Tremendous views of the Mogollon Rim and a grand welcome to Red Rock Country (Click here).
Monument Valley (Hwy 163) Stupendous drive past crimson monoliths rising abruptly from the barren desert floor northeast of Kayenta (Click here).
Oak Creek Canyon (Hwy 89A) Winds northeast from Sedona through dizzyingly narrow walls and dramatic rock cliffs before climbing up to Flagstaff (Click here).
Sky Island Parkway Traverses ecozones equivalent to a trip from Mexico to Canada as it corkscrews up to Mt Lemmon (9157ft), northeast of Tucson (Click here).
Vermilion Cliffs to Fredonia (Hwy 89A) Climbs through the remote Arizona Strip from fiery red Vermilion Cliffs up the forested Kaibab Plateau (Click here).
## GREATER PHOENIX
It's hard to put a label on Phoenix. Just when you've dismissed it as a faux-dobe wasteland of cookie-cutter subdivisions, bland shopping malls and water-gobbling golf courses, you're pulled short by a golden sunset setting the urban peaks aglow. Or a stubborn desert bloom determined to make a go of it in the dry, scrubby heat. Or maybe it's the mom-and-pop breakfast joint drawing crowds and thumbing its nose at the ubiquitous chains that dominate the landscape.
It's these little markers of hope – or defiance – that let travelers know there's more substance here than initially meets the eye. The catch? You've got to pull off the interstate and get out of the car to appreciate them. And with more than 300 days of sunshine a year – hence the nickname 'Valley of the Sun' – this isn't a disagreeable proposition (except in June, July and August when the mercury tops 100°F, or about 40°C).
Culturally, Phoenix offers an opera, a symphony, several theaters, and two of the state's finest museums: the Heard Museum and the Phoenix Art Museum. The Desert Botanical Garden is a stunning introduction to the region's flora and fauna. For sports fans, there are local teams in the national football, baseball and ice hockey leagues, and the area is dotted with more than 200 golf courses.
Greater Phoenix – also referred to as the Valley – may be vast and amorphous, but the areas of visitor interest are limited to three or four communities. Phoenix is the largest city and combines a businesslike demeanor with a burgeoning cultural scene and top-notch sports facilities. Southeast of here, student-flavored Tempe (tem- _pee_ ) is a lively district hugging 2-mile-long Tempe Town Lake. Further east it segues smoothly into ho-hum Mesa, which has a couple of interesting museums. North of Phoenix, Paradise Valley and Scottsdale are both ritzy enclaves. While the former is mostly residential, Scottsdale is known for its cutesy old town, galleries and lavish resorts.
#### Sights
Since the Phoenix area is so spread out, attractions are broken down by community. Opening hours change seasonally for many of the area's museums and restaurants, with earlier hours in summer.
##### PHOENIX
At first glance, Downtown Phoenix appears to be all buttoned-up business and bureaucracy (the state capitol is here), but there's actually plenty of partying going on in its cultural venues, sports stadiums, bars and restaurants. There's even a small alternative art scene.
Phoenix
Top Sights
Desert Botanical Garden G4
Heard Museum C4
Pueblo Grande Museum & Archaeological Park E5
Sights
1'A' Mountain G5
2ASU Art Museum G6
3Gammage Auditorium G6
4Hall of Flame F5
5Mill Avenue G6
6Phoenix Zoo F5
Splash Playground (see 7)
7Tempe Beach Park G5
8Tempe Center for the Arts G5
Activities, Courses & Tours
9Piestewa Peak/Dreamy Draw
Recreation Area D1
Tempe Town Lake Boat Rentals (see 7)
Sleeping
10Aloft Phoenix-Airport E5
11Arizona Biltmore Resort & Spa D2
12Best Western Inn of Tempe G5
13Clarendon Hotel B3
14FireSky Resort & Spa G3
15Hermosa Inn E2
16Royal Palms Resort & Spa F3
17Sanctuary on Camelback Mountain F2
Eating
18Barrio Café C4
19Chelsea's Kitchen E2
20Da Vang B3
21Dick's Hideaway C2
22Durant's C4
23Essence F6
24Noca D2
25Pane Bianco C3
26Pita Jungle G6
27Tee Pee Mexican Food E3
Drinking
Edge Bar (see 17)
28Four Peaks Brewing Company G6
Lux Coffeebar (see 25)
29Postino Winecafé Arcadia E3
30Vig E3
Entertainment
31Char's Has the Blues B3
32Phoenix Theatre C4
33Rhythm Room C3
Shopping
34Biltmore Fashion Park D2
35Borgata G2
36Garden Shop at the Desert Botanical Garden G4
37Heard Museum Shop C4
Heard Museum MUSEUM
( 602-252-8848; www.heard.org; 2301 N Central Ave; adult/child 6-12/student/senior $15/7.50/7.50/13.50; 9:30am-5pm Mon-Sat, 11am-5pm Sun; ) This extraordinary museum is a magical mystery tour through the history, life, arts and culture of Native American tribes in the Southwest. It emphasizes quality over quantity and is one of the best museums of its kind in America.
There are rooms of ethnographic displays, art galleries, a get-creative kids exhibit and an unrivaled Hopi kachina gallery (many of the pieces were a gift from Barry Goldwater). Most disturbing is the Boarding School Experience gallery about the controversial federal policy of removing Native American children from their families and sending them to remote boarding schools in order to 'Americanize' them. Overall, allow two to three hours to explore, and keep a lookout for unexpected treasures – like the Harry Potter bowl tucked in among more traditional pottery in the Native People in the Southwest gallery. Guided tours run at noon, 2pm or 3pm at no extra charge. Also check out the busy events schedule and the superb gift shop.
Selections from the Heard's vast collection are also displayed at the Heard Museum North ( 480-488-9817; 32633 N Scottsdale Rd; adult/child 6-12/student/senior $6/2/2/4; 10am-5pm Mon-Sat, 11am-5pm Sun) in Scottsdale.
Parking at both locations is free. Valley Metro light-rail stops beside the downtown museum at Encanto/Central Ave.
Desert Botanical Garden GARDENS
( 480-941-1225; www.dbg.org; 1201N Galvin Pkwy; adult/child/student/senior $18/8/10/15; 8am-8pm Oct-Apr, 7am-8pm May-Sep) This inspirational garden is a refreshing place to reconnect with nature and it offers a great introduction to desert plant life. Looping trails lead past an astonishing variety of desert denizens, arranged by theme (including a desert wildflower loop and a Sonoran Desert nature loop). It's pretty dazzling year-round, but the flowering season of March to May is the busiest and most colorful time to visit. Another highlight is December's nighttime luminarias _,_ when plants are draped in miles of twinkling lights.
Pueblo Grande Museum & Archaeological Park MUSEUM
( 602-495-0901; www.pueblogrande.com; 4619 E Washington St; adult/child 6-17/senior $6/5/3; 9am-4:45pm Mon-Sat, 1-4:45pm Sun) The juxtaposition of the ancient and modern makes this former Hohokam village memorable. Don't be surprised if a plane glides into view as you squint across ancient sightlines built into an age-old astronomy chamber. Excavations at the site, which is tucked between Phoenix and Tempe, have yielded many clues about the daily lives of anancient people famous for building such a well-engineered 1000-mile network of irrigation canals that some modern canals follow their paths. Study this fascinating culture at the small museum then stroll past the park's excavations, which include a ball court, a ceremonial platform and a section of the original canals.
Phoenix Art Museum MUSEUM
( 602-257-1222; www.phxart.org; 1625 N Central Ave; adult/child 6-17/student/senior $10/4/8/8, free Wed 3-9pm; 10am-9pm Wed, 10am-5pm Thu-Sat, noon-5pm Sun; ) The Phoenix Art Museum is Arizona's premier repository of fine art. Galleries include works by Claude Monet, Diego Rivera and Georgia O'Keeffe. The striking landscapes in the Western American gallery will get you in the mind-set for adventure. Take kids to the ingeniously crafted miniature period rooms in the Thorne Rooms, borrow a family audio guide or a KidPack, or visit the PhxArtKids Gallery (see www.phxartkids.org).
Grown-ups might want to join the free guided tours at noon, 1pm and 2pm. The museum's contemporary Arcadia Farms Café is a great place to grab a meal, and it's not only for museum-goers.
### PHOENIX IN...
#### One Day
Before the day heats up, hike to the top of Piestewa Peak then replenish your fuel supplies at Matt's Big Breakfast. Afterward, head to the Heard Museum for a primer on Southwestern tribal history, art and culture. If it's not too hot, take a prickly postprandial stroll through the exquisite Desert Botanical Garden; otherwise, steer toward your hotel pool or Wet 'n' Wild Phoenix to relax and cool off. Wrap up the day with a sunset cocktail on the slopes of Camelback Mountain at Edge Bar before reporting to dinner at Dick's Hideaway or Chelsea's Kitchen.
#### Two Days
On day two, head to Taliesin West to learn about the fertile mind of architectural great Frank Lloyd Wright, then grab a gourmet sandwich at the Herb Box before browsing the galleries and souvenir shops of Old Town Scottsdale. In the afternoon hit the pool and, if you've got one, see a masseuse back at your hotel ahead of getting all dressed up for a gourmet dinner at Kai Restaurant. Families might prefer an Old West afternoon of cowboys and shoot 'em ups at Rawhide followed by casual Mexican cuisine at Tee Pee.
Heritage & Science Park PLAZA
Tune out the surrounding skyscrapers and imagine thundering hooves and creaking stagecoaches as you amble around Historic Heritage Square ( 602-262-5029; http://phoenix.gov/PARKS/heritage.html; 115 N 6th St), a cluster of stately Victorians. Join a tour of the 1895 Rosson House (www.rossonhousemuseum.org; tours adult/child/senior $7.50/4/6; 10am-4pm Wed-Sat, noon-4pm Sun) or take the tots to the Arizona Doll & Toy Museum ( 602-253-9337; cnr 7th & Monroe Sts; adult/child $3/1; 10am-4pm Tue-Sat, noon-4pm Sun Sep-Jul; ) in the nearby 1901 Stevens House. The 1912 schoolroom with antique dolls squeezed behind the wooden desks is adorable. Star Wars figurines and GI Joe keep things from getting too frou-frou.
Too quaint? Make a beeline to the Arizona Science Center ( 602-716-2000; www.azscience.org; 600 E Washington St; adult/child 3-17/senior; $12/10/10; 10am-5pm; ), a high-tech, interactive temple of discovery where kids can slide through a stomach or investigate kinetic energy before winding down at the five-story IMAX Theatre (adult/child 3-17/senior $14/12/11) or the recently overhauled Planetarium (general admission plus adult/child/senior $8/8/7).
Hall of FlameMUSEUM
( 602-275-3473; www.hallofflame.org; 6101 E Van Buren St, Phoenix; adult/child 3-5/student 6-17/senior $6/1.50/4/5; 9am-5pm Mon-Sat, noon-4pm Sun; ) There are more than 90restored firefighting machines and relatedparaphernalia from 1725 onward. The National Firefighting Hall of Heroes lists the names of American firefighters killed on the job since 1981. There's also a tributeto the firefighters and police officers who died during the attack on September 11, 2001. Kids can don firefighting gear and clamber on one of the fire trucks.
##### SCOTTSDALE
Scottsdale sparkles with self-confidence, her glossy allure fuelled by good looks, charm and money. Distractions include a pedestrian-friendly downtown, chic hotels and a vibrant food and nightlife scene. A free trolley links Old Town Scottsdale with Scottsdale Fashion Square mall via the new Scottsdale Waterfront, a retail and office complex on the Arizona Canal.
Old Town Scottsdale NEIGHBORHOOD
Tucked among the glitzy malls and chichi bistros is Old Town Scottsdale, a tiny Wild West-themed enclave filled with cutesy buildings, covered sidewalks and stores hawking mass-produced 'Indian' jewelry and Western art. One building with genuine history is the 1909 Little Red School House, now home of the Scottsdale Historical Museum ( 480-945-4499; www.scottsdalemuseum.com; 7333 E Scottsdale Mall; admission free; 10am-5pm Wed-Sun Oct-May, 10am-2pm Wed-Sun Jun & Sep), where low-key exhibits highlight Scottsdale's history. Old Town is centered on Main St and Brown Ave.
In a cleverly adapted ex-movie theater, the Scottsdale Museum of Contemporary Arts ( 480-874-4666; www.smoca.org; 7374 E 2nd St; adult/child/student $7/free/5, free on Thu; 10am-5pm Tue-Wed & Fri & Sat, 10am-8pm Thu, noon-5pm Sun, closed Wed Sep-May) showcases global art, architecture and design, including James Turrell's otherworldly Knight Rise skyspace in the sculpture garden. The museum is across from the local performing arts center.
Taliesin West ARCHITECTURE
( 480-860-2700; www.franklloydwright.org; 12621 Frank Lloyd Wright Blvd; 9am-5pm) Frank Lloyd Wright was one of the seminal American architects of the 20th century. Taliesin West was his desert home and studio, built between 1938 and 1940. Still home to an architecture school and open to the public for guided tours, it's a prime example of organic architecture with buildings incorporating elements and structures found in surrounding nature. Duringthe popular Insights Tour (adult/child 4-12/student/senior $32/17/28/28; half-hourly 9am-4pm Nov–mid-Apr, hourly 9am-4pm mid-Apr–Oct), a docent lead visitors to Wright's office with its slanted canvas roof, the grand stone-walled living room where you can sit on original Wright-designed furniture, and the half-sunken Cabaret Theater. This informative tour feels much quicker than its 90 minutes. Shorter and longer tours are also available.
Cosanti ARCHITECTURE
( 480-948-6145; www.arcosanti.org; 6433 E Doubletree Ranch Rd; donation appreciated; 9am-5pm Mon-Sat, 11am-5pm Sun) The home and studio of Wright student Paolo Soleri, this unusual complex of cast-concrete structures served as a stepping stone for Soleri's experimental Arcosanti village, 65 miles north (Click here). Cosanti is also where Soleri's signature bronze and ceramic bells are crafted. You're free to walk around, see the bells poured (usually between 10:30am and 12:30pm weekdays) and browse the gift shop. Located about 9 miles south of Taliesin West.
##### TEMPE
Sandwiched between downtown Phoenix and Mesa, just south of Scottsdale, Tempe is a fun and energetic district enlivened by the 58,000 students of Arizona State University (ASU; www.asu.edu). Founded in 1885, the vast campus is home to Sun Devil Stadium, performance venues, galleries and museums.
ASU Art Museum MUSEUM
( 480-965-2787; http://asuartmuseum.asu.edu/http; cnr Mill Ave & 10th St; admission free; 11am-5pm Wed-Sat year-round, to 8pm Tue) This airy, contemporary gallery space has eye-catching art and intriguing exhibits. Architecture fans can tour the circular Gammage Auditorium ( 480-965-3434 box office; 480-965-6912 tours; www.asugammage.com; cnr Mill Ave & Apache Blvd; admission free, tickets from $20; 1-4pm Mon-Fri Oct-May), Frank Lloyd Wright's last major building. A popular performance venue, it stages primarily Broadway-style musicals and shows.
### ART WALKS
It may not have the mystique of Santa Fe or the cachet of New York, but Phoenix has almost imperceptibly worked its way up the ladder of art cities that matter. Scottsdale in particular teems with galleries laden with everything from epic Western oil paintings to cutting-edge sculpture and moody Southwestern landscapes. Every Thursday evening some 100 of them keep their doors open until 9pm for Art Walk (www.scottsdalegalleries.com), which centers on Marshall Way and Main St.
The vibe is edgier and the setting more urban during First Fridays (www.artlinkphoenix.com; 6-10pm), which draws up to 20,000 people to the streets of downtown Phoenix on the first Friday of every month, primarily for art but also for music, poetry slams and other events. Stop by the Central Phoenix Library for a brochure, map and shuttle-bus schedule before joining the fun.
Mill AveNEIGHBORHOOD
Situated along the campus' western edge, Mill Ave is Tempe's main drag and lined with restaurants, bars and a mix of national chains and indie boutiques. It's a fine place to browse for old vinyl records and vintage dresses. For cool metro and mountain views, huff it up for half a mile to the top of 'A' Mountain, so-called because of the giant letter 'A' painted there by ASU students, but officially known as Tempe Butte or Hayden Butte. The trailhead is on E 3rd St, near Mill Ave.
Mill Ave spills into Tempe Town Lake (www.tempe.gov/lake), a 2-mile-long recreational pond created by reclaiming the long-dry Salt River in the 1990s. Have a picnic at Tempe Beach Park and watch kids letting off steam at the waterfalls, rock slides and shallow pools of the ingenious Splash Playground (admission free; May-Sep; ). There's no swimming in the lake, but Tempe Town Lake Boat Rentals ( 480-517-4050; http://boats4rent.com; 72 W Rio Salado Pkwy; pedalboats/kayaks/16ft pontoon for 2hr $25/40/130) rents human-powered and motorized watercraft. Free outdoor concerts and festivals bring crowds to the park on weekends. The lakeshore has the shiny new lakefront Tempe Center for the Arts (www.tempe.gov/tca).
To get around downtown Tempe on weekdays, use the free Orbit bus (www.tempe.gov/tim/Bus/Orbit.htm; 6am-10pm Mon-Fri, 8am-10pm Sat, 8am-7pm Sun) that runs along Mill Ave and around the university every 15 minutes Monday to Saturday and every 30 minutes on Sunday.
Central Phoenix
Sights
Arizona Doll & Toy Museum (see 2)
1Arizona Science Center C4
2Historic Heritage Square C3
3Phoenix Art Museum C1
Rosson House (see 2)
Sleeping
4Budget Lodge Downtown B3
5HI Phoenix Hostel D2
Eating
Arcadia Farms Café (see 3)
6Matt's Big Breakfast B2
7Pizzeria Bianco C4
Drinking
8Alice Cooperstown B4
9Lost Leaf C2
Entertainment
Arizona Opera (see 11)
10Chase Field C4
Phoenix Symphony (see 11)
11Symphony Hall C3
12US Airways Center C4
##### MESA
Founded by Mormons in 1877, low-key Mesa is one of the fastest-growing cities in the nation and the third-largest city in Arizona with a population of nearly 500,000.
Arizona Museum of Natural History MUSEUM
( 480-644-2230; www.azmnh.org; 53 N MacDonald St; adult/child 3-12/student/senior $10/6/8/9; 10am-5pm Tue-Fri, 11am-5pm Sat, 1-5pm Sun; ) Even if you're not staying in Mesa, this museum is worth a trip, especially if your kids are into dinosaurs (and aren't they all?). In addition to the multi-level Dinosaur Mountain, there are loads of life-size casts of the giant beasts plus a touchable apatosaurus thighbone. Other exhibits highlight Arizona's colorful past, from a prehistoric Hohokam village to an eight-cell territorial jail.
Rawhide Western Town & Steakhouse THEME PARK
( 480-502-5600; www.rawhide.com; 5700 W N Loop Rd, Chandler; admission free, per attraction or show $5, unlimited day pass $15; 5-9pm Wed-Fri, noon-9:30pm Sat, noon-8:30pm Sun, varies seasonally; ) Every 'howdy' sounds sincere at this re-created 1880s frontier town located about 20 miles south of Mesa on the Gila River Indian Reservation. Test your mettle on a mechanical bull or a stubborn burro, ride a cutesy train, pan for gold, and join in all sorts of other hokey-but-fun shenanigans. The steakhouse has rattlesnake and Rocky Mountain oysters (bull testicles) for adventurous eaters and mesquite-grilled slabs of beef for everyone else.
#### Activities
In Phoenix, taking a walk on the wild side feels like a micro-vacation from the urban bustle. Find maps and trail descriptions for Piestewa Peak and South Mountain Park at http://phoenix.gov/recreation/rec/index.html.
Both parks described below have trails designated for mountain bikers.
Piestewa Peak/Dreamy Draw Recreation AreaHIKING
( 602-261-8318; Squaw Peak Dr, Phoenix; 5am-11pm, but last entry at 6:59pm) Dotted with saguaros, ocotillos and other localcacti, this convenient park was previously known as Squaw Peak. It was renamed for local Native American soldier Lori Piestewa who was killed in Iraq in 2003. Be forewarned: the trek to the 2608ft summit is hugely popular and the park can get jammed on winter weekends. Parking lots northeast of Lincoln Dr between 22nd and 24th Sts fill early. Dogs are allowed on some trails.
South Mountain Park HIKING
( 602-262-7393; 10919 Central Ave, Phoenix; 5am-11pm, but last entry at 6:59pm) At 25 sq miles, this local favorite is larger than Manhattan. The 51-mile trail network (leashed dogs allowed) dips through canyons, over grassy hills and past granitewalls, offering city views and access to Native American petroglyphs.
Cactus Adventures BIKING
( 480-688-9170; www.cactusadventures.com; 4747Elliot Rd, Suite 21; half-day rental from $30; 9am-7pm Mon-Sat, 9am-5pm Sun) A quarter-mile pedal from South Mountain Park,Cactus Adventures rents bikes and offers guided hiking and biking tours.
Ponderosa Stables HORSEBACK RIDING
( 602-268-1261; www.ponderosastablesaz.com; 10215 S Central Ave, Phoenix; 1/2hr rides $33/55; 8am-4pm Mon-Sat, 9am-4pm Sun Oct-May, shorter hours Jun-Sep) This outfitter leads rides through South Mountain Park. Reservations required for most trips.
Salt River Recreation TUBING
( 480-984-3305; www.saltrivertubing.com; 1320 N Bush Hwy; tubes & shuttle $15, cash only; 9am-6:30pm May-late Sep; ) Floating down the Salt River in an inner tube is loads of fun and a great way to cool down on a hot summer day. On this trip, you'll take the Lower Salt River through the stark Tonto National Forest. The launch is in northeast Mesa, about 15 miles north of Hwy 60 on Power Rd. Floats are two, three or five hours long, including the shuttle-bus ride back. Kids must be at least 4ft tall and at least eight years old.
#### Festivals & Events
The most popular event in Phoenix is the Fiesta Bowl football game ( 480-350-0911; www.fiestabowl.org; 1 Cardinals Dr, Glendale) held in early January at the University of Phoenix Stadium. It's preceded by one of the largest parades in the Southwest.
The Arizona State Fair (www.azstatefair.com; 1826 W McDowell Rd) lures folks to the Arizona State Fairgrounds the last two weeks of October and first week of November with a rodeo, livestock displays, a pie-eating contest and concerts.
#### Sleeping
Greater Phoenix is well stocked with hotels and resorts, but you won't find many B&Bs, cozy inns or charming mom-and-pops'. Locals know that prices plummet in summer, and you'll see plenty of Valley residents taking advantage of super-low prices at their favorite resorts when the mercury rises.
##### PHOENIX
Royal Palms Resort & Spa RESORT $$$
( 602-840-3610; www.royalpalmsresortandspa.com; 5200 E Camelback Rd; r $329-429, ste from $366; ) This posh boutique resort at the base of Camelback Mountain was once the winter retreat of New York industrialist Delos Cook. Today, it's a hushed and elegant place, dotted with Spanish Colonial villas, flower-lined walkways and palms imported from Egypt. Pets can go Pavlovian for soft beds, personalized biscuits and walking services. The $28 daily resort fee covers parking, wi-fi, the fitness center and gratuities.
Arizona Biltmore Resort & Spa RESORT $$$
( 602-955-6600, 800-950-0086; www.arizonabiltmore.com; 2400 E Missouri Ave; r $300-459, ste from $489; ) With architecture inspired by Frank Lloyd Wright, the Biltmore is perfect for connecting to the magic of yesterday: when Irving Berlin penned 'White Christmas' in his suite and Marilyn Monroe splashed around in the pool. It boasts more than 700 discerning units, two golf courses, several pools, a spa, a kids' club and more luxe touches. Unfortunately wi-fi can be spotty beyond the lobby and the main pool. Daily resort fee is $28.
Clarendon Hotel HOTEL $$
( 602-252-7363; www.theclarendon.net; 401 W Clarendon Ave; r $160-199; ) This upbeat indie hotel has a finger-snapping, minimalist cool that manages to be both welcoming and hip. In the standard rooms look for 42-inch flat-screen TVs, artsy prints and dark custom furniture. Unwind in the Oasis pool with its glass waterwall, then ride up to the breezy skydeck for city-wide views. Only bummer? The $20 daily fee covering wi-fi, parking and phone calls. Pets are $50 per stay.
Aloft Phoenix-Airport HOTEL $$
( 602-275-6300; www.aloftphoenixairport.com; 4450 E Washington St; r $129-160; ) Rooms blend a pop-art sensibility with the cleanest rounded edges of modern design. The hotel is near Tempe and across the street from the Pueblo Grand Museum. No extra fee for pets.
HI Phoenix Hostel HOSTEL $
( 602-254-9803; www.hiusa.org/phoenix; 1026 N 9th St; dm $20-23, d $35-50; ) This is the kind of hostel that makes you fall back in love with backpacking. It's a veritable UN of half-mad guests with fun owners who know Phoenix and want to enjoy it with you. The 14-bed hostel sits in a working-class residential neighborhood and has relaxing garden nooks. Check-in is from 8am to 10am and 5pm to 10pm. Closed in July and August.
Budget Lodge Downtown MOTEL $
( 602-254-7247; www.blphx.com; 402 W Van Buren St; r incl breakfast $50-55; ) The Budget Lodge doesn't have time for sassiness or charisma. It's got a job to do, and it does it well: providing a clean, low-cost place to sleep. Rooms have a microwave and fridge.
##### SCOTTSDALE
Boulders RESORT $$$
( 480-488-900; www.theboulders.com; 34631 N Tom Darlington Dr, Carefree; casitas $350-850, villas $1050-1250; ) Tensions evaporate the moment you arrive at this desert oasis that blends nearly imperceptibly into a landscape of natural rock formations – and that's before you've put in a session at the massage table or steam room at the ultraposh on-site Golden Door Spa. Basically, everything here is calculated to take the edge off travel, making it a perfect destination for recovering from jet lag or rediscovering your significant other. For extra privacy book an individual casita, to which you will be whisked on a golf cart past the 18-hole Jay Morris-designed championship golf course. Daily resort fee is $30. Weekend rates can drop as low as $139 in summer.
Old Town Scottsdale
Sights
1Scottsdale Historical Museum C3
2Scottsdale Museum of Contemporary Arts C4
Sleeping
3Hotel Indigo Scottsdale D1
4Hotel Valley Ho A3
Eating
5Cowboy Ciao B2
6Herb Box B2
7Oregano's B4
8Sugar Bowl C3
Drinking
9Rusty Spur Saloon C3
Entertainment
10BS West B2
11Crown Room D1
Shopping
12Scottsdale Fashion Square B1
Hotel Valley Ho BOUTIQUE HOTEL $$$
( 480-248-2000; www.hotelvalleyho.com; 6850 E Main St; r $289-339, ste $399-439; ) Everything's swell at the Valley Ho, where midcentury modern gets a 21st-century twist. This jazzy joint once bedded Bing Crosby, Natalie Wood and Janet Leigh, and today it's a top pick for movie stars filming on location in Phoenix. Bebop music, upbeat staff and eye-magnets like the 'ice fireplace' recapture the Rat Pack-era vibe, and the theme travels well to the balconied rooms. Don't ignore the VH Spa, whose expert staff put the 'treat' in treatments. Pets stay free, but wi-fi is $10 per day.
Sanctuary on Camelback Mountain RESORT $$$
( 480-948-2100; www.sanctuaryoncamelback.com; 5700 E McDonald Dr; r $419-629, houses $1800-3500; ) Draped across the northern slopes of Camelback Mountain, this luxe resort feels like a hideaway of the gods. Mountain suites, spa casitas, private homes – no matter your choice, you will feel pampered, protected and deserving. Lodgings are decorated with the beautiful warm tones of the desert and outfitted with whatever amenities your craving heart desires. Make sure you enjoy a cocktail at Edge Bar, Sanctuary's swank outdoor watering hole with sweeping views of the Valley. Daily resort fee $18.
### PHOENIX FOR CHILDREN
Phoenix is a great family town with plenty to keep the tykes occupied. If your child loves animals, head to Phoenix Zoo ( 602-273-1341; www.phoenixzoo.org; 455 N Galvin Pkwy, Phoenix; adult/child $18/9; 9am-5pm early Jan-May, 7am-2pm Jun-Aug, 9am-5pm Sep & Oct, 9am-4pm Nov-early Jan; ). A wide variety of animals, including some rare ones, are housed in several distinct and natural-looking environments. Watch the giraffes nibble on a lofty lunch from the overlook beside the African savanna, then walk through Monkey Village – those squirrel monkeys are pretty darn cute.
If that's too tame, make the trip out to the private Wildlife World Zoo ( 623-935-9453; www.wildlifeworld.com; 16501 W Northern Ave, Litchfield Park; adult/child $28/15, aquarium only/aquarium after 5pm $17/9; zoo 9am-6pm, aquarium 9am-9pm; ) 35 miles northwest of downtown Phoenix. View exotic creatures, many of them endangered, and predators like crocodiles and piranhas in the aquarium.
Older kids will likely get more out of Castles N' Coasters ( 602-997-7575; www.castlesncoasters.com; 9445 E Metro Pkwy, Phoenix; unlimited rides Sat & Sun $21, activities individually priced Mon-Fri; hours vary; ), a big amusement park by the Metrocenter Mall about 20 miles northwest of downtown, near exit 207 off I-17. From chickens to bravehearts, there's a coaster (or ride) for everyone.
To cool off in summer, Wet 'n' Wild Phoenix ( 623-201-2000; www.wetnwildphoenix.com; 4243 W Pinnacle Peak Rd, Glendale; over/under 48in tall $35/28, senior $28; 10am-6pm Sun-Wed, 10am-10pm Thu-Sat, 11am-7pm Sun Jun-Jul, varies May, Aug & Sep; ) has pools, tube slides, wave pools, waterfalls, floating rivers and other splash zones. It's located in Glendale, 2 miles west of I-17 at exit 217, about 30 miles northwest of downtown Phoenix.
Hermosa Inn BOUTIQUE HOTEL $$$
( 602-955-8614; www.hermosainn.com;5532 N Palo Cristi Rd; r & casitas $289-449; ) The signage is discreet but the flowersare not at this gorgeous retreat. The 34 rooms and casitas give off soothing vibes thanks to Spanish Colonial decor that makes perfect useof color and proportion. There's an excellent restaurant on site. Pets OK and no extra fee.
FireSky Resort & Spa RESORT $$$
( 480-945-7666; www.fireskyresort.com; 4925 N Scottsdale Rd; r $275-330; ) This all-inclusive resort is certainly plush, but it feels less stuffy than some of its highfalutin neighbors. The vibe from the lobby to the rooms in this cozy Kimpton property is a blend of classic elegance, Sonoran desert aesthetics and modern amenities.
Hotel Indigo Scottsdale HOTEL $$
( 480-941-9400; www.scottsdalehiphotel.com; 4415 N Civic Center Plaza; r $174-184, ste $204-224; ) Sleek, spacious rooms are adorned with a wall-sized desert photo, and the sumptuous bedding is perfect hangover prevention after a night of cavorting. Other hot-spot trappings include outdoor fire pits, club music in the lobby, fancy toiletries and plasma TVs. Dogs welcome at no extra charge.
Sleep Inn HOTEL $
( 480-998-9211; www.sleepinnscottsdale.com; 16630 N Scottsdale Rd; r incl breakfast $99-114; ) It's part of a chain, but this Sleep Inn wins points for its extensive complimentary breakfast, afternoon cookies, friendly staff and proximity to Taliesin West. There's also a laundry and free 24hr hotel shuttle that runs within five miles of the hotel. Pets $20 per night.
##### TEMPE
Sheraton Wild Horse
Pass Resort & Spa RESORT $$$
( 602-225-0100; www.wildhorsepassresort.com; 5594 W Wild Horse Pass Blvd, Chandler;r $239-579; ) At sunset, scan the lonely horizon for the eponymous wild horses silhouetted against the South Mountains. Owned by the Gila River tribe and nestled on their sweeping reservation south of Tempe, this 500-room resort is a stunning alchemy of luxury and Native American traditions. The domed lobby is a mural-festooned roundhouse and rooms reflect the traditions of local tribes. The spa offers Bahn (Blue Coyote) wraps and a Pima Medicine massage. The award-winning Kai Restaurant (Click here) serves indigenous Southwestern cuisine. That, plus two 18-hole golf courses, an equestrian center, tennis courts, sumptuous rooms and a waterslide modeled after Hohokam ruins round out the appeal. Wi-fi is available in the lobby.
Best Western Inn of Tempe HOTEL $
( 480-784-2233; www.innoftempe.com; 670 N Scottsdale Rd; r incl breakfast $75-90; ) This well-kept, accommodating contender sits right next to the busy 202 freeway but within walking distance from Tempe Town Lake. ASU and lively Mill Ave are within staggering distance. Perks include a free airport shuttle that also runs to stops within three miles of the hotel.
InnSuites MOTEL $$
( 480-897-7900; www.innsuites.com/tempe; 1651 W Baseline Rd; r incl breakfast $109-179; ) Shopaholics: this property sits right across from the Arizona Mills mall, and there's plenty of space in your Southwest-styled room to store your loot. Airport shuttle available from 6am to 10pm.
#### Eating
Phoenix has the biggest selection of restaurants in the Southwest. Reservations are recommended at the more fashionable places. And yes, our picks are heavy on Mexican restaurants, but isn't that part of the reason you're here?
##### PHOENIX
Matt's Big Breakfast BREAKFAST $
( 602-254-1074; 801 N 1st St, at McKinley St; mains $5-8; 6:30am-2:30pm Tue-Sun) First, a warning: even on weekdays lines are often out the door. There are no reservations, so sign your name on the clipboard and expect a 20-minute wait (and bring quarters for the meter). The upside? Best. Breakfast. Ever. Every regular menu item is great but daily specials – such as eggs scrambled with peppers and chorizo into fluffy-spicy-ohmygoodness on a bed of mouthwatering crispy home fries – are supremely yummy. A true Phoenix institution.
Dick's Hideaway NEW MEXICAN $$
( 602-241-1881; http://richardsonsnm.com; 6008 N 16th St; breakfast $8-16, lunch $12-16, dinner $17-37; 7am-midnight) A mysterious stranger at a bar in Bisbee recommended this pocket-sized ode to New Mexican cuisine, and boy are we glad he did. Grab a small table beside the bar or settle in at the communal table in the side room and prepare for hearty servings of savory, chile-slathered New Mexican fare, from enchiladas to tamales to rellenos. We especially like the Hideaway for breakfast, when the Bloody Marys arrive with a shot of beer. A tip: the unmarked entrance is between the towering shrubs.
Durant's STEAKHOUSE $$
( 602-264-5967; 2611 N Central Ave; most mains $17-34; lunch & dinner) This dark and manly place is a gloriously old-school steak house. You will get steak. It will be big and juicy. There will be a potato. The ambiance is awesome too: red velvet cozy booths and the sense that the Rat Pack is going to waltz in at any minute.
Pizzeria Bianco PIZZERIA $$
( 602-258-8300; 623 E Adams St; pizza $12-16; 11am-10pm Tue-Sat) James Beard-winner Chris Bianco may have stepped back from the ovens at his famous downtown pizza joint (allergies are to blame), but the thin-crust gourmet pies remain as tasty as ever. The tiny restaurant is now open for lunch, good news for travelers exploring the adjacent Heritage Square.
Barrio Café MEXICAN $$
( 602-636-0240; 2814 N 16th St; mains $11-26, brunch $10-15; lunch Tue-Fri & Sun, dinner Tue-Sun) Barrio's T-shirts are emblazoned with _comida chingona_ , which translates as 'fucking good food'. Crude, maybe. To the point, definitely. Barrio makes Mexican food at its most creative: how many menus featuring guacamole spiked with pomegranate seeds or goat-milk-caramel-filled churros have you seen?
Da Vang VIETNAMESE $
( 602-242-3575; 4538 N 19th Ave; most mains $6-13; 8am-8pm) Gosh dang, da Vang, how'd you get so good? Our favoriteVietnamese in the Valley is served in a Spartan dining room; it's as if the plainness of the location is in direct proportion to the awesomeness of the food. The _pho_ is fantastic, and you'd be remiss not to try some of the lovely 'dry' rice noodle dishes.
Tee Pee Mexican Food MEXICAN $
( 602-956-0178; www.teepeemexicanfood.com; 4144 E Indian School Rd; mains $8-11; 11am-10pm Mon-Sat, to 9pm Sun) If you're at all snobby about Mexican food, you will not be happy at Tee Pee. If, however, you like piping-hot plates piled high with cheesy, messy, American-style Mexican food, with a side of friendly service, then grab a booth at this 40-year-old Phoenix fave. George W Bush ate here in 2004 and ordered two enchiladas, rice and beans – now called the Presidential Special. Dig in!
Arcadia Farms Café AMERICAN $$
( 602-257-2191; 1625 N Central Ave; mains $11-15; 10am-8:30pm Wed, 10am-4pm Thu-Sat, 10:30am-4pm Sun) Hmm, the smoked-salmon club? Or the wild mushroom, spinach and goat-cheese tart? Perhaps the strawberry chicken salad on baby greens? The problem with this chic bistro, tucked inside the Phoenix Art Museum (Click here), is that everything sounds delectable. This welcoming eatery uses only seasonal organic ingredients for its light yet satisfying dishes. And for ladies who lunch, there's always the peach Bellini.
Chelsea's Kitchen AMERICAN $$
( 602-957-2555; 5040 N 40th St; lunch $10-17, dinner $10-27; lunch & dinner daily, brunch Sun) Kick up the wardrobe for this see-and-be-seen eatery (you will get a once-over); but then again, looking nice just feels right. Brick walls, lofty industrial ceiling, leather booths: this casual place wouldn't be out of place in New York's Chelsea. The cuisine, however, is distinctly Western-inspired. Burgers, salads and tacos make appearances, but we're partial to the organic meats tanned to juicy perfection in the hardwood rotisserie. There's a nice patio too.
Noca AMERICAN $$$
( 602-956-6622; 3118 E Camelback Rd; mains $20-33; lunch & dinner Tue-Sun, open Mon Dec-Mar) Short for north of Camelback, Noca is where foodies go to die content. The restaurant serves New American fare using American ingredients in the style of classical innovator French Laundry. The tasting menu costs $50, but a better deal is the $27 multi-course simple Sunday suppers.
Pane Bianco SANDWICHES $
( 602-234-2100; 4404 N Central Ave; sandwiches $8; 11am-8pm Mon-Sat) Part of the Pizzeria Bianco empire, Pane Bianco is one of the best spots in town for an artisan sandwich. You can't eat inside but there are picnic tables just out the door.
##### SCOTTSDALE
Fresh Mint VIETNAMESE $
( 480-443-2556; www.freshmint.us.com; 13802 N Scottsdale Rd; mains $6-14; 11am-9pm Mon-Sat; ) What? Never had kosher Vietnamesevegan? Us too, but there's always a first time – and if it tastes anything like the food at Fresh Mint, you'll want to get more. If you're skeptical of soy chicken and tofu (served many ways; we like it in the lemongrass curry) we understand, but we respectfully submit that this stuff is as tasty as any bacon cheeseburger.
Oregano's PIZZERIA $$
( 480-970-1860; 3622 N Scottsdale Rd; mains $6-15, pizza $9-23; 11am-10pm) This outpost of the popular local pizza chain earns its kudos: savory, Chicago-style pies, welcoming service and a patio near-to-bursting with happy people. Not up for pizza? Try one of the hearty pastas. At the Old Town location the hostess stand is beside the patio out back. Everybody loves the Pizza Cookie.
Herb Box AMERICAN $$
( 480-289-6160; www.theherbbox.com; 7134 E Stetson Dr; lunch $10-15, dinner $14-25; lunch daily, dinner Mon-Sat) It's not just about sparkle and air kisses at this chichi bistro in the heart of Old Town's Southbridge. It's also about fresh, regional ingredients, artful presentation and attentive service. For a light, healthy, ever-so-stylish lunch (steak salad, turkey avocado wrap, pear-gorgonzola flatbread), settle in on the patioand toast your good fortune – with an organic chamomile citrus tea, of course.
Mastro's Ocean Club SEAFOOD $$$
( 480-443-8555; www.mastrosrestaurants.com; 15045 N Kierland Blvd; mains $30-50; dinner) Mastro's is gunning for the title of best seafood in the Valley of the Sun, and we think it may deserve the crown. The allure of the restaurant, part of an upscale chain, is in its incredibly rich, decadent take on everything that swims under the waves. The restaurant is located in Kierland Commons.
Sugar Bowl ICE CREAM $
( 480-946-0051; 4005 N Scottsdale Rd; ice cream under $5, mains $6-9; 11am-10pm Sun-Thu, 11am-midnight Fri & Sat; ) Get your ice cream fix at this pink-and-white Valley institution. Also serves a whole menu of sandwiches and salads.
Cowboy Ciao AMERICAN $$
( 480-946-3111; www.cowboyciao.com; 7133 E Stetson Dr; lunch $13-15, dinner $15-35; lunch & dinner) At this mood-lit cantina dishes are a veritable cauldron of textures and flavors. The elk loin, for instance, is paired with crunchy hazelnut pesto, creamy mushroom risotto and a rich cabernet demi-glace. Sometimes it works, sometimes it's too complex for comfort.
##### TEMPE
Kai Restaurant NATIVE AMERICAN $$$
( 602-225-0100; www.wildhorsepassresort.com; 5594 W Wild Horse Pass Blvd, Chandler; mains $40-49, 8-course tasting menu $200; dinner Tue-Sat) Native American cuisine soars to new heights at Kai, enhanced and transformed by traditional crops grown along the Gila River. Dinners are like fine tapestries – with such dishes as pecan-crusted Colorado lamb with native seeds mole or caramelized red mullet with cereal of chia seeds – striking just the right balance between adventure and comfort. Service is unobtrusive yet flawless, the wine list handpicked and the room decorated with Native American art. Dress nicely (no shorts or hats). It's at the Sheraton Wild Horse Pass Resort & Spa on the Gila River Indian Reservation.
Essence CAFE $
( 480-966-2745; 825 W University Dr; breakfast $5-7, lunch $8-9, 7am-3pm Mon-Fri, 8am-3pm Sat, closed Sun). The iced caramel coffee at this breezy box of deliciousness may be the best drink on the planet. Essence has the chic allure of a French bistro but the service is friendly and, on our visit, fairly quick. Look for French toast and egg dishes at breakfast, and salads, gourmet sandwiches and a few Mediterranean specialties at lunch. The eco-minded cafe strives to serve organic, locally grown fare.
Pita Jungle MIDDLE EASTERN $
( 480-804-0234; 1250 E Apache Blvd; dishes $6-15; 10:30am-10pm; ) One bite and you're hooked by the tangy hummus, crispy falafel and chicken shawarma at this upbeat, funky industrial joint – a local chain – that's on the radar of tousled students.
##### MESA
Landmark AMERICAN $$
( 480-962-4652; 809 W Main St; lunch $8-13, dinner $10-25; lunch & dinner, closes 7pm Sun) If you worship at the culinary altar of steak and prime rib, you'll want to make the pilgrimage to this converted 1908 Mormon church that's been a family-owned local mainstay for decades. Lighter eaters, meanwhile, have an entire 'Salad Room' with over 100 items for grazing (lunch/dinner $11/15).
#### Drinking
Posh watering holes are found in the most unlikely of spots in the Phoenix area, even amid chain stores in strip malls. Scottsdale has the greatest concentration of trendy bars and clubs as well as a convivial line-up of patios on Scottsdale Rd in Old Town; Tempe attracts the student crowd.
###### Cafes
Lux Coffeebar COFFEE $
(www.luxcoffee.com; 4400 N Central Ave 7am-10pm; ) Bowie's 'Rebel, Rebel' may be spilling from the speakers but we're not convinced that the hipsters tapping away on their MacBooks in porkpie hats are going to be breaking too many rules. But hey, the staff schmoozes just fine, the espresso is organic and the vibe is welcoming, so it's all good.
###### Bars
Postino Winecafé Arcadia WINE BAR $$
(www.postinowinecafe.com; 3939 E Campbell Ave, at 40th St, Phoenix; 11am-11pm Mon-Thu, 11am-midnight Fri & Sat, 11am-10pm Sun) Your mood will improve the moment you step into this convivial, indoor-outdoor wine bar. It's a perfect gathering spot for friends ready to enjoy the good life – but solos will do fine too. Highlights include the misting patio, rave-worthy bruschetta, and $5 wines by the glass between 11am and 5pm. This spot used to be the home of the Arcade Post Office.
Vig BAR $
(4041 N 40th St, Scottsdale; 11am-1am, bar until 2am) Ignore the imposing Soviet-style exterior and step inside. The Vig is where the smart set – stylish, well-scrubbed, happy – comes to knock back a few cocktails. Sleek booths, a dark bar, a bustling patio, an upbeat vibe: be careful or you might find yourself tossing your hair and flashing your tan like the rest of 'em. Park in the grocery store lot across the street in designated Vig spots.
Edge Bar BAR $
(5700 E McDonald Dr, Sanctuary on Camelback Mountain, Paradise Valley) Enjoy a sunset 'on the edge' at this stylish cocktail bar perched on the side of Camelback Mountain. No room outside? The equally posh, big-windowed Jade Bar should do just fine. Both are within the plush confines of Sanctuary on Camelback Mountain. Free valet.
Rusty Spur Saloon BAR $
( 480-425-7787; 7245 E Main St, Scottsdale; 11am-2am) Nobody's putting on airs at this fun-lovin', pack-'em-in-tight country bar where the grizzled Budweiser crowd gathers for cheap drinks and twangy country bands. It's in an old bank building that closed during the Depression; the vault now holds liquor instead of greenbacks – except for the dollar bills hanging from the ceiling. Pardner, we kinda like this place.
Alice Cooperstown SPORTS BAR $
(www.alicecooperstown.com; 101 E Jackson St, Phoenix; 11am-9pm Mon-Thu, 11am-10pm Fri, noon-10pm Sat) This beer hall really is the original shock rocker's (and Phoenix resident's) baby. Cooperstown is a play on Alice Cooper's name and the real location of the Baseball Hall of Fame. On game days it floods with giddy sports lovers toasting their teams. For music fans, rock-and-roll memorabilia covers the walls.
Four Peaks Brewing Company BREWERY $
( 480-303-9967; www.fourpeaks.com; 1340 E 8th St, Tempe; 11am-2am Mon-Sat, 10am-2am Sun) Beer lovers rejoice: you're in for a treat at this quintessential neighborhood brewpub in a cool Mission Revival-style building.
Greasewood Flat BAR $
( 480-585-9430; www.greasewoodflat.net; 27375 N Alma School Pkwy, Scottsdale; 11am-11pm) At this beer-garden-sized outdoor pub and ex-stagecoach stop, rough-and-tumble types – cowboys, bikers, preppy golfers – gather around the smoky barbecue and knock back the whisky. Cash only.
Lost Leaf BAR $
(www.lostleaf.org; 914 N 5th St, Phoenix; 5pm-2am) Yeah, it's an average-sized house from the outside. But inside? Pop-art paintings, cozy wood furnishings, an intimate patio for smoking and a beer menu that made us snap a salute in respect. Live music nightly.
###### Nightclubs & Live Music
Char's Has the Blues BLUES $
( 602-230-0205; www.charshastheblues.com; 4631 N 7th Ave, Phoenix; no cover Mon-Thu, cover Fri-Sun; 8pm-1am Sun-Wed, 7:30pm-1am Thu-Sat) Dark and intimate – but very welcoming – this blues cottage packs 'em in with solid acts most nights of the week, but somehow still manages to feel like a well-kept secret.
Rhythm Room LIVE MUSIC $-$$
( 602-265-4842; www.rhythmroom.com; 1019 E Indian School Rd, Phoenix) Some of the Valley's best live acts take the stage at this small venue, where you feel like you're in the front row of every gig. It tends to attract more local and regional talent than big names, which suits us just fine. Check the calendar for show start times.
BS West GAY $
( 480-945-9028; www.bswest.com; 7125 E 5th Ave, Scottsdale; 2pm-2am) A high-energy gay video bar and dance club in the Old Town Scottsdale area, this place has pool tables and a small dance floor, and hosts karaoke on Sunday. Most agree that when it comes to the Valley's gay clubs, this is the place to be; the boys are hot, the music is loud and the straight interlopers, while present, haven't overwhelmed the dance floor.
Crown Room DJ $
( 480-423-0117; 1019 E Indian School Rd, Phoenix; 9pm-2am Sun, Mon & Wed, 8pm-2am Thu-Sat) Combine Scottsdale's sophistication with its sun-kissed, carefree sexuality and you get the Crown: a thumping nightclub so cool it wears sunglasses in the dark. The Crown isn't just a meat market, but it is very much a place to see and be seen.
### CACTUS LEAGUE SPRING TRAINING
Before the start of the major league baseball season, teams spend March in Arizona (Cactus League) and Florida (Grapefruit League) auditioning new players, practicingand playing games. Tickets are cheaper (from $6 to $8 depending on the venue), the seats better, the lines shorter and the games more relaxed. Check www.cactusleague.com for schedules and links to tickets.
#### Entertainment
The entertainment scene in Phoenix is lively and multifaceted, if not particularly edgy. You can hobnob with high society at the opera or symphony, mingle with the moneyed at a chic nightclub, or let your hair down at a punk concert in a local dive. Spectator sports are huge.
These publications will help you plug into the local scene in no time:
Arizona Republic Calendar (www.azcentral.com/thingstodo/events) The Thursday edition of this major daily newspaper includes a special section with entertainment listings.
Phoenix New Times (www.phoenixnewtimes.com) This free, alternative weekly is published on Thursday and available citywide.
###### Performing Arts
The following are the most acclaimed venues and companies in Phoenix. Not much goes on during summer.
Phoenix Symphony SYMPHONY
( administration 602-495-1117, box office 602-495-1999; www.phoenixsymphony.org; 75 N 2nd St & 1 N 1st St) Arizona's only full-time professional orchestra plays classics and pops, mostly at Symphony Hall and sometimes at its 1st St outpost, from September to May.
Arizona Opera OPERA
( 602-266-7464; www.azopera.com; 75 N 2nd St) The state ensemble produces five operas per season, usually big-ticket favorites such as Mozart's _Magic Flute_ and Verdi's _La Traviata_. Performances are at Symphony Hall.
Phoenix Theatre PERFORMING ARTS
( 602-254-2151; www.phoenixtheatre.com; 100 E McDowell Rd) The city's main dramatic group puts on a good mix of mainstream and edgier performances. The attached Cookie Company does children's shows.
Gammage Auditorium PERFORMING ARTS
( 480-965-3434; www.asugammage.com; 1200 S Forest Ave, Tempe) At the ASU Tempe campus, this venue presents crowd-pleasing plays and musicals.
###### Sports
Phoenix has some of the nation's top professional teams, and tickets for the best games sell out fast. Many of the following teams play at the US Airways Center .
Arizona Cardinals FOOTBALL
( 602-379-0101; www.azcardinals.com; 1 Cardinals Dr, Glendale) In 2006 this National Football League (NFL) team moved from Tempe to the brand-new and architecturally distinguished University of Phoenix Stadium in the western Valley city of Glendale. The season runs from fall to spring.
Arizona Diamondbacks BASEBALL
( 602-462-6500; www.arizona.diamondbacks.mlb.com; 201 E Jefferson St, Phoenix) This major-league baseball team won the World Series in 2001 and plays at Chase Field in downtown Phoenix.
Phoenix Coyotes HOCKEY
( 480-563-7825; www.phoenixcoyotes.com; 9400 Maryland Ave, Glendale) Hosted by the Jobing.com Arena, this National Hockey League (NHL) team plays from October to March.
Phoenix Mercury BASKETBALL
( 602-252-9622; www.wnba.com/mercury; 201 E Jefferson St, Phoenix) The women's 2007 National Basketball Association (NBA) winners play professional basketball from June to September at the US Airways Center.
Phoenix Suns BASKETBALL
( 602-379-7900; www.nba.com/suns; 201 E Jefferson St, Phoenix) The NBA Suns play at the US Airways Center from December to April.
#### Shopping
The Valley of the Sun is also the Valley of theconsumer. From western wear to arts and crafts and Native Americana, it's easy to find asouvenir. Mall culture is also huge. Old Town Scottsdale is known for its art galleries and Southwestern crafts shops. Mill Ave in Tempe has a nice mix of indie and chain boutiques.
###### Bookstores
Bookmans BOOKS
( 602-433-0255; www.bookmans.com; 8034 N 19th Ave; 9am-10pm; ) The bibliophile's indie mecca, with a neighborhood vibe, events and aisle after aisle of new and used books, mags and music. Free wi-fi.
Changing Hands BOOKS
( 480-730-0205; www.changinghands.com; 6428 S McClintock Dr, Tempe; 10am-9pm Mon-Fri, 9am-9pm Sat, 10am-6pm Sun) _Publisher Weekly_ 's 2007 Bookstore of the Year has used, new, hard-to-find and out-of-print books and magazines, plus lots of events.
###### Malls
Biltmore Fashion ParkMALL
(www.shopbiltmore.com; 2502 E Camelback Rd, at 24th St, Phoenix) This exclusive mall preens on Camelback just south of the Arizona Biltmore.
Kierland CommonsMALL
(www.kierlandcommons.com; 15205 N Kierland Blvd, Scottsdale) This new outdoor mall in northern Scottsdale is pulling in crowds.
Scottsdale Fashion SquareMALL
(www.fashionsquare.com; 7014 E Camelback, at Scottsdale Rd, Scottsdale) From Abercrombie & Fitch to Z Tejas Grill, this upscale mall has chains, department stores and restaurants.
BorgataMALL
(www.borgata.com; 6166 N Scottsdale Rd, Scottsdale) One of the fancier outdoor malls, with lots of boutiques and galleries, it was designed to look like a medieval Italian town.
###### Museum Shops
For unique gifts, some of the best finds are in the shops attached to Phoenix's best museums. You do not need to pay admission to the museum to access the shops (but you're missing out).
Heard Museum Shop ARTS & CRAFTS
(www.heardmuseumshop.com; 2301 N Central Ave, Phoenix; 9:30am-5pm, from 11am Sun) The museum store at the Heard Museum has one of the finest collections of Native American original arts and crafts in the world. Their kachina collection alone is mind-boggling. Jewelry, pottery, Native American books and a wide array of fine arts are also on offer.
Garden Shop at the
Desert Botanical Garden GARDENING
(www.dbg.org; 1201 N Galvin Pkwy; 9am-5pm) Plant your own desert garden with a starter cactus from this indoor-outdoor gift shop. Eye-catching Southwestern cards, loads of cactus jellies and desert-minded gardening books are also on sale.
#### Information
###### Emergency
Police ( 602-262-6151; http://phoenix.gov/police; 620 W Washington St, Phoenix)
###### Internet Access
Burton Barr Central Library ( 602-262-4636; www.phoenixpubliclibrary.org; 1221 N Central Ave, Phoenix; 9am-5pm Mon, 11am-9pm Tue-Thu, 9am-5pm Fri & Sat, 1-5pm Sun; ) Free internet; see website for additional locations.
###### Medical Services
Both hospitals have 24-hour emergency rooms.
Banner Good Samaritan Medical Center ( 602-839-2000; www.bannerhealth.com; 1111 E McDowell Rd, Phoenix)
St Joseph's Hospital & Medical Center ( 602-406-3000; www.stjosephs-phx.org; 350 W Thomas Rd)
###### Post
Downtown post office ( 602-253-9648; 522 N Central Ave, Phoenix; 9am-5:30pm Mon-Fri)
###### Telephone
Greater Phoenix has three telephone area codes: 480, 602 and 623. You need to dial the area code even if you're in it.
###### Tourist Information
Downtown Phoenix Visitor Information Center ( 602-452-6282, 877-225-5749; www.visitphoenix.com; 125 N 2nd St, Suite 120; 8am-5pm Mon-Fri) The Valley's most complete source of tourist information.
Mesa Convention & Visitors Bureau ( 480-827-4700, 800-283-6372; www.mesacvb.com; 120 N Center St; 8am-5pm Mon-Fri)
Scottsdale Convention & Visitors Bureau ( 480-421-1004, 800-782-1117; www.scottsdalecvb.com; 4343 N Scottsdale Rd, Suite 170; 8am-5pm Mon-Fri) Inside the Galleria Corporate Center.
Tempe Convention & Visitors Bureau ( 480-894-8158, 800-283-6734; www.tempecvb.com; 51 W 3rd St, Suite 105; 8:30am-5pm Mon-Fri)
###### Websites
Lonely Planet (www.lonelyplanet.com/usa/southwest/phoenix) Planning advice, author recommendations, traveler reviews and insider tips.
#### Getting There & Away
Sky Harbor International Airport ( 602-273-3300; http://skyharbor.com; ) is 3 miles southeast of downtown Phoenix and served by 17 airlines, including United, American, Delta and British Airways. Its three terminals (Terminals 2, 3 and 4; Terminal 1 was demolished in 1990) and the parking lots are linked by the free 24-hr Airport Shuttle Bus.
Greyhound ( 602-389-4200; www.greyhound.com; 2115 E Buckeye Rd) runs buses to Tucson ($20-27, two hours, eight daily), Flagstaff ($32-42, three hours, five daily), Albuquerque ($71-89, 10 hours, five daily) and Los Angeles ($42-54, 7½ hours, 10 daily). Valley Metro's No 13 buses link the airport and the Greyhound station.
#### Getting Around
###### To/From the Airport
All international car-rental companies have offices at the airport.
The citywide door-to-door shuttle service provided by Super Shuttle ( 602-244-9000, 800-258-3826; www.supershuttle.com) costs about $14 to downtown Phoenix, $16 to Tempe, $21 to Mesa and $20 to Old Town Scottsdale.
Three taxi companies serve the airport: AAA/Yellow Cab ( 480-888-8888), Apache ( 480-557-7000) and Mayflower ( 602-955-1355). The charge is $5 for the first mile and $2 for each additional mile; from the airport there's a $1 surcharge and $15 minimum fare. Expect to pay $17 to $19 to downtown.
A free shuttle (look for the silver and black bus) provides the 15-minute connection to the 44th St/Washington light-rail station; from here it's a 35-minute ride in the light-rail to downtown. The PHX Sky Train is scheduled to replace the shuttle in late 2013. Bus route 13 also connects airport to town for the same fare.
###### Car & Motorcycle
The network of freeways, most of them built in the last 15 years, is starting to rival Los Angeles and so is the intensity of traffic. Always pad your sightseeing day for traffic jams. The I-10 and US 60 are the main east–west thoroughfares, while the I-17 and SR 51 are the major north–south arteries. Loops 101 and 202 link most of the suburbs. Parking is plentiful outside of the downtown area.
###### Public Transportation
Valley Metro ( 602-253-5000; www.valleymetro.org) operates buses all over the Valley and a 20-mile light-rail line linking north Phoenix with downtown Phoenix, Tempe/ASU and downtown Mesa. Fares for both light-rail and bus are $1.75 per ride (no transfers) or $3.50 for a day pass. Buses run daily at intermittent times. FLASH buses (www.tempe.gov/tim/bus/flash.htm) operate daily around ASU and downtown Tempe, while the Scottsdale Trolley (www.scottsdaleaz.gov/trolley) loops around downtown Scottsdale, both at no charge.
## CENTRAL ARIZONA
Much of the area north of Phoenix lies on the Colorado Plateau and is cool, wooded and mountainous. It's draped with the most diverse and scenic quilt of sites and attractions in all of Arizona. You can clamber around a volcano, channel your inner goddess on a vortex, taste wine in a former mining town, hike through sweet-smelling canyons, schuss down alpine slopes, admire 1000-year-old Native American dwellings anddelve into Old West and pioneer history. The main hub, Flagstaff, is a lively and delightful college town and gateway to the Grand Canyon South Rim. Summer, spring and fall are the best times to visit.
You can make the trip between Phoenix and Flagstaff in just over two hours if you put the pedal to the metal on I-17, which provides a straight 145-mile shot between the two cities. Opt for one of the more leisurely routes along Hwys 87 or 89, though, and you'll be rewarded with beautiful scenery and intriguing sites along the way.
### Verde Valley & Around
##### ROCK SPRINGS CAFÉ
A slice of fresh pie from Rock Springs Café ( 623-374-5794; www.rockspringscafe.com; 35769 S Old Black Cyn Hwy; slice of pie $4.29, mains $7-18; breakfast, lunch & dinner) shouldn't be missed. Only problem? This Old West eatery, off exit 242, will drive you crazy with choices – apple crumble, blueberry, rhubarb, banana cream – all sitting pretty in a cooler in the dining room. Heartier grub includes burgers, steaks and fried catfish. The attached Farmers Market sells produce, hot sauce, beef jerky and cactus arrangements. On the first Saturday of the month, roll in for Hogs N Heat ( 1-11pm) when the barbecue smokers fire up out back. This party draws Harley riders and, well, everybody within sniffin' distance.
##### ARCOSANTI
Two miles east of I-17 exit 262 (Cordes Junction; 65 miles north of Phoenix), Arcosanti ( 928-632-7135; www.arcosanti.org; suggested donation for tours $10; tours 10am-4pm) is an architectural experiment in urban living that's been a work in progress since 1970. The brainchild of groundbreaking architect and urban planner Paolo Soleri, it is based on Soleri's concept of 'arcology', which seeks to create communities in harmony with their natural surroundings, minimizing the use of energy, raw materials and land. If and when it is finished, Arcosanti will be a self-sufficient village for 5000 people with futuristic living spaces, large-scale greenhouses and solar energy.
Hour-long tours take you around the site and provide background about the project's history and design philosophy. A gift shop sells the famous bronze bells cast at the foundry in Cosanti (Click here), near Phoenix. Tours start on the hour beginning at 10am, with no tour at noon.
##### CAMP VERDE & FORT VERDE STATE HISTORIC PARK
Camp Verde was founded in 1865 as a farming settlement only to be co-opted soon after by the US Army, who built a fort to prevent Native American raids on Anglo settlers. TontoApache chief Chalipun surrendered here in April 1873. Today, the town's Fort Verde State Historic Park ( 928-567-3275; http://azstateparks.com/Parks/FOVE/index.html; 125 E Hollamon St; adult/child $4/2; 9am-5pm Thu-Mon), operating on a five-day schedule, offers an authentic snapshot of frontier life in the late 19th century. Exploring the well-preserved fort, you'll see the officers' and doctor's quarters, the parade grounds and displays about military life and the Indian Wars. Take exit 287 off I-17, go south on Hwy 260, turn left at Finnie Flat Rd and left again at Hollamon St.
Mediocre chain motels cluster near exit 287.
##### MONTEZUMA CASTLE NATIONAL MONUMENT
Like nearby Tuzigoot (Click here), Montezuma Castle ( 928-567-3322; www.nps.gov/moca; adult/child $5/free, combination pass with Tuzigoot National Monument $8; 8am-6pm Jun-Aug, 8am-5pm Sep-May) is a stunningly well-preserved 1000-year-old Sinagua cliff dwelling. The name refers to the splendid castlelike location high on a cliff; early explorers thought the five-story-high pueblo was Aztec and hence dubbed it Montezuma. A museum interprets the archaeology of thesite, which can be spotted from a short self-guiding, wheelchair-accessible trail. Entrance into the 'castle' itself is prohibited, but there's a virtual tour on the website. Access the monument from I-17 exit 289, drive east for half a mile, then turn left on Montezuma Castle Rd.
Montezuma Well ( 928-567-4521; admission free; 8am-6pm Jun-Aug, 8am-5pm Sep-May) is a natural limestone sinkhole 470ft wide, surrounded by both Sinaguan and Hohokam dwellings. Water from the well was used for irrigation by the NativeAmericans and is still used today byresidents of nearby Rimrock. Access is from I-17 exit 293, 4 miles north of the Montezuma Castle exit. Follow the signs for another 4 miles through McGuireville and Rimrock.
### Hwy 87: Payson & Mogollon Rim
A considerably more scenic route takes you northeast out of Phoenix on Hwy 87 (the Beeline Hwy) to Payson, just below the sheer cliffs of the Mogollon Rim. From here, hook northwest on Hwy 260 via Pine and Strawberry to the I-17. Then you can either head straight up north for the quick 55-mile trip to Flagstaff or take the more circuitous and slower 60-mile drive continuing on Hwy 260 to Cottonwood, and from there north to Sedona and Oak Creek Canyon before reaching Flagstaff.
##### PAYSON & THE MOGOLLON RIM
Founded by gold miners in 1882, Payson's real riches turned out to be above the ground. Vast pine forests fed a booming timber industry; ranchers ran cattle along the Mogollon Rim and down to the Tonto Basin; and wild game was plentiful. Frontier life here captivated Western author Zane Grey, who kept a cabin outside town. Today, Payson is a recreational and retirement destination for Phoenix citizens. The biggest attractions are hunting and fishing in the forests, lakes and streams around the Rim.
#### Sights
Rim Country Museum MUSEUM
( 928-474-3483; www.rimcountrymuseums.com; 700 Green Valley Pkwy; adult/child/student/senior$5/free/3/4; 10am-4pm Wed-Mon, 1-4pm Sun) This lakeside museum is the only real sight in Payson, with exhibits that illustrate the native, pioneer and resource-extraction history of the region. Highlights include a replica of a blacksmith shop and a walk-through of the Zane Grey Cabin, faithfully rebuilt here after the author's original homestead burned in the 1990 Dude Fire. You can only check out the museum on a guided tour which, at about 1½ hours, seems a bit long, especially for kids.
Tonto Natural Bridge State Park PARK
( 928-476-4202; www.azstateparks.com; off Hwy 87; adult/child $5/2; 8am-6pm daily Jun-Aug, open Thu-Mon Sep-May) Long ago, 11 miles north of Payson, a curious thing happened as Pine Creek flowed downhill – it ran smack into a massive dam of calcium carbonate. As creeks will, it gradually cut its way through, carving out the world's largest natural travertine bridge, which is 183ft high and spans a 150ft-wide canyon. You can walk over it and view it from multiple angles, and there are steep trails down into the canyon for close-ups.
The park entrance is 3 miles off Hwy 87; the final stretch of the access road is precipitous and winding, and an adventure in itself. Heavy snow may close the park in winter. Website updated daily.
#### Festivals
Payson hosts a dizzying variety of events, from dog shows to doll sales, including the World's Oldest Continuous Rodeo, held every August since 1884. Arizona's Old Time Fiddlers Contest is in late September. Visit www.paysonrimcountry.com for more details about these and other events.
#### Sleeping
Payson is surrounded by Tonto National Forest, so it's easy to find spots to camp for free along forest roads. If you're looking for basic facilities like toilets and drinking water, there are a few established USFS campgrounds (campsite $14-16; Apr-Oct) spread along Hwy 260, 15 to 21 miles east of town. Hotel rates in Payson vary depending on demand, so you might find yourself paying $20 more or less depending on the day or the season. Chain motels are scattered along Beeline Hwy and Hwy 260.
Houston Mesa Campground CAMPGROUND $
( 928-468-7135; RV no hookups & tent sites both $20; Feb-Nov) Two miles north of Payson along Hwy 87, this USFS campground has showers and a short nature trail through a mixed juniper and pine forest. Some sites available by reservation, see www.recreation.gov.
Majestic Mountain Inn MOTEL $$
( 928-474-0185; www.majesticmountaininn.com;602 E Hwy 260; r $80-136; ) Set among landscaped pines and grassy lawns, this is easily the nicest lodging in Payson – and a good value one, too. The two-story property is more of a motel than a lodge-like inn, but the luxury rooms have double-sided gas fireplaces, sloped wooden ceilings and spa tubs.
Super 8 MOTEL $
( 928-474-5241; www.super8.com; 809 Hwy 260 E; r incl breakfast $85-155; ) It's a chain, but rooms have a bit of sleek style and come with a flat-screen TV, microwave and refrigerator. Top it off with a helpful front desk and continental breakfast, and you've got a nice base for regional adventure.
#### Eating & Drinking
Gerardo's Italian Bistro ITALIAN $$
( 928-468-6500; www.gerardosbistro.com; 512 N Beeline Hwy; lunch $7-16, dinner $12-18; lunch & dinner Tue-Sun) This award-winning bistro is helmed by Italian-trained chef Gerardo Moceri who, judging by the family photos on the wall, looks like he might have red sauce flowing in his veins. Belly-stuffing dishes zing with freshness; even our exacting lasagna critic says 'bravo!'
Buffalo Bar & Grill AMERICAN $$
( 928-474-3900; 311 S Beeline Hwy; mains $8-16; 10am-1am) So this is where everybody is. A fun, casual pub; it has a pool table, kids' menu and live music a couple of nights a week.
Beeline Cafe DINER $
( 928-474-9960; 815 S Beeline Hwy; mains $4-13; 5am-9pm) This home-style restaurant could be called the beehive, mornings are so busy with locals swarming in for massive breakfasts. Cash only.
### WHAT THE...?
One of the most famous alien abductions ever reported supposedly occurred in the Apache-Sitgreaves National Forest, not far from Show Low. In 1975 Travis Walton, a member of a logging crew, vanished from the forest for five days. He claimed to have been taken into a flying saucer before being deposited back on Earth at the gas station in Heber. Witnesses – who were fellow loggers and not your typical New Age believers – corroborated the story of the UFO and of Walton's mysterious disappearance. The incident became national news and was the basis for the 1993 movie _Fire in the Sky._ Walton did fail a polygraph test but he never wavered in his insistence that he was telling the truth.
#### Information
Hwy 87 is known as Beeline Hwy through Payson. The town of Payson maintains a very helpful website about area activities and attractions at www.paysonrimcountry.com.
Hospital ( 928-474-3222; www.paysonhospital.com; 807 S Ponderosa)
Post office ( 928-474-2972; 100 W Frontier St; 8:30am-4pm Mon-Fri, 9am-noon Sat)
Tonto National Forest Payson Ranger Station ( 928-474-7900; 1009 E Hwy 260; 8am-noon, 1-4:30pm Mon-Fri) All the info you need about the forest.
Visitor center ( 928-474-4515; www.rimcountrychamber.com; 100 W Main at Hwy 87; 9am-5pm Mon-Fri, 10am-2pm Sat) At the chamber of commerce; there are plenty of brochures about local activities and events.
#### Getting There & Away
White Mountain Passenger Lines ( 928-537-4539; www.wmlines.com) runs shuttles Monday to Saturday from Phoenix ($35) and Show Low ($35).
##### NORTH ON HWY 89
The longest but most rewarding route from Phoenix to Flagstaff is via Hwys 89/89A (Alt 89), which follows a sight-packed old stagecoach route. For a summary of one of the most scenic sections of this road trip, from Wickenburg to Sedona, see Click here.
The rest of this section is structured following this route.
### Wickenburg
Wickenburg looks like it fell out of the sky – directly from the 1890s. Downtown streets are flanked by Old West storefronts, historic buildings and several life-size statues of the prospectors and cowboys who brought this place to life in the 1800s. In later years, once the mining and ranching played out, guest ranches began to flourish, drawing people in search of the romance of the open range. Today, the one-time 'dude ranch capital of the world' still hosts weekend wranglers, but it has also evolved (quietly and discreetly) into a 'rehab capital' for A-listers. The town, located 60 miles northwest of Phoenix via Hwy 60, is pleasant anytime but summer, when temperatures can top 110°F (43°C).
#### Sights & Activities
The small downtown is dotted with statues of the town's founders as well as a few colorful characters. One of the latter was George Sayers, a 'bibulous reprobate' who was once chained to the town's Jail Tree on Tegner St in the late 1800s.
Desert Caballeros Western Museum MUSEUM
( 928-684-2272; www.westernmuseum.org; 21 NFrontier St; adult/child/senior $7.50/free/6; 10am-5pm Mon-Sat, noon-4pm Sun, closed Mon Jun-Aug) The Spirit of the Cowboy collection examines the raw materials behind the cowboy myth, showcasing bridles and saddles, bits and spurs, and even some angora woolies. Hopi kachina dolls, colorful Arizona minerals and eye-catching art by Western artists, including Charles M Russell and Frederic Remington, are additional highlights. The annual Cowgirl Up! exhibit and sale in March and April is a fun tribute to an eclectic array of Western women artists.
Hassayampa River PreserveNATURE RESERVE
( 928-684-2772; www.nature.org; admission $5; 7-11am Fri-Sun mid-May–mid-Sep, 8am-5pm Wed-Sun mid-Sep–mid-May) The Hassayampa River normally runs underground, but just outside downtown it shows off its crystalline shimmer. Managed by the Nature Conservancy, this is one of the few riparian habitats remaining in Arizona and a great place for birders to go gaga for the 280 or so feathered resident and migrating species. It's on the west side of Hwy 60, 3 miles south of town.
Vulture Mine MINE
( 602-859-2743; Vulture Mine Rd; admission $10; 8am-4pm winter, to 2pm summer) Town founder Henry Wickenburg discovered gold nuggets here in 1863. The mine itself spat out gold until 1942, but today it's a crusty ghost town, one that recently spooked the hosts of the Travel Channel's _Ghost Adventures_. A self-guided tour winds past the main shaft, the blacksmith shop and the Hanging Tree where 18 miners were strung up for stealing chunks of gold-filled ore, an illegal practice known as high-grading. Decaying buildings and mine shafts here may not be safe for young children. Pets on leashes are OK. No credit cards. Head west on Hwy 60, turn left onto Vulture Mine Rd and follow it for 12 miles. It may be worth calling first to confirm opening hours because they occasionally change.
#### Sleeping
Dude ranches typically close for the summer in southern Arizona.
Flying E Ranch DUDE RANCH $$
( 928-684-2690; www.flyingeranch.com; 2801 W Wickenburg Way; s $192-263, d $308-392; Nov-Apr; ) This down-home workingcattle ranch on 20,000 acres in the Hassayampa Valley is a big hit with families. Rooms are Western-themed and rates include activities and three family-style meals daily. It's open to guests from November to April, with two- or three-night minimum stays. Two-hour horseback rides cost $40. There's no bar; BYOB. Wi-fi available in certain areas.
Wickenburg Inn HOTEL $
( 928-684-5461; www.wickenburginn.com; 850 E Wickenburg Way, N Tegner St; r incl breakfast $82-92; ) Lost? Get your bearings with a quick look at the giant map painted on the lobby wall inside this welcoming motel. Colorful prints, comfy chairs and granite countertops add oomph to mid-size rooms. The extensive continental breakfast is outstanding, and the sausage gravy is some of the best we tasted in Arizona. Small pets OK; $15 per day per pet.
Rancho de los Caballeros DUDE RANCH $$$
( 928-684-5484; www.ranchodeloscaballeros.com;1551 S Vulture Mine Rd; r include breakfast $465-625; Oct–mid-May; ) With an 18-hole championship golf course, exclusive spa, special kids' program and fine dining, this sprawling ranch feels more _Dallas_ than _Bonanza_. The lovely main lodge – with flagstone floor, brightly painted furniture and copper fireplace – gives way to cozy rooms decked out stylishly with Native American rugs and handcrafted furniture. Dinner is a dress-up affair, but afterwards you can cut loose in the saloon with nightly cowboy music. Open to guests October to early-May.
#### Eating & Drinking
Horseshoe Cafe DINER $
( 928-684-7377; 207 E Wickenburg Way; mains under $10; 5am-9pm Mon & Tue, to 1pm Wed & Thu, to 2pm Fri-Sun) If you judge the quality of a restaurant by the number of cowboy hats in the dining room, then this charming place has got to be the best eatery in town. It's gussied up with chaps, a saddle or two and, of course, some horseshoes. The service is super welcoming, and the biscuit with a side of gravy is lick-the-platter good.
Anita's Cocina MEXICAN $$
( 928-684-5777; 57 N Valentine St; mains $7-16; 7am-9pm) In the heart of downtown, this happenin' hacienda is a perfect spot for winding down south-of-the-border style. Think margaritas, burritos, combo platters and a heaping basket of free chips with hot or mild salsa (or both). Good for groups and families, but solos will be just fine. Sports fans will find games on the many flat-screen TVs.
Screamer's Drive-In AMERICAN $
( 928-684-9056; 1151 W Wickenburg Way; dishes $3-6; 6am-8pm Mon-Sat, 10:30am-8pm Sun) If you've got a hankering for a big and juicy green chile burger with a side of crispy fries and a shake, this '50s-style diner (not really a drive-in) will steer you toward contentment. Indoor and outdoor seating.
Hog Trough Smokehouse BBQ BARBECUE $
(www.hogtroughbbq.com; 169 E Wickenburg Way; mains $5-16; 11am-8pm daily Sep-May, 11am-8pm Wed, Thu & Sun, to 9pm Fri & Sat) Not sure we love the name but... oink-oink, the pulled pork sure is tasty.
Pony Espresso CAFE $
(223 E Wickenburg Way; pastries under $3, mains $5-8; 8am-6pm; ) This funky, friendly little coffee shop also serves scones, brownies and sandwiches.
#### Information
Chamber of Commerce ( 928-684-5479; www.outwickenburgway.org; 216 N Frontier St; 9am-5pm Mon-Fri, 10am-2pm Sat & Sun) Inside an 1895 Santa Fe Railroad depot; offers local info and a walking tour of downtown.
Wickenburg Community Hospital ( 928-684-5421; www.wickhosp.com; 520 Rose Ln) 24hr emergency room.
#### Getting There & Away
Wickenburg is about equidistant (60 miles) from Phoenix and Prescott off Hwy 60. There is no bus service. Coming from Kingman and the I-40 you can reach it via Hwy 93, which runs a lonely 105 miles to Wickenburg. It's dubbed Joshua Tree Forest Pkwy because pretty much the only living things growing here are those spiny bushes that are a member of the lily family – but it's a gorgeous drive nonetheless.
### Prescott
Fire raged through Whiskey Row in downtown Prescott (press-kit) on July 14, 1900. Quick-thinking locals managed to save the town's most prized possession: the 24ft-long Brunswick Bar that anchored the Palace Saloon. After lugging the solid oak bar across the street onto Courthouse Plaza, they grabbed their drinks and continued the party.
Prescott's cooperative spirit lives on, infusing the historic downtown and mountain-flanked surroundings with a welcoming vibe. This easy-to-explore city, which served as Arizona's first territorial capital, also charms visitors with its eye-catching Victorian buildings, breezy sidewalk cafes, tree-lined central plaza and burgeoning arts scene. But it's not all artsy gentility and Victorian airs. Whiskey Row hasn't changed much from the 1800s, and there's always a party within its scrappy saloons.
Prescott also offers some of Arizona's best outdoor scenery. Hikers, cyclists and campers in search of memorable views don't have to travel far from downtown to find them. The boulder-strewn Granite Dells rise to the north, while in the west the landmark Thumb Butte sticks out like the tall kid in your third-grade picture. To the south, the pine-draped Bradshaw Mountains form part of the Prescott National Forest.
#### Sights
Historic Downtown NEIGHBORHOOD
Montezuma St west of Courthouse Plaza was once the infamous Whiskey Row, where 40 drinking establishments supplied suds to rough-hewn cowboys, miners and wastrels. A devastating 1900 fire destroyed 25 saloons, five hotels and the red-light district, but several early buildings remain. Many are still bars, mixed in with boutiques, galleries and restaurants. Take a stroll through the infamous Palace Saloon, rebuilt in 1901. A museum's worth of photographs and artifacts (including the fire-surviving Brunswick Bar) are scattered throughout the bar and restaurant. A scene from the Steve McQueen movie _Junior Bonner_ was filmed here, and a mural honoring the film covers an inside wall.
The columned County Courthouse anchoring the elm-shaded plaza dates from 1916 and is particularly pretty when sporting its lavish Christmas decorations. Cortez St, which runs east of the plaza, is a hive of antique and collectible stores, as well as home to Ogg's Hogan ( 928-443-9856; 111 N Cortez St), with its excellent selection of Native American crafts and jewelry, mostly from Arizona tribes.
Buildings east and south of the plaza escaped the 1900 fire. Some are Victorian houses built by East Coast settlers and are markedly different from adobe Southwestern buildings. Look for the fanciest digs on Union St; No 217 is the ancestral Goldwater family mansion (yes, of Barry Goldwater fame).
Sharlot Hall Museum MUSEUM
( 928-445-3122; www.sharlot.org; 415 W Gurley St; adult/child $5/free; 10am-5pm Mon-Sat, noon-4pm Sun May-Sep, 10am-4pm Mon-Sat, noon-4pm Sun Oct-Apr) Although Prescott's most important museum is named for its 1928 founder, pioneer woman Sharlot Hall (1870-1943), it's actually a general historical museum highlighting Prescott's period as territorial capital. A small exhibit in the lobby commemorates Miss Hall, who distinguished herself first as a poet and activist before becoming Territorial Historian. In 1924, she traveled to Washington DC to represent Arizona in the Electoral College dressed in a copper mesh overcoat –currently in the display case – provided by a local mine. There would be no mistaking that Arizona was the 'Copper State!'
### WHISKEY ROW TO GALLERY ROW
There's still plenty of drinkin' and dancin' going on in Whiskey Row's fine historic saloons, but more recently the infamous strip has taken on a second life as Gallery Row. Standouts include Arts Prescott Gallery ( 928-776-7717; www.artsprescott.com; 134 S Montezuma St), a collective of 24 local artists working in all media, including painting, pottery, illustration and jewelry. Prices are quite reasonable. Deeper pockets are required at Van Gogh's Ear ( 928-776-1080; www.vgegallery.com; 156 S Montezuma St), where you can snap up John Lutes' ethereal glass bowls, Dale O'Dell's stunning photographs or works by three dozen other nationally known artists making their home in the Prescott area. A great time to sample Prescott's growing gallery scene is during the monthly 4th Friday Art Walk (www.artthe4th.com).
The most interesting of the nine buildings making up this museum campus is the 1864 Governor's Mansion, a big log cabin where Hall lived in the attic until her death. It's filled with a hodgepodge of memorabilia from guns to opium pipes and letters. The Sharlot Hall Building next door is the main exhibit hall. Small but informative displays cover the area's historical highlights. Outside, the Rose Garden pays homage to Arizona's pioneer women.
Phippen Museum MUSEUM
( 928-778-1385; www.phippenartmuseum.org; 4701Hwy 89; adult/student/senior $7/free/5; 10am-4pm Tue-Sat, 1-4pm Sun) The Phippen, located 7 miles north of Prescott en route to Jerome, is named after cowboy artist George Phippen and hosts changing exhibits of celebrated Western artists, along with contemporary art depicting the American West. At press time, the museum was wrapping up a major expansion. On Memorial Day weekend the museum hosts the Western Art Show & Sale at Courthouse Plaza.
Smoki Museum MUSEUM
( 928-445-1230; www.smokimuseum.org; 147 N Arizona St; adult/child/student/senior $5/free/3/4; 10am-4pm Mon-Sat, 1-4pm Sun) This pueblo-style museum displays Southwestern Native American objects – baskets, pottery, kachina dolls – dating from prehistoric times to the present. One surprising exhibit addresses the true origins of the 'Smoki' tribe. The tribe was a philanthropic society created by white Prescottonians to raise money for the city's rodeo. The group's annual Hopi Snake Dance was considered a religious mockery by local tribes and was discontinued in 1990. Today, the museum works with area tribes to instill understanding and respect for the region's indigenous cultures. The correct pronunciation is 'smoke-eye.'
#### Activities
Prescott sits in the middle of the Prescott National Forest, a 1.2 million acre playground well stocked with mountains, lakes and ponderosa pines. The Prescott National Forest Office has information about local hikes, drives, picnic areas and campgrounds. Be aware that a $5 day-use fee is required – and payable – at many area trailheads. Intra-agency passes, including the America the Beautiful pass, cover this fee. You can buy passes at the Forest Service office but, for basic questions, the busy folks here ask that travelers first check out the website for answers.
If you only have time for a short hike, get a moderate workout and nice views of the town and mountains on the 1.75-mile Thumb Butte trail. The trailhead is about 3.5 miles west of downtown Prescott on Gurley St, which changes to Thumb Butte Rd. Leashed dogs are OK.
There are five lakes within a short drive of town. The dazzling Lynx Lake, 4 miles east of Prescott on Hwy 69 then 3 miles south on Walker Rd, offers fishing, hiking and camping. The most scenic lake for our money is Watson Lake, where the eerily eroded rock piles of the Granite Dells are reflected in the crystalline stillness. About 4 miles north of town, off Hwy 89, the city-run Watson Lake Park is great for boating, picnicking and bouldering, as well as summer tent camping (www.cityofprescott.net; camping $15, parking $2 Thu-Mon nights Apr-Sep).
North of town, the Granite Mountain Wilderness attracts rock climbers in the warmer months.
For two rugged, off-the-main-road drives past some of the area's old mining sites, pick up the Forest Service's _Bradshaw Mountains' Motor Tour_ pamphlet. High clearance vehicles are suggested for this tour.
#### Festivals & Events
Prescott has a packed year-round events calendar. See www.visit-prescott.com for the full scoop.
Territorial Days Arts & Crafts Show ART
( 928-445-2000; www.prescott.org) Arts, crafts, demonstrations, performances; in June.
World's Oldest Rodeo RODEO
(www.worldsoldestrodeo.com) Bronco busting (since 1888), a parade and an arts-and-crafts fair the week before July 4.
#### Sleeping
Don't expect many lodging bargains in Prescott. Check out www.prescottbb.com for links to area B&Bs and inns.
Free dispersed camping is permitted at designated sites next to several fire roads in Prescott National Forest. The Forest Service also manages nine fee-based campgrounds with spots available on a first-come, first- served basis. See www.fs.fed.us/r3/prescott for details.
Motor Lodge BUNGALOW $$
( 928-717-0157; www.themotorlodge.com; 503 S Montezuma St; r $89-139; ) Open the fridge upon arrival and you'll find two Fat Tire beers. This sudsy welcome is one of many personal touches at the Motor Lodge, where 12 snazzy bungalows are horseshoed around a central driveway. This hospitality, along with whimsical prints and stylish but comfy bedding, makes the Motor Lodge one of the finest budget choices we've seen. Rooms and bathrooms can be on the small side, butmany have kitchens and porches for extra space. The lime-green bungalows, built as summer cabins in the early 1900s, are within cycling distance of downtown.
Rocamadour B&B B&B $$
( 928-771-1933, www.prescottbb.com/inns/10.html; 3386 N Hwy 89; r $149-219; ) The enchanting Rocamadour – meaning 'lover of rocks' in old French – is a 10-acre haven for wildlife nestled among the boulders of the Granite Dells. The three-room B&B is a great place for road-weary travelers to relax, and guests can access city-managed trails near the Dells that link up with other trail systems. Owners Mike and Twyla managed a chateau hotel in France, and they've brought back elegant furniture and a healthy dose of _savoir vivre_. Breakfasts are gourmet affairs.
Hotel Vendome HISTORIC INN $$
( 928-776-0900; www.vendomehotel.com; 230 S Cortez St; r $99-139, d $159-199, rate incl breakfast; ) This dapper two-story inn, datingfrom 1917, charms guests with lace curtains, old-fashioned quilts and a few bathrooms with clawfoot tubs. If you ask, the welcoming hosts might even tell you about the ghost.
Hassayampa Inn HISTORIC HOTEL $$
( 928-778-9434; www.hassayampainn.com; 122 E Gurley St; r incl breakfast $139-209; ) One of Arizona's most elegant hotels when it opened in 1927, today the restored inn has many original furnishings, hand-painted wall decorations and a lovely dining room. The 67 rooms vary, but all include rich linens and sturdy dark-wood furniture. It has an on-site restaurant, the Peacock Room & Bar. Pets under 45lbs are allowed for an extra $10 per night.
Hotel St Michael HOTEL $
( 928-776-1999; www.stmichaelhotel.com; 205W Gurley St; r $89-99, ste $99-119, rate incl breakfast; ) Gargoyles, ghosts and a 1925 elevator keep things refreshingly offbeat atthis Victorian-era hotel in the heart of downtown. The no-frills, old-fashioned rooms, which include three family units, are within staggering distance of Whiskey Row. Rate includes a cooked-to-order breakfast in the downstairs bistro from 7am until 9am.
Apache Lodge MOTEL $
( 928-445-1422, www.apachelodge.com; 1130 E Gurley St; s/d $67/79; ) The well-worn Apache won't impress domestic divas, but for everyone else, the accommodating service, wallet-friendly price and awesome communal coffee-machine should be enough of a draw.
Point of Rocks RV Park CAMPGROUND $
( 928-445-9018; www.pointofrockscampground.com; 3025 N Hwy 89; RV sites $28; ) Commercial campground tucked among beautiful granite boulders behind Watson Lake. Most sites are level, tree-shaded and have full hookups. No tent sites.
#### Eating
Iron Springs Cafe CAFE $$
( 928-443-8848; www.ironspringscafe.com; 1501Iron Springs Rd; lunch $8-11, dinner $8-20; 8am-7pm Wed-Sat, 9am-2pm Sun) Cajun and Southwestern specialties chug into this former train station, all of them packed tight on aone-page menu that's loaded with savory,often spicy, palate pleasers. From the n'awlins muffaletta with sliced ham, salami and mortadella, to the black-and-blue steak with blue-cheese butter, it all sounds delicious. Train decor, colorful blankets and easy-bantering waitstaffenliven three tiny rooms. The green chile pork stew has an addictively spicy kick. Recently started serving breakfast.
Lone Spur Cafe BREAKFAST $
( 928-445-8202; 106 W Gurley St; mains $7-16; 8am-2pm) Mornin' cowboy, there's just one rule at the Lone Spur Cafe: always order the biscuit with sausage gravy as your side dish at breakfast. Never the toast. You can't count calories at a place this good, and the sausage gravy will knock your hat off. Even better, portions are huge and there are three bottles of hot sauce on every table. Decor includes stuffed mounts, cowboy gear and a chandelier made out of antlers. Waitstaff are super-nice.
Raven Café CAFE $$
( 928-717-0009; 142 N Cortez St; breakfast $5-9, lunch & dinner $8-18; 7:30am-11pm Mon-Fri, 7:30am-midnight Sat, 8am-3pm Sun; ) This may be the closest you'll get to skinny jeans in Prescott: a cool, loftlike spot that changes its stripes from daytime coffee hangout to after-dark pub with live music and 30 beers on tap. The mostly organic menu offers a mix of sandwiches, burgers, salads and a few 'big plates' – and lots of vegetarian options, too.
Peacock Room & Bar FINE DINING $$
( 928-777-9563; www.hassayampainn.com; 122E Gurley St; breakfast $7-12, lunch $9-16, dinner $16-31; breakfast, lunch & dinner) The stuffily stylish dining room at the Hassayampa Inn is famous for its classic American dinners, but we like it best before noon. Huevos rancheros (a Mexican fried-egg dish with chile sauce and cheese) should get your day off to a scrumptious start. Unwind with after-work cocktails at the bar, which hums with sweet live jazz Wednesday to Saturday evenings.
Bill's Pizza PIZZERIA $
(www.billspizzaprescott.com; 107 S Cortez St; slice $2.50, pizza $7-21; 11am-9pm Mon-Thu, 11am-10pm Fri & Sat, noon-6pm Sun) The name of this downtown pizza joint doesn't arouse much excitement, but that's OK – the creativity has been left for the six sauces and 36 toppings that can be slathered over your thin-crusted gourmet pizza. Local art, microbrews and feta-loaded salads round out the appeal.
Prescott Brewing Company AMERICAN $$
(www.prescottbrewingcomany.com; 130 W GurleySt; mains $9-20; lunch & dinner; ) This popular brewpub, across from Courthouse Plaza, works well for families. Bangers and mash, fish tacos and pizzas are on the menu; Lodgepole Light, Pine Tar Stout and Willow Wheat are on tap.
#### Drinking & Entertainment
Prescott is not afraid to have a good time. The chamber of commerce prints its own 'Prescott Pub Crawl' handout, and there's live music at clubs downtown every night of the week. For a saloon crawl, there's no better place than historic Whiskey Row.
Palace Saloon BAR
( 928-541-1996; 120 S Montezuma St; mains $8-20; lunch & dinner) Kick open the swinging doors and time-warp to 19th-century Whiskey Row days, back when the Earp brothers would knock 'em back with Doc Holliday at the huge Brunswick Bar.
Matt's Saloon HONKY-TONK
( 928-778-9914; 112 S Montezuma St) This dark bar is similar in appearance to the Palace but has, in fact, only been around since the 1960s. Buck Owens and WaylonJennings used to perform live back then, and today it's still Prescott's kickiest two-stepping place.
Cupper's COFFEE SHOP
(www.cupperscoffee.com; 226 S Cortez St; 7am-5pm Mon-Sat, 8am-4pm Sun; ) An inviting coffee shop brewing up business inside a Victorian-style cottage. Surf the net while savoring a tasty hunk of blueberry bread with a Mexican mocha (dark chocolate with cinnamon).
Bird Cage Saloon BAR
( 928-771-1913; 148 Whiskey Row; 10am-2am) Dive bar filled with stuffed birds and motorcycle riders.
#### Information
Police ( 928-777-1988; 222 S Marina St)
Post office Downtown (101 W Goodwin St; 8:30am-5pm Mon-Fri), Miller Valley Rd (442 Miller Valley Rd, 8:30am-5pm Mon-Fr, 10am-2pm Sat)
Prescott National Forest office ( 928-443-8000; www.fs.fed.us/r3/prescott; 344 S Cortez St; 8am-4:30pm Mon-Fri) Info on camping, hiking and more in the surrounding national forest.
Tourist office ( 928-445-2000, 800-266-7534; www.visit-prescott.com; 117 W Goodwin St; 9am-5pm Mon-Fri, 10am-2pm Sat & Sun) Information and brochures galore, including a handy walking tour pamphlet ($1) of historical Prescott.
Yavapai Regional Medical Center ( 928-445-2700; www.yrmc.org; 1003 Willow Creek Rd; 24hr emergency room)
#### Getting There & Away
Prescott's tiny airport (www.cityofprescott.net) is about 9 miles north of town on Hwy 89 and is served by Great Lakes Airlines with daily flights to and from Denver and Ontario, CA.
Prescott Transit Authority ( 928-445-5470; www.prescotttransit.com; 820 E Sheldon St) Runs buses to/from Phoenix airport (one-way adult/child $28/15, two hours, 16 daily) and Flagstaff ($22, 1½ hours, daily). Also offers a local taxi service. Shuttle U ( 800-304-6114; www.shuttleu.com; 1505 W Whipple St) runs the same route on an almost identical schedule (one-way adult/child $36/20, 2¼ hours, 16 daily).
### Jerome
It's hard to describe Jerome without using the phrase 'precariously perched.' This stubborn hamlet, which enjoys one of the most spectacular views in Arizona, is wedged into steep Cleopatra Hill. Jerome was the home of the fertile United Verde Mine, nicknamed the 'Billion Dollar Copper Camp.' It was also dubbed the 'Wickedest Town in the West,' and teemed with brothels, saloons and opium dens.
When the mines petered out in 1953, Jerome's population plummeted from 15,000 to just 50 stalwarts practically overnight. Then came the '60s, and scores of hippies with an eye for the town's latent charm. They snapped up crumbling buildings for pennies, more or less restored them and, along the way, injected a dose of artistic spirit that survives to this day inside the numerous galleries scattered across town. A groovy joie de vivre permeates the place, and at times it seems every shop and restaurant is playing a hug-your-neighbor folk song from the 1960s or '70s.
Quaint as it is, the most memorable aspect of Jerome is its panoramic views of the Verde Valley embracing the fiery red rocks of Sedona and culminating in the snowy San Francisco Peaks. Sunsets? Ridiculously romantic, trust us.
More than 1.2 million visitors – most of them day-trippers and weekend-warrior bikers – spill into Jerome each year, but the tiny town doesn't feel like a tourist trap. It's far from over-gentrified; as one bumper sticker plastered on a downtown business put it: 'We're all here because we're not all there.'
To experience Jerome's true magic, spend the night. Who knows, you might even see a ghost. This is, after all, 'Arizona's ghost capital.'
#### Sights
If you're interested in the town's unique history, take an hour to stroll past some of Jerome's most historic buildings. Start at the corner of Main St and Jerome Ave at the Connor Hotel, the town's first solid stone lodging. From there, a leg-stretching climb leads to the Jerome Grand Hotel, the one-time home of the United Verde Hospital. This sturdy facility served miners and the community between 1927 and 1951. Known for its ghosts, it's actually a relaxing place to enjoy expansive views of the crimson-gold rocks of Sedona and the Verde Valley.
Heading back downhill, consider the fact that there are 88 miles of tunnel under your feet. Combine these tunnels with steep hills and periodic dynamiting, and it's easy to see why buildings in Jerome regularly collapsed, caught fire or migrateddownhill. The Sliding Jail, southeast of the visitor center, has moved 225ft from its original 1927 location.
Jerome
Top Sights
Jerome Artists Cooperative Gallery B2
Jerome State Historic Park B1
Mine Museum A2
Sights
1Audrey Headframe Park B1
Sleeping
2Connor Hotel A2
3Ghost City B&B B3
4Jerome Grand Hotel B3
5Mile High Inn B2
Eating
615.Quince Grill & Cantina B2
Asylum Restaurant (see 4)
7Flatiron Café B2
8Grapes A1
9Haunted Hamburger B2
Drinking
Bitter Creek Winery & Jerome Gallery 10 B1
11Caduceus Cellars A1
12Jerome Winery A1
Spirit Room Bar (see 2)
Shopping
13Jerome Artists Cooperative Gallery B2
14Nellie Bly A1
Jerome State Historic Park MUSEUM
( 928-634-5381; www.pr.state.az.us; adult/child 7-13 $5/2; 8:30am-5pm Thu-Mon) Recently re-opened after extensive structural repairs, this state park preserves the 1916 mansion of eccentric mining mogul Jimmy 'Rawhide' Douglas. Exhibits offer insight into the town's mining heyday. Just outside the entrance, at the Audrey Headframe Park (admission free; 8am-5pm daily), stand on a glass platform and look down into a 1900ft mining shaft dating from 1918. The shaft is longer than the Empire State Building by 650ft!
Mine Museum MUSEUM
( 928-634-5477; www.jeromehistoricalsociety.com;200 Main St; adult/child/senior $2/free/1; museum 9am-5pm, gift shop until 5:30pm) Two halves of a 4-ton flywheel mark the entryway to this small but informative museum that highlights Jerome's hardscrabble past. Displays include a claustrophobic mining cage, a Chinese laundry machine and a wall dedicated to an old-school sheriff who gunned down three vigilantes on Main St then went home and ate lunch – without mentioning to his wife what had happened.
Gold King Mine GHOST TOWN
( 928-634-0053; adult/child/senior $5/3/4; 9am-5pm; ) Kids and antique-car buffs will most appreciate the rambling, slightly kitschy attractions at this miniature ghost town a mile north of Jerome via Perkinsville Rd. Walk among rusting mining equipment and an impressive stash of old autos, trucks, service vehicles and chickens. Don't shriek if owner Don Robertson, the spitting image of a white-bearded, 19th-century prospector, pops out from behind a truck to say hello.
#### Sleeping
Historic hotels, cozy inns and a few B&Bs are your choices in Jerome, and you won't find a single national chain. In fact, most accommodations are as charmingly eccentric as the town itself. (And many are home to a ghost or two.)
Jerome Grand Hotel HOTEL $$
( 928-634-8200; www.jeromegrandhotel.com; 200 Hill St; r $120-205, ste $270-460; ) This former hospital looks like the perfect setting for a sequel to _The Shining._ Built in 1926 for the mining community, this sturdy fortress plays up its unusual history. The halls are filled with relics of the past, from incinerator chutes to patient call lights. There's even a key-operated Otis elevator. Rooms are more traditionally furnished, with a nod to the Victorian era. Spend an extra few dollars for a valley-side room; they're brighter and offer better views. For $20 hotel guests can join the evening ghost tour of the premises. Enjoy a fine meal and a dazzling valley panorama at the attached Asylum Restaurant.
Connor Hotel HISTORIC HOTEL $$
( 928-634-5006; www.connorhotel.com; 164 Main St; r $90-165; ) The 12 restored rooms at this rambling 1898 haunt convincingly capture the Victorian period, with such touches as pedestal sinks, flowery wallpaper and a pressed-tin ceiling. It's above the popular Spirit Room Bar, which has live music on weekends; rooms one to four get most of the bar noise and allow smoking. Enter through the gift shop.
Mile High Inn B&B $$
( 928-634-5094; www.jeromemilehighinn.com; 309 Main St; r $85-130; ) Rooms are dapper and a bit pert at this snug B&B, which once had a stint as a bordello. The seven newly remodeled rooms have unusual furnishings, and the ghost of the former madam supposedly haunts the room dubbed Lariat & Lace. A full breakfast is served at the downstairs restaurant. Four rooms have shared bathrooms.
Ghost City B&B B&B $$
( 928-634-4678; www.ghostcityinn.com; 541 Main St; r $105-155, ) In an 1898 building, this B&B is owned by Jerome's police chief Allen Muma and his wife Jackie. Each room has a different theme, from the cowboy-inspired Western room to the more girly Verde Valley room with an antique brass bed and killer views.
#### Eating
Jerome is a gourmand's delight, and you'll probably be happy at any of the restaurants in town. Enjoy!
15.Quince Grill & Cantina NEW MEXICAN $$
( 928-634-7087; www.15quincejerome.com; 363 Main St; mains $8-17; 11am-8pm Mon & Wed, 11am-9pm Tue, Thu & Fri, 8am-9pm Sat, 8am-8pm Sun) Even the quesadillas have personality at 15.Quince, a cozy cantina in the heart of downtown. Energized by bold colors, upbeat music, amiable waitstaff and Grand Canyon beer, it's a festive spot for gathering after a long day of road tripping. New Mexican-style dishes are the house specialty, and the joint's known for its chile sauces. A smattering of low-heat salads, sandwiches and burgers are available for the timid.
Flatiron Café CAFE $
( 928-634-2733; www.flatironcafejerome.com; 416 Main St; breakfast $7-13, lunch $9-13; 7am-3pm Wed-Mon) This captivating cafe may be tiny but it packs a big, delicious punch. Savor a cheesy scrambled-egg-and-salmon quesadilla at breakfast or a walnut-and-cranberry chicken salad sandwich at lunch. Order at the counter then grab one of three inside tables, or head across the street to the small patio. The mocha latte gets rave reviews.
Grapes AMERICAN $$
( 928-639-8477; www.grapesjerome.com; 111 Main St; lunch & dinner $9-17; 11am-9pm Mon-Fri, 8am-9pm Sat & Sun) Wine newbies and grape connoisseurs are equally happy at this breezy, brick-walled bistro that serves ahi tuna burgers, a Tuscan berry salad with feta, and 10 different gourmet pizzas. Wine selections come with a bin number, and these numbers are helpfully paired with food listings on the menu. From 5pm to 9pm on weekdays all wines by the glass are $5.
Asylum Restaurant AMERICAN $$$
( 928-639-3197; www.theasylum.biz; 200 Hill St; lunch $9-15, dinner $21-32; lunch & dinner) Deep-red walls, lazily twirling fans, gilded artwork and views, views, views make this venerable dining room at the Jerome Grand Hotel one of the state's top picks for fine dining. Orderthe roasted butternut-squash soup with cinnamon-lime crème and the prickly-pear barbecue pork tenderloin, and you'll see what we mean. Superb wine list too. We've heard Senator John McCain loves it here.
Haunted Hamburger BURGERS $$
( 928-634-0554; 410 N Clark St; mains $8-21; 11am-9pm) Perched high on a hill and often packed, this patty-and-bun joint is definitely a candidate for 'burger king' of the town.
#### Drinking
The bar at Asylum Restaurant is a genteel place for a cocktail and the views are stunning, but if you want to let your hair down, head to the Spirit Room Bar ( 928-634-8809; www.spiritroom.com; 166 Main St; 11am-1am). Whether you sip a pint at the bar, shoot pool, strike up a conversation with (friendly) Harley riders or study the bordello scene mural, you'll have a fine time at this dark, old-time saloon. There's live music on weekend afternoons and an open-mic night on Wednesday.
### VERDE VALLEY WINE TRAIL
Several new vineyards, wineries and tasting rooms have opened along Hwy 89A and I-17, bringing a dash of style and energy to the area. Bringing star power is Maynard James Keenan, lead singer of the band Tool and owner of Caduceus Cellars and Merkin Vineyards. His 2010 documentary _Blood into Vine_ takes a no-holds-barred look at the wine industry.
In Cottonwood, start with a drive or a float to Verde River-adjacent Alcantara Vineyards (www.alcantaravineyard.com; 7500 E Alcantara Way) then stroll through Old Town where two new tasting rooms, Arizona Stronghold (www.azstronghold.com; 1023 N Main St) and Pillsbury Wine Company (www.pillsburywine.com; 1012 N Main S) sit across from each other on Main St.
In Jerome there's a tasting room on every level of town, starting with Bitter Creek Winery/Jerome Gallery (www.bittercreekwinery.com; 240 Hull Ave) near the visitor center. From there, stroll up to Keenan's Caduceus Cellars (www.caduceus.org; 158 Main St; 11am-6pm Sun-Thu, until 8pm Sun) then finish up with a final climb to Jerome Winery ( 928-639-9067; 403 Clark St; 11am-5pm Mon-Thu, 11am-8pm Sat, 11am-4pm Sun Jun-Aug, slightly shorter hours rest of the year), a wine shop with an inviting patio, more valley views and your pick of 19 different sips.
Three wineries with tasting rooms hug a short, scrubby stretch of Page Springs Rd east of Cornville: bistro-housing Page Springs Cellars (www.pagespringscellars.com; 1500 N Page Springs Rd), the welcoming Oak Creek Vineyards (www.oakcreekvineyards.net; 1555 N Page Springs Rd), and the mellow-rock-playing Javelina Leap Vineyard (www.javelinaleapwinery.com; 1565 Page Springs Rd).
Leave the driving to others with Sedona Adventure Tours (www.sedonaadventuretours.com), or Arizona Grape Escapes (www.arizonagrapeescapes.com), which leaves from Phoenix. For a wine-trail map and more details about the wineries, visit www.vvwinetrail.com.
New wine-tasting rooms have opened in and around Jerome, adding another level of fun.
#### Shopping
In the downtown business district, galleries are mixed in with souvenir shops.
Jerome Artists Cooperative Gallery ARTS & CRAFTS
( 928-639-4276; www.jeromeartistscoop.com; 502N Main St; 10am-6pm) Need a gift? At this bright and scenic gallery more than 30 local artists work in pottery, painting, jewelry and other media, before selling their creations at very fair prices.
Nellie Bly SPECIALTY
( 928-634-0255; www.nbscopes.com; 136 Main St) This cool place is an Aladdin's cave of kaleidoscopes in all shapes and sizes. Also sells art glass.
Downhill, the Old Jerome High School harbors seven artist studios and galleries. Many are open to the public most days, but the best time to visit them all is during the Jerome Art Walk (www.jeromeartwalk.com) on the first Saturday of the month from 5pm to 8pm. During the 26-gallery art walk, a free shuttle runs between the high school, galleries downtown and the Jerome Grand Hotel. Some galleries have openings, live music and refreshments.
#### Information
Remember the board game Chutes & Ladders? There's a similar concept at work in Jerome. The town is essentially stacked up the side of Cleopatra Hill, on three distinct levels. Hwy 89A twists tightly between the different levels and splits into two one-way streets (Hull Ave and Main St) at the Y-intersection in front of the Flatiron Café. On crowded weekends grab a parking spot as soon as you can, then walk through town.
Chamber of Commerce ( 928-634-2900; www.jeromechamber.com; Hull Ave, Hwy 89A north after the Flatiron Café split; 11am-3pm) Offers tourist information.
Police ( 928-634-8992; www.jeromepd.org; 305 Main St) Visit the website just for the music!
Post office ( 928-634-8241; 120 Main St; 8am-noon, 12:30-2:45pm Mon-Fri)
#### Getting There & Away
To reach Jerome from Prescott follow Hwy 89A north for 34 miles. The drive is slow and windy, and not recommended for large trailers.
### Cottonwood
Cottonwood doesn't get the respect it deserves. Yes, it's afflicted with a bit of cookie cutter sprawl, but its walkable Old Town district buzzes with new restaurants, two stylish wine-tasting rooms and an eclectic array of indie shops. Cottonwood is also a cheap and convenient base for regional exploring. Located in the Verde Valley, it's only 16 miles from Sedona and 9 miles from Jerome. The main approach is via Hwy 89A, a faceless, busy thoroughfare.
For information, head to the helpful chamber of commerce ( 928-634-7593; www.cottonwoodchamberaz.com; 1010 S Main St; 9am-5pm Mon-Fri, 9am-1pm Sat & Sun) at the intersection of Hwy 89A and Hwy 260. For a list of shops and restaurants in Old Town, visit www.oldtown.org.
#### Sights
Dead Horse Ranch State Park PARK
( 928-634-5283; www.azstateparks.com; 675 DeadHorse Ranch Rd; day use per vehicle $7, tent/RV site/cabins from $15/25/55) The Verde River runs past this 423-acre park which offers picnicking, fishing, multi-use trails (for bikes, horses and hikers) and a playground. Overnighters can choose between cabins orcampsites, some with hookups, and enjoyhot showers. Camping reservations are nowavailable online, as well as by phone ( 520-586-2283; 8am-5pm). Bird-watchers will want to make the short trek to the bird-watching stand at Tavasci Marsh to train their binoculars on the least bittern, the Yuma clapper rail and the belted kingfisher. For the horse-lover, Trail Horse Adventures( 928-634-5276; www.trailhorseadventures.com; rides $64-125) will saddle you up for rides lasting one to 2½ hours. There's also a three-hour lunch ride.
#### Sleeping
Cottonwood is the land of motels, mostly of the chain variety, but prices are as low as you'll find in the area.
View Motel MOTEL $
( 928-634-7581; www.theviewmotel.com; 818 S Main St; r $59-75; ) Professionally run, this motel delivers the views its name promises. It's an older property and the furniture is back-to-basics, but rooms are very clean and come with a refrigerator and microwave. A few have kitchenettes. Dogs are $10 per night.
Little Daisy Motel MOTEL $
( 928-634-7865; www.littledaisy.com; 34 S Main St; r $56-61, house $125; ) Named after a local mine, this motel won't spoil you with frilly extras or fancy furnishings, but it's a good choice if all you want is a solid night's sleep. A two-bedroom house is available for up to four people. Dogs OK ($10 per night), but no felines or ferrets allowed.
Pines Motel MOTEL $
( 928-634-9975; www.azpinesmotel.com; 920 S Camino Real; r $85-94; ) This two-story motel, also on a hill with nice views, offers mini-suites with kitchenettes, in addition to standard king and queen units. Pets are $20 the first night, then $5 each night after that.
#### Eating & Drinking
Old Town is packed tight with good cafes and restaurants. For more information on its wine tasting rooms, see Click here.
Crema Coffee & Creamery COFFEE SHOP, SANDWICHES $
(www.cremacoffeeandcreamery.com; 917 N Main St; breakfast under $6, lunch $6-9; 7am-4pm Mon-Fri, 8am-4pm Sat & Sun; ) The patio is a pleasant place to surf the web while nibbling a fresh-from-the-oven blueberry scone (try to visit at 8:30am). Salads and gourmet sandwiches are available for lunch, and there's also yummy gelato.
Nic's Italian Steak & Crab House STEAKHOUSE, SEAFOOD $$$
( 928-634-9626; www.nicsaz.com; 925 N Main St; lunch $8-14, dinner $11-31; lunch, dinner) You wouldn't really expect an old Chicago vibe – dark, cozy, woodsy – in Cottonwood, but this joint gets it right. Same goes for the grilled steaks, even better when smothered in mushrooms and onions. This place draws a crowd.
Tavern Grille AMERICAN $$
(www.taverngrille.net; 914 N Main St; mains $9-24; 11am-9pm) The folks behind Nic's also own the patio-fronted Tavern Grille across the street. Inside, booths, flat-screen TVs and a convivial happy-hour crowd surround a large central bar. Upscale pub grub includes Southwestern sourdough burgers and Cajun-blackened halibut.
Blazin' M Ranch AMERICAN $$
( 928-634-0334, 800-937-8643; www.blazinm.com; 1875 Mabery Ranch Rd; adult/child/senior $35/25/33; site opens at 5pm; ) Near Dead Horse Ranch State Park, here you can yee-haw with the rest of them at chuckwagon suppers paired with rootin' tootin' cowboy entertainment. Kids big and small love it. Call for dates and reservations.
### CLARKDALE: THE TRAIN & TUZIGOOT
Clarkdale is a former mining town with two star attractions. On the Verde Canyon Railroad ( 928-639-0010, 800-293-7245; www.verdecanyonrr.com; 300 N Broadway; coach adult/child/senior $55/35/50, 1st class all passengers $80) vintage FP7 engines pull climate-controlled passenger cars on leisurely four-hour narrated round trips into the splendid canyon north of Cottonwood Pass, traveling through roadless wilderness with views of red-tinged rock cliffs, riparian areas, Native American sites, wildlife and, from December to April, bald eagles. Monthly schedules are posted on the website. An adults-only wine trip, the Grape Train, is offered in the summer. Reservations are recommended for all trips.
Draped across a ridge about 2 miles east of Clarkdale, Tuzigoot National Monument ( 928-634-5564; www.nps.gov/tuzi; adult/child $5/free, combination ticket with Montezuma Castle National Monument $8/free; 8am-6pm Jun-Aug, 8am-5pm Sep-May), a Sinaguan pueblo like nearby Montezuma, is believed to have been inhabited from AD 1000 to 1400. At its peak, as many as 250 people may have lived in its 110 rooms. A short, steep trail (not suitable for wheelchairs) winds in and around the structure's limestone walls. A short climb to the roof leads to panoramic views of the Verde River Valley and Mingus Mountain. A half-mile round-trip trail leads to an overlook with views of the bird-attracting Tavasci Marsh.
Orion Bread Company BAKERY $
(www.orionbread.com; 1028 N Main St; loaves & pastries under $6, sandwiches $7-8; 7am-5pm; ) Stop by for preservative-free loaves, baked goods, sandwiches (between 11am and 3pm) and coffee.
Bing's Burger Station BURGERS $
(www.bingsburgers.com; 794 N Main St; mains $4-7; 11am-7pm Tue-Sat) Fuel up on burgers '50s-style at this spiffy diner fronted by gas pumps and a cherry red Plymouth (the place used to be a service station, natch). Shakes and malts sold too.
### Sedona
Sedona's a stunner, but it's intensely spiritual as well – some even say sacred. Nestled amid alien-looking red sandstone formations at the south end of the 16-mile gorge that is Oak Creek Canyon, Sedona attracts spiritual seekers, artists and healers, and day-trippers from Phoenix trying to escape the oppressive heat. Many New Age types believe that this area is the center of vortexes (not 'vortices' here in Sedona) that radiate the Earth's power, and Sedona's combination of scenic beauty and mysticism draws throngs of tourists year-round. You'll find all sorts of alternative medicines and practices, and the surrounding canyons offer excellent hiking and mountain biking.
The town itself bustles with art galleries and expensive gourmet restaurants. In summer the traffic and the crowds can be heavy.
The town's main drag is Hwy 89A. Sedona's navigational center is the roundaboutat the intersection of Hwys 89A and 179, known as the Y. Northeast of the Y is Uptown Sedona, the pedestrian center where you'll find most of Sedona's hotels, boutiques and restaurants. Turning south at the Y will take you to Tlaquepaque Village; from here you can cross over Oak Creek and continue down to the Village, where you'll find more shopping, restaurants and hotels. West of the Y is West Sedona, where strip malls line the highway and lead to Red Rock State Park.
#### Sights
###### Scenic Drives
In town, the short drive up paved Airport Rd opens up to panoramic views of the valley. At sunset, the rocks blaze a psychedelic red and orange that'll have you burning up the pixels in your camera. Airport Mesa is the closest vortex to town.
Any time is a good time to drive the winding 7-mile Red Rock Loop Rd, which is all paved except one short section and gives access to Red Rock State Park as well as Red Rock Crossing/Crescent Moon Picnic Area (day-use $8). A small army of photographers usually gather at the crossing at sunset to record the dramatic light show unfolding on iconic Cathedral Rock, another vortex. There's also swimming in Oak Creek. Access is via Upper Red Rock Loop Rd off Hwy 89A, 4 miles west of the Y.
For a breathtaking loop, follow Dry Creek Rd to Boynton Pass Rd, turn left, then left again at Forest Rd 525. It's mostly paved but there are some lumpy, unpaved sections. The route passes two of the most memorable rock formations, Vultee Arch and Devil's Bridge. Extend this trip by turning right on FR 525 and taking in the Palatki ruins.
Sedona
Activities, Courses & Tours
1Fat Tire Bike Shop H1
Sleeping
2La Vista Motel H1
3Lantern Light Inn A3
4L'Auberge de Sedona H1
5Matterhorn Inn H1
6Rancho Sedona RV Park H2
7Sedona Motel G2
Eating
8Bashas' C2
9Black Cow Café H1
10Coffee Pot Restaurant C2
11Dahl & DiLuca Ristorante C2
12Elote Cafe G3
13Heartline Café D2
L'Auberge Restaurant on Oak Creek (see 4)
14New Frontiers Natural Marketplace E2
Oak Creek Brewery & Grill (see 20)
Sedona Memories (see 1)
15Shugrue's Hillside Grill G3
16Wildflower Bread Company H2
Drinking
Heart of Sedona (see 14)
17Oak Creek Brewing Company C2
Shopping
18Center for the New Age H2
19Garland's Navajo Rugs H2
20Tlaquepaque Village G2
Red Rock State Park PARK
( 928-282-6907; www.azstateparks.com/Parks/RERO; 4050 Red Rock Loop Rd; per car/bicycle or pedestrian $10/3; 8am-5pm) Not to be confused with Slide Rock State Park, this low-key
park includes an environmental education center, a visitor center ( 9am-5pm), picnic areas and 5 miles of well-marked trails in a riparian habitat amid gorgeous scenery. Ranger-led activities include nature walks, bird walks and full-moon hikes during the warmer months.
Chapel of the Holy Cross &
Buddhist Stuppas RELIGIOUS
( 928-282-4069; www.chapeloftheholycross.com; 780 Chapel Rd; 9am-5pm Mon-Sat, 10am-5pm Sun) Situated between spectacular, statuesquered-rock columns 3 miles south of town, this modern, nondenominational chapel was built in 1956 by Marguerite Brunwig Staude in the tradition of Frank Lloyd Wright. There are no services, but even if you're not affiliated with any religion, the soaring chapel and the perch it occupies may move you as it did its architect. There are no restrooms on the site.
Another example of sacred architecture can be admired across town in the West Sedona hills at the Amitabha Stupa ( 928-300-4435; www.stupas.org), a consecrated Buddhist shrine set quite stunningly amid piñon and juniper pine and the ubiquitous rocks. There's a smaller stupa further down and an entire park is being planned. Heading along Hwy 89A west from the Y, turn right on Andante Dr, left on Pueblo Dr, then head up the gated trail on your right.
Palatki Heritage Site RUINS
( 928-282-3854; www.fs.fed.us/r3/coconino; admission free, Red Rock Pass required; 9:30am-3pm) Thousand-year-old Sinagua cliff dwellings and rock art are good-enough reasons to brave the 9-mile dirt road leading to this enchantingly located archaeological site on the edge of the wilderness. There's a small visitor center and two easy trails suitable for strollers but not for wheelchairs. With only limited parking, reservations are required. No pets. True ruin groupies should ask here about exploring the Honanki Ruins, a further 3 miles north.
To get to the site, follow Hwy 89A west of the Y for about 10 miles, then hook a right on FR 525 (Red Canyon Rd, a dirt road) and follow it 8 miles north to the parking lot.
#### Activities
Hiking and mountain-biking trails crisscross the surrounding red-rock country and the woods and meadows of green Oak Creek Canyon. Available at the visitor centers and ranger stations, the free Red Rock Country recreation guide describes hiking and biking trails for all skill levels and includes a map of scenic drives. One popular hiking trail in Oak Creek Canyon is the West Fork Trail, which follows the creek for 7 miles – the canyon walls rise more than 200ft in places. Wander up as far as you want, splash around and turn back when you've had enough. The trailhead lies about 3 miles north of Slide Rock, in the Call of the Canyon Recreation Area.
Rent bikes at the Fat Tire Bike Shop ( 928-852-0014; www.thefattire.com; 325 Jordan Rd; per day $75; 9am-5pm Mon-Sat). They also do group rides several days a week; call the shop for more info.
Oak Creek holds several good swimming holes. If Slide Rock is too crowded, check out Grasshopper Point ($8 per car) a few miles south. Southwest of town you can splash around and enjoy splendid views of Cathedral Rock at Red Rock Crossing, a USFS picnic area along a pretty stretch of Oak Creek; look for the turnoff about 2 miles west of the hospital on Hwy 89A.
For an easy hike that leads almost immediately to gorgeous views, check out Airport Mesa. From Hwy 89A, follow Airport Dr about half a mile up the side of the mesa to a parking turnout on your left. From here, the short Yavapai Loop Trail leads to an awe-inspiring view of Courthouse Butte and, after a brief scramble, a sweeping 360-degree panorama of the city and its flanking red rocks. This is one of Sedona's vortex sites. Try to start this hike in the morning – before 8:30am, when the parking lot starts to fill. There's a Red Rock Pass machine in the parking lot. The Yavapai Loop Trail links onto the longer Airport Loop Trail.
Another stunningly beautiful place to hike is through the red rock of Boynton Canyon, an area that exudes spiritual energy and where some have reported experiencing the antics of such energetic spirits (who may not necessarily want them trekking through)! Look for the rock formation known as Kachina Woman and try not to be moved. Boynton Canyon is about 5 miles north of Hwy 89A up Dry Creek Rd; get an early start to avoid crowds.
###### Horseback Riding
M Diamond Ranch HORSEBACK RIDING
( 928-300-6466; www.sedonahorsebackrides.com; 1hr trail ride incl transportation adult/child $70/50, trail ride & cookout $85-115; Mon-Sat; ) This working cattle ranch takes small groups of people on trail rides through eye-catching countryside. Staff will give you a ride from your hotel. Children receive 15% off the adult price for the trail ride and cookout.
#### Tours
Sedona's scenery is the backdrop for many a rugged adventure, and numerous tour operators stand by to take you into the heart of it. Bumpy off-road jeep tours are the most popular, but it can be confusing distinguishing one company from the next. One thing to check is backcountry accessibility – the companies have permits for different routes and sites. If there's a specific rock formation or region you'd like to explore, be sure to ask. Some companies expect a minimum of four participants and charge more per person for smaller groups. Many offer discounted tour prices if you reserve online.
A Day in the West JEEP
( 928-282-4320; www.adayinthewest.com) Thoserootin' tootin' cowboys strolling through Uptown are most likely guides for this Western-themed jeep tour company. It offers a combo jeep tour/horseback ride with Western-style dinner and show (adult/child $149/129). Also leads a jeep and winery trip ($99) and several backcountry-only trips (adult $45 to $75, child $35 to $60).
Earth Wisdom Jeep Tours SPIRITUAL
( 928-282-4714; www.earthwisdomtours.com; 293N Hwy 89A; tours $49-98) Groovy jeep tours with a metaphysical bent and Native American focus, with journeys to vortexes and sacred Native American sites.
Evening Sky Tours ASTRONOMY
( 928-203-0006; www.eveningskytours.com) Viewplanets, stars, galaxies and nebula with the naked eye and through large Dobsonian telescopes. Ninety-minute tours cost $50 to $60, depending on group size. Kids are $25.
Northern Light Balloon Expeditions BALLOON
( 928-282-2274; www.northernlightballoon.com) Spend about one hour floating in the air at sunrise ($195 per person) then enjoy a champagne picnic back on solid ground.
Pink Jeep Tours JEEP
( 928-282-5000; www.pinkjeep.com; 204 N Hwy 89A) This company must be doing something right because it recently celebrated its 50th anniversary. The company runs 13 different thrilling and funny, if bone-rattling, off-road tours lasting from about two hours (adult/child $55/42) to four hours ($167/144). Tours to the Grand Canyon are also offered.
### RED ROCK PASS
If you want to park anywhere in the forest surrounding Sedona, you'll need to buy a Red Rock Pass, which is available at the ranger station, visitor centers and vending machines at some trailheads and picnic areas. Passes cost $5 per day or $15 per week (and $20 per year) and must be displayed in the windshield of your car. You don't need a pass if you're just stopping briefly for a photograph or to enjoy a viewpoint, or if you have an America the Beautiful pass ($80). With the latter, place it in the windshield with your signature facing out. You can also swing by a visitor center for a hangtag – the passes have been known to melt! For additional details see www.redrockcountry.org. Passes are not valid at other fee areas, including state parks, national monuments and the day-use areas of Banjo Bill, Crescent Moon, Call of the Canyon and Grasshopper Point; these four day-use areas charge $8 to $10 per vehicle.
Red Rock Jeep Tours JEEP
( 928-282-6667; www.redrockjeep.com; 270 N Hwy 89A) Guides in cowboy garb take you on mild to wild jeep adventures; this is the only company going out to the historic Soldier Pass Trail (adult/child $69/55), used by General George Crook during his campaign against the Apaches. Also offers a vortex tour (adult/child $109/75).
Sedona Adventure Tours RIVER
( 928-204-6440; www.sedonaadventuretours.com; 2020 Contractors Rd; ) Specializes in river trips, with a funyak trip down the Verde River and a 'Water to Wine' float to Alcantara Vineyard. Water to Wine tours range from $85 to $172. Funyak and inner-tube rentals too.
Sedona Trolley SCENIC
( 928-282-4211; www.sedonatrolley.com; 276 N Hwy89A; adult/child $12/6, both tours $22/11; 9am-5pm, may vary seasonally) Choose from two narrated tours, both lasting 55 minutes and departing on the hour. 'Sedona Highlights' covers Tlaquepaque Village and the Chapel of the Holy Cross, while 'Seven Canyons Scenic' runs to West Sedona and Boynton Canyon.
#### Festivals & Events
Sedona Arts Festival ARTS & CRAFTS
( 928-282-1177; www.sedonaartsfestival.org) Finearts, crafts and non-stop entertainment in early October.
Sedona International Film Festival FILM
( 928-282-1177; www.sedonafilmfestival.com) Usually takes place during the month of February, but screenings and events occur throughout the year.
#### Sleeping
Sedona is rich with beautiful B&Bs, creekside cabins and full-service resorts. Rates at chain motels range from $75 to $130, reasonable by Sedona standards. For lodging in Oak Creek Canyon, see (Click here).
Apart from camping, tiny Sedona doesn't have many options for the budget traveler.
Rancho Sedona RV Park CAMPING
( 928-282-7255, 888-641-4261; www.ranchosedona.com; 135 Bear Wallow Ln; RV sites $31-63) Offers a laundry, showers and 30 RV sites, most with full hookups.
Briar Patch Inn CABIN $$$
( 928-282-2342; www.briarpatchinn.com; 3190 N Hwy 89A; cottages $219-395; ) Nestled in nine wooded acres along Oak Creek, this lovely inn offers 19 log cottages with Southwestern decor and Native American art. All cottages include patios, many have fireplaces, and several lie beside the burbling creek. In summer, a hearty buffet breakfast is served on a stone patio that overlooks the creek and is accompanied by live chamber music (Wednesday to Sunday). There's a two-night minimum on weekends and it's best to book at least a few months ahead.
L'Auberge de Sedona RESORT $$$
( 928-282-1661; www.lauberge.com; 301 L'Auberge Ln; ) Situated creekside in Uptown Sedona, the red-rock backdrop looms within reaching distance. With well-appointed cabins amid the green lawns, luxuries include Jacuzzis, wine and cheese every evening and free yoga classes daily –and even a gift bag for your dog, who is most welcome here ($35 to $50 fee applies).
### VORTEX PRIMER
Several vortexes (swirling energy centers where the Earth's power is said to be strongly felt) are located around Sedona, which is one of the reasons it has become a mecca of spiritual seekers and New-Age types. The four best-known vortexes are in Sedona's Red Rock Mountains. These include Bell Rock, near the Village of Oak Creek, Cathedral Rock, near Red Rock Crossing, Airport Mesa, along Airport Rd, and Boynton Canyon. Local maps show these four main sites, although some individuals claim that others exist. Stop by the Sedona Chamber of Commerce Visitor Center to find out about different tours.
Cozy Cactus B&B $$
( 928-284-0082; www.cozycactus.com; 80 Canyon Circle Dr, Village of Oak Creek; r $165-325; ) This five-room B&B, run by Carrie, Mark and black lab Margi, works well for adventure-loving types ready to enjoy the great outdoors. The Southwest-style abode bumps up against a National Forest trail and is just around the bend from cyclist-friendly Bell Rock Pathway. Post-adventuring, get comfy beside the firepit on the back patio for wildlife watching and stargazing. Breakfasts alternate between savory and sweet (huevos rancheros; apple-pie French toast) and come with fruit and Mark's famous muffins.
Lantern Light Inn B&B $$-$$$
( 928-282-3419; www.lanternlightinn.com; 3085 W Hwy Alt 89; r $139-195, ste $195-309; ) The lovely couple running this small inn in West Sedona put you right at ease in their comfortable antique-filled rooms. Rooms range from small and cozy, overlooking the back deck and garden, to the huge guesthouse in back (breakfast not included), but all feel comfortably overstuffed. There's a common room (more of a family library with musical instruments) that can be used for meetings. Credit cards not accepted.
Sky Ranch Lodge MOTEL $-$$
( 928-282-6400; www.skyranchlodge.com; Airport Rd; r $80-164, cottages $194; ) At the top of Airport Rd, with spectacular views of the town and surrounding country, this lodge offers spacious motelrooms, six landscaped acres, and a pool and hot tub. Rates vary according to type of bed and your view. Some include balconies, fireplaces, kitchenettes and/or refrigerators; also available are cottages with vaulted ceilings.
La Vista Motel MOTEL $
( 928-282-7301; www.lavistamotel.com; 500 N Hwy Alt 89; r $66-90, s $90-100; ) Right on the side of the highway leading into Oak Creek Canyon, this friendly, family-run motel has clean rooms and suites. Some suites are decked out with full kitchens, porches, tile floors, sofas, refrigerators and bathtubs.
Sedona Motel MOTEL $
( 928-282-7187; www.thesedonamotel.com; 218Hwy 179; r $79-89; ) Directly south of the Y, this friendly little motel offers big value within walking distance of Tlaquepaque and Uptown Sedona. Rooms are basic but clean, but the fantastic red rock views may be all the luxury you need.
Matterhorn Inn MOTEL $$
( 928-282-7176; www.matterhorninn.com; 230 Apple Ave; r $150; ) All rooms at this friendly, central motel include refrigerators and have balconies or patios overlooking Uptown Sedona and Oak Creek.
#### Eating
Elote Cafe MEXICAN $$
( 928-203-0105; www.elotecafe.com; King's Ransom Hotel, 771 Hwy 179; mains $17-22; 5pm-late Tue-Sat) Some of the best, most authentic Mexican food you'll find in the region. Serves unusually traditional dishes you won't find elsewhere, like the fire-roasted corn with lime and cotija cheese, or the tender, smoky pork cheeks. Reservations are not accepted, so if you want to eat at a reasonable hour, line up by 4:30pm or resign yourself to waiting with a white sangria.
L'Auberge Restaurant on Oak Creek AMERICAN $$$
( 928-282-1661; www.lauberge.com; 301 L'Auberge Lane; mains $34-52; 7am-9pm Mon-Sat, 9am-2pm & 5:30-9pm Sun) Featuring refined American cuisine with a French accent, the menu at L'Auberge changes seasonally (you might find ramps and morels in the spring, and roast duck and beets in the fall). The creekside spot is a local favorite for celebrating special occasions in elegant environs, with a select wine list to complement your meal.
Dahl & DiLuca Ristorante ITALIAN $$$
( 928-282-5219; www.dahlanddiluca.com; 2321 Hwy 89A; mains $13-33; 5-10pm) Though this lovely Italian place fits perfectly into the groove and color scheme of Sedona, at the same time it feels like the kind of place you'd find in a small Italian seaside town. It's a bustling, welcoming spot serving excellent, authentic Italian food.
Heartline Café AMERICAN $$
( 928-282-0785; www.heartlinecafe.com; 1600-1610 W Hwy 89A; mains $18-28; 8am-4pm & 5-9:30pm) This restaurant's name refers to a Zuni Native American symbol for good health and long life, and indeed the imaginative menu offersfresh and clean gourmet victuals. A cozy ambience and creative, seasonal menu make it a long-running favorite. Nowadays, the Heartline Gourmet Express next door serves breakfast and lunch.
Oak Creek Brewery & Grill PUB
( 928-282-3300; www.oakcreekpub.com; 336 Hwy 179; beers $5.75; 11:30am-9pm; ) At Tlaquepaque Village, this spacious brewery serves a full menu that includes upmarket pub-style dishes like crab cakes and 'fire-kissed' pizzas.
Shugrue's Hillside Grill AMERICAN $$-$$$
( 928-282-5300; www.jamrestaurants.com; Hillside Plaza, 671 Hwy 179; mains $15-38; 11am-3pm Mon-Fri, 9am-3pm Sat & Sun, 5-9pm daily) Promising panoramic views, an outdoor deck from which to enjoy them and consistently excellent food, this restaurant is a great choice for an upscale meal. If it's too chilly to sit outside, don't fret – the walls are mostly glass, so you can still enjoy the scenery. The menu offers everything from steak to ravioli, but it is best known for its wide variety of well-prepared seafood.
Coffee Pot Restaurant BREAKFAST $
( 928-282-6626; www.coffeepotsedona.com; 2050 W Hwy Alt 89; mains $4-11; 6am-2pm; ) This has been the go-to breakfast and lunch joint for decades. It's always busy and service can be slow, but it's friendly, the meals are reasonably priced and the selection is huge – 101 types of omelets, for a start. (Jelly, peanut butter and banana omelet, anyone?)
Sedona Memories DELI $
( 928-282-0032; 321 Jordan Rd; mains $7; 10am-2pm Mon-Fri) This tiny local spot assembles gigantic sandwiches on slabs of homemade bread (which they don't sell seperately). There are several vegetarian options, and you can nosh on their quiet porch. Cash only.
Black Cow Café ICE CREAM $
( 928-203-9868; 229 N Hwy 89A; ice creams $4-5; 10:30am-9pm) Many claim the Black Cow has the best ice cream in town. It also does sandwiches and soup.
Pick up groceries and healthy picnic components at New Frontiers Natural Marketplace (Native American 928-282-6311; 1420 W Hwy 89A; mains $4-10; 8am-9pm Mon-Sat, to 8pm Sun; ) or stop by for smoothies, vegetarian salads or paninifrom the deli. Another good Arizona grocery chain is Bashas' ( 928-282-5351; 160 Coffee Pot Dr; 6am-11pm).
#### Drinking & Entertainment
Check the listings at _Sedona Red Rock News_ (www.redrocknews.com) for current local entertainment.
Heart of Sedona CAFE
( 928-282-5777; 1370 W Hwy 89A; coffee $2-5; 6am-11pm; ) Offering a pleasant outdoor patio with good views, this coffee shop is the best spot for a jolt of caffeine and a pastry while you check your email on their free wi-fi network.
Oak Creek Brewery & Grill BREWERY
( 928-282-3300; www.oakcreekpub.com; 336 Hwy 179; beers $5.75; 11:30am-9pm; ) Wash the pub food down with a house brew – we're partial to the Oak Creek Amber.
Oak Creek Brewing Company BREWERY
(www.oakcreekbrew.com; 2050 Yavapai Dr) In West Sedona, with a limited menu, has bands on the weekend.
#### Shopping
Shopping is a big draw in Sedona, and visitors will find everything from expensive boutiques to T-shirt shops. Uptown along Hwy 89A is the place to go souvenir hunting.
Tlaquepaque Village MALL
( 928-282-4838; www.tlaq.com; 10am-5pm) Just south of Hwy 89A on Hwy 179, this is a series of Mexican-style interconnected plazas that is home to dozens of high-end art galleries, shops and restaurants. It's easy to lose a couple of hours meandering the lovely maze here.
Garland's Navajo Rugs HANDICRAFTS
( 928-282-4070; www.garlandsrugs.com; 411 Hwy 179; 10am-5pm) This 35-year-old institution offers the area's best selection of rugs, and also sells other Native American crafts. It's an interesting shop to visit even if you don't plan on buying anything – it displays naturally dyed yarns with their botanical sources of color, as well as bios of the weavers and descriptions of how many hours it takes to create a handwoven rug.
Center for the New Age NEW AGE
( 928-282-5910; 313 Hwy 179; 8:30am-8:30pm) On Hwy 179 across the street from Tlaquepaque Village is this interesting purveyor of New Age books and gifts. Come here for a vortex guide.
#### Information
Police station ( 928-282-3100; www.sedonaaz.gov; 100 Roadrunner Dr; emergency 24hr)
Post office ( 928-282-3511; 190 W Hwy 89A; 8:45am-5pm Mon-Fri, 9am-1pm Sat)
Sedona Chamber of Commerce Visitor Center ( 928-282-7722, 800-288-7336; www.visitsedona.com; 331 Forest Rd; 8:30am-5pm Mon-Sat, 9am-3pm Sun) Located in Uptown Sedona, pick up free maps, brochures and get last-minute hotel bookings.
USFS South Gateway Visitor Center ( 928-203-7500; www.redrockcountry.org; 8379 Hwy 179; 8am-5pm) Get a Red Rock Pass here, as well as hiking guides, maps and local national forest information. It's just south of the Village at Oak Creek.
Verde Valley Medical Center ( 928-204-3000; www.verdevalleymedicalcenter.com; 3700 W Hwy 89A; 24hr)
#### Getting There & Away
While scenic flights depart from Sedona, the closest commercial airport is Phoenix (two hours) or Flagstaff (30 minutes).
Ace Express ( 928-649-2720, 800-336-2239; www.acexshuttle.com; one way/round-trip $60/99) Door-to-door shuttle service running between Sedona and Phoenix Sky Harbor.
Amtrak ( 800-872-7245; www.amtrak.com) Stops in Flagstaff, about 40 miles north of Sedona.
Greyhound ( 800-231-2222; www.greyhound.com) Stops in Flagstaff.
Sedona-Phoenix Shuttle ( 928-282-2066, 800-448-7988; www.sedona-phoenix-shuttle.com; one way/round-trip $50/90) Runs between Phoenix Sky Harbor and Sedona eight times daily; call to make reservations.
#### Getting Around
Barlow Jeep Rentals ( 928-282-8700, 800-928-5337; www.barlowjeeprentals.com; 3009 W Hwy 89A; 9am-6pm)
Bob's Taxi ( 928-282-1234) Local cab service.
Enterprise ( 928-282-2052; www.enterprise.com; 2090 W Hwy 89A; 8am-6pm Mon-Fri, 9am-noon Sat) Rental cars available here.
### Oak Creek Canyon
Hwy 89A from Sedona into Oak Creek Canyonis a surreally scenic drive that won't soon be forgotten. The canyon is at its narrowest here, and the crimson, orange and golden cliffs at their most dramatic. Pine and sycamore cling to the canyon sides and the air smells sweet and romantic. Giant cottonwoods clump along the creek, providing a scenic shady backdrop for trout-fishing and swimming, and turn a dramatic golden in fall. Unfortunately, traffic can be brutal in summer.
#### Sights & Activities
About 2 miles into the drive north from Sedona, Grasshopper Point (day-use $8) is a great swimming hole. Another splash zone awaits a further 5 miles north at Slide Rock State Park ( 928-282-3034; www.azstateparks.com/Parks/SLRO; 6871 N Hwy 89A; per car Memorial Day-Labor Day $20, Sep-May $10; 8am-7pm Memorial Day-Labor Day, 8am-5pm Sep-May), a historic homestead and apple farm along Oak Creek. Short trails ramble past old cabins, farming equipment and an apple orchard, but the park's biggest draw is the fun rock slides. Picture people swooshing down the creek through rock-lined chutes and over water-covered rock 'slides'. It's an all-natural waterpark. Unfortunately, water quality can be an issue, but it's tested daily; call the hotline on 602-542-0202. This park gets jam-packed in summer, so come early or late in the day to avoid the worst congestion.
About 13 miles into the canyon, the road embarks on a dramatic zigzag climb, covering 700ft in 2.3 miles. Pull into Oak Creek Vista and whip out your camera to capture the canyon from a bird's-eye perspective. A small visitor center is open seasonally, and there's a year-round Native American arts and crafts market.
Beyond here, the highway flattens out and reaches I-17 and Flagstaff in about 8 miles.
#### Sleeping
###### Camping
Dispersed camping is not permitted in Red Rock Canyon. The USFS ( 928-282-4119, 877-444-6777; www.recreation.gov) runs the following campgrounds along Hwy 89A in Oak Creek Canyon (none with hookups). All are nestled in the woods just off the road. It costs $20 to camp, but you don't need a Red Rock Pass. Reservations are accepted for all campgrounds but Pine Flat East.
Manzanita Eighteen sites; open year-round; 6 miles north of town.
Cave Springs Eighty-two sites; showers; 11.5 miles north.
Pine Flat East and Pine Flat West Fifty-seven sites; 12.5 miles north.
###### Lodging
Garland's Oak Creek Lodge LODGE $$$
( 928-282-3343; www.garlandslodge.com; Hwy 89A; cabins $180-295; closed Sun & mid-Nov–Apr 1; ) Set back from Oak Creek on eight secluded acres with broad lawns, woods and an apple orchard, this lodge offers nicely appointed Western log cabins, many with fireplaces. Rates include a full hot breakfast, 4pm tea and a superb gourmet dinner. Catering to guests who crave peace and quiet amid verdant surroundings, Garland's is 8 miles north of Sedona and is often booked up a year in advance. If you can't stay overnight, booking dinner is a delicious alternative; there are sometimes a few spots are available for nonguests.
Junipine Resort LODGE $$-$$$
( 928-282-3375; www.junipine.com; 8351 N Hwy 89A; creekhouses $135-400; ) In the Oak Creek Canyon woodland, 8 miles north of Sedona, this resort offers lovely, spacious one- and two-bedroom creekhouses. All have kitchens, living/dining rooms, wood-burning stoves and decks – and some even have lofts. The on-site restaurant serves great food as well as microbrews and wine.
Slide Rock Lodge MOTEL $$
( 928-282-3531; www.sliderocklodge.com; 6401 N Hwy 89A; r $99-149, ste $179; ) This log-cabinlonghouse has rooms along the canyonwall that tend toward the simple and rustic. Some rooms have fireplaces, all are clean and there's a large grassy area outside to relax and grill. The atmosphere is friendly, quiet and conducive to a laid-back stay.
### Flagstaff
Flagstaff's laid-back charms are countless, from its pedestrian-friendly historic downtown crammed with eclectic vernacular architecture and vintage neon, to its high-altitude pursuits like skiing and hiking. Buskers play bluegrass on street corners while bike culture flourishes. Locals are a happy, athletic bunch, skewing more toward granola than gunslinger. Northern Arizona University (NAU) gives Flag its college-town flavor, while its railroad history still figures firmly in the town's identity. Throw in a healthy appreciation for craft beer, freshly-roasted coffee beans and an all-around good time and you have the makings of a town you want to slow down and savor.
Approaching Flagstaff from the east, I-40 parallels Old Route 66. Their paths diverge at Enterprise Rd: I-40 veers southwest, while Old Route 66 curls northwest, hugging the railroad tracks, and is the main drag through the historic downtown. NAU sits between downtown and I-40. From downtown, I-17 heads south toward Phoenix, splitting off at Hwy 89A (also known as Alt 89), a spectacularly scenic winding road through Oak Creek Canyon to Sedona. Hwy 180 is the most direct route northwest to Tusayan and the South Rim (80 miles), while Hwy 89 beelines north to Cameron (59 miles), where it meets Hwy 64 heading west to the canyon's East Entrance.
#### Sights
With its wonderful mix of cultural sites, historic downtown and access to outdoorsy pursuits, it's hard not to fall for Flagstaff.
Museum of Northern ArizonaMUSEUM
( 928-774-5213; www.musnaz.org; 3101 N Fort Valley Rd; adult/child/senior $7/4/6; 9am-5pm) This small but excellent museumfeatures exhibits on local Native American archaeology, history and culture, as well as geology, biology and the arts. Don't miss the extensive collection of Hopi kachina (also spelled katsina, Click here) dolls and a wonderful variety of Native American basketry and ceramics.
Flagstaff
Sights
1Lowell Observatory B3
2Mt Elden Trailhead G1
3Pioneer Museum B1
4Riordan Mansion State Historic Park B4
Sleeping
5Little America Hotel D4
6Starlight Pines F1
Eating
7New Frontiers Natural Marketplace C4
Entertainment
8Museum Club F2
Riordan Mansion State Historic ParkHISTORIC SITE
( 928-779-4395; www.azstateparks.com/Parks/RIMA; 409 W Riordan Rd; adult/child $7/3; 9:30am-5pm May-Oct, 10:30am-5pm Nov-Apr) Having made a fortune from their Arizona Lumber Company, brothers Michael and Timothy Riordan had the house built in 1904. The Craftsman-style design was the brainchild of architect Charles Whittlesey, who also designed El Tovar on the South Rim. The exterior features hand-split wooden shingles, log-slab siding and rustic stone. Filled with Edison, Stickley, Tiffany and Steinway furniture, the interior is a shrine to Arts and Crafts. Visitors are welcome to walk the grounds and picnic, but entrance to the house is by guided tour only. Tours leave daily and on the hour; advance reservations are accepted.
Lowell Observatory OBSERVATORY
( 928-774-3358; www.lowell.edu; 1400 W Mars Hill Rd; adult/child $6/3; 9am-5pm Mar-Oct, noon-5pm Nov-Feb, call for evening hours) This national historic landmark was built in 1894 by Percival Lowell. The observatory has witnessed many important discoveries,the most famous of which was the first sighting of Pluto – in 1930 through the 1896 24-inch Clark Telescope. In the '60s NASA used the Clark telescope to map the moon. Weather permitting, visitors can stargaze through the telescope; check the website for the evening schedule. The short, paved Pluto Walk climbs through a scale model of our solar system, providing descriptions of each planet. You can stroll the grounds and museum on your own, but the only way to see the telescopes and lovely observatories is on a tour (on the hour from 10am to 4pm in summer; on the hour from 1pm to 4pm in winter).
Arboretum GARDENS
( 928-774-1442; 4001 S Woody Mountain Rd; www.thearb.org; adult/child $7/3; 9am-5pm Apr-Oct; ) The Arboretum is a lovely spot to rejuvenate your spirit and enjoy a picnic. Two short wood-chip trails enfold a meadow and wind beneath ponderosa pines, passing an herb garden, native plants, vegetables and wildflowers. The Arboretum offers tours (11am, 1pm and 3pm), as well as a summer adventure program for children aged four to 12. From Route 66 west of Milton Ave, follow Woody Mountain Rd 3.8 miles south – most of this stretch is unpaved but it should be driveable for most cars.
Pioneer MuseumMUSEUM
( 928-774-6272; www.arizonahistoricalsociety.org/museums/flagstaff.asp; 2340 N Fort Valley Rd; adult/child $5/free; 9am-5pm Mon-Sat)Housed in the old 1908 hospital, this museum preserves Flagstaff's early history in photographs and an eclectic mix of memorabilia, including a piece of luggage recovered from Bessie and Glenn Hyde's ill-fated honeymoon trip down the Grand Canyon's Colorado River in 1928.
#### Activities
###### Hiking & Biking
Ask at the USFS ranger stations for maps and information about the scores of hiking and mountain-biking trails in and around Flagstaff. Another useful resource is _Flagstaff Hikes: 97 Day Hikes Around Flagstaff_ , by Richard and Sherry Mangum (Hexagon Press, 2007); available at the visitor center and Babbitt's Backcountry Outfitter, among other places.
Consider tackling the steep, 3-mile one-way hike up 9299ft Mt Elden to the ranger station at the top of the peak's tower, which has stairs you can climb to the ranger's lookout. Arizona Snowbowl offers several trails, including the strenuous 4.5-mile one-way hike up 12,633ft Humphreys Peak, the highest point in Arizona; wear decent boots as sections of the trail cross crumbly volcanic rock. In summer, ride the scenic chairlift (adult/child $12/8; 10am-4pm Fri-Sun, Mon hols Memorial Day-Labor Day) at Arizona Snowbowl to 11,500ft, where you can hike, attend ranger talks and take in the desert and mountain views. Children under eight ride for free.
There's also a beautiful stretch of the Arizona Trail running through the area. If you head toward Walnut Canyon (Click here), you'll see a turnoff on the right leading to the Walnut Canyon Trailhead. Drive 1.7 miles down the graded dirt road and you'll come to the trailhead. There are no restrooms, no water, no nothin' – come prepared with a map and supplies if you want to do the Fisher Point Trail (6.7 miles one way) or hike up to Marshall Lake (13.4 miles one way).
Central Flagstaff
Activities, Courses & Tours
1Absolute Bikes D3
Sleeping
2Dubeau Hostel B4
3Grand Canyon International Hostel C4
4Hotel Monte Vista C3
5Inn at 410 C1
6Weatherford Hotel C3
Eating
7Beaver Street Brewery B4
8Brix D1
9Café Ole C4
10Criollo Latin Kitchen C3
11Diablo Burger C2
12Fratelli Pizza B3
La Bellavia (see 13)
13Macy's B4
14MartAnne's Burrito Palace C3
15Mountain Oasis C3
16Pato Thai Cuisine C3
Drinking
Charly's Pub & Grill (see 6)
17Cuvee 928 C3
18Late for the Train C3
Monte Vista Cocktail Lounge (see 4)
19Pay 'n Take C3
Shopping
20Peace Surplus B3
For an inside track on the local mountain-biking scene, check out the super-friendly gearheads at Absolute Bikes ( 928-779-5969; www.absolutebikes.net; 202 E Rte 66; bike rentals per day from $40; 9am-7pm Mon-Fri, 10am-6pm Sat, 10am-4pm Sun). Though Flagstaff is blessed with several excellent bike shops, this is the only one that offers rentals.
###### Other Activities
If you can't guess by glancing around at the townsfolk, Flagstaff is full of active citizens. So there's no shortage of outdoor stores and places to buy or rent camping, cycling and skiing equipment. For ski rentals, swing by Peace Surplus (14 W Rte 66).
Arizona Snowbowl SKIING
( 928-779-1951; www.arizonasnowbowl.com; Hwy 180 & Snowbowl Rd; lift ticket adult/child $49/26; 9am-4pm) About 7 miles north of downtown, AZ Snowbowl is small but lofty, with four lifts that service 30 ski runs between 9200ft and 11,500ft.
Flagstaff Nordic Center SKIING
( 928-220-0550; www.flagstaffnordiccenter.com; Mile Marker 232, Hwy 180; weekend/weekday from $16/10; 9am-4pm weather permitting) Fifteen miles north of Flagstaff, the Nordic Center offers 30 groomed trails for cross-country skiing, as well as lessons, rentals and food. Past the Nordic Center off Hwy 180 you'll find plenty of USFS cross-country skiing pullouts, where you can park and ski for free.
Northern Arizona Trail Rides HORSEBACK RIDING
( 928-225-1538; www.northernarizonaridingstables.com; 9215 Old Munds Hwy; 1/1½/2hr rides $35/55/75) On your way to the Grand Canyon but have an extra day in Flagstaff? Try this friendly company for a short ride. Reservations are helpful, but they may be able to fit you in last minute – call 'em and see!
#### Sleeping
Dozens of nondescript, independent motels,with rates ranging from $30 to $50, line Old Route 66 and the railroad tracks east of downtown (exit 198 off I-40). Check the room before you pay – some are much worse than others. For the money, you're far better off at one of the hostels or historic hotels downtown.
Chain motels and hotels line Milton Rd, Beulah Blvd and Forest Meadows St, clustering around exit 198 off I-40.
##### CAMPING
Free dispersed camping is permitted in the national forest surrounding Flagstaff. Also check out Click here for information about USFS campgrounds in Oak Creek Canyon, 15 to 30 miles south of town.
Woody Mountain Campground CAMPGROUND
( 928-774-7727, 800-732-7986; www.woodymountaincampground.com; 2727 W Rte 66; tent/RV sites $20/$30; Mar-Oct; ) Has 146 sites, playground and coin laundry; off I-40 at exit 191.
Flagstaff KOA CAMPGROUND
( 928-526-9926, 800-562-3524; www.flagstaffkoa.com; 5803 N Hwy 89; tent sites $26-33, RV sites $33-44; year-round; ) This big campground lies a mile north of I-40 off exit 201, 5 miles northeast of downtown. A path leads from the campground to trails at Mt Elden.
##### LODGING
Inn at 410 B&B $$-$$$
( 928-774-0088; www.inn410.com; 410 N Leroux St; r $125-200; ) This elegant and fully renovated 1894 house offers nine spacious, beautifully decorated and themed bedrooms, each with a refrigerator and private bathroom. Many rooms have four-poster beds and views of the garden or the San Francisco Peaks. A short stroll from downtown, the inn has a shady garden with fruit trees and a cozy dining room, where the full gourmet breakfast and afternoon snacks are served.
England House B&B $$
( 928-214-7350; www.englandhousebandb.com; 614 W Santa Fe Ave; r $129-199; ) This Flagstaff B&B has a distinctive stone exterior made of local Moenkopi and Coconino sandstones. Even more elegant is the meticulously designed interior, from the original stamped-tin ceilings to the carefully curated antique French furniture. Gourmet meals are healthy and delicious.
Starlight Pines B&B $$
( 928-527-1912; www.starlightpinesbb.com; 3380 E Lockett Rd; r $135-189; ) Starlight Pines has four spacious rooms in a Victorian-style house, each decorated with Tiffany-style lamps, antique clawfoot tubs, Stickley chairs and other lovely touches. Your hosts, Michael and Richard, are as welcoming and warm as the house itself and are happy to give travel advice on the canyon and local attractions.
Comfi Cottages BUNGALOW $$
( 928-774-0731; www.comficottages.com; cottages$140-285; ) These bungalows, which are spread out in residential areas around town, are all less than a mile from the historic district. Most were built in the 1920s and '30s and have a homey feel to them, with wood floors, Craftsman-style kitchens and little lawns. Cabinets are filled with breakfast foods, and each cottage includes a TV, VCR, telephone, bicycles, tennis rackets, a BBQ grill, a picnic table and picnic baskets.
Arizona Mountain Inn CABIN $$-$$$
( 928-774-8959; www.arizonamountaininn.com;4200 Lake Mary Rd; cabins $130-230; ) With cute cabins tucked here and there in a peaceful, sun-dappled pine grove, this place brings to mind a magical village in a book about hobbits and wood nymphs. Hobbits aside, the sturdy but stylish cabins here come with porches, kitchens, grills and wood-burning fireplaces. They don't have TVs or wi-fi. There are three B&B-style rooms inside the adjacent inn, and guests there enjoy an extended continental breakfast. Dogs OK for a small fee.
Grand Canyon International Hostel HOSTEL $
( 928-779-9421; www.grandcanyonhostel.com; 19½ S San Francisco St; dm $18-20, r with shared bath $36-43, both incl breakfast; ) Housed in a historic building with hardwood floors and Southwestern decor, this bright, homey hostel offers private rooms or dorms with a four-person maximum. It has a slightly more mellow feel than the DuBeau, which is owned by the same proprietors. The kitchens are spotless, and there's a TV room with a video library.
DuBeau Hostel HOSTEL $
( 928-774-6731; www.grandcanyonhostel.com; 19 W Phoenix Ave; dm $21-24, r $46-66, both incl breakfast; ) This independent hostel offers the same friendly service and clean, well-run accommodations as the Grand Canyon International Hostel. There are also laundry facilities and bright kitchens. Convivial common areas include a nonsmoking lounge with a fireplace, as well as a jukebox, foosball and pool table – it's a bit livelier over here.
Weatherford Hotel HOTEL $-$$
( 928-779-1919; www.weatherfordhotel.com; 23 N Leroux St; r with shared bath $49-79, r with private bath $89-139; ) This historic three-story brick hotel offers 11 charmingly decorated rooms with a turn-of-the-20th-century feel. Three of the rooms are newly renovated and incorporate modern amenitiessuch as TVs, phones and air-conditioning. Since the Weatherford's three bars often feature live music, it can get noisy; if you need silence for sleeping, consider staying elsewhere. If you do stay, note that there's a 2am curfew.
Hotel Monte Vista HOTEL $-$$
( 928-779-6971; www.hotelmontevista.com; 100 N San Francisco St; d $65-130, ste $120-175; ) A huge, old-fashioned neon sign towers over this allegedly haunted 1926 hotel, hinting at what's inside: feather lampshades, vintage furniture, bold colors and eclectic decor. Rooms are named for the movie stars who slept in them, such as the Humphrey Bogart room, with dramatic black walls, yellow ceiling and gold-satin bedding. Several resident ghosts supposedly make regular appearances. Though lacking in high-end amenities, the Monte Vista's appeal comes from all of its glorious funkiness.
Little America Hotel MOTEL $$
( 928-779-7900; http://flagstaff.littleamerica.com; 2515 E Butler Ave; r $119-159, ste $269-349; ) When you reach the Sinclair truck stop, don't drive away thinking you have the wrong place. A little further down the side-driveway is a sprawling boutique-style motel with spacious rooms, immaculately decorated in French Provincial style and furnished with goose-down bedding, refrigerators and large bathrooms.
#### Eating
Criollo Latin Kitchen FUSION $$
( 928-774-0541; www.criollolatinkitchen.com; 16 N San Francisco St; mains $13-30; 11am-10pm Mon-Thu, 11am-11pm Fri, 9am-11pm Sat, 9am-2pm & 4-10pm Sun) This Latin fusion spot has a romantic, industrial setting for cozy cocktail dates and delectable late-night small plates, but the blue-corn blueberry pancakes make a strong argument for showing up for brunch on weekends. The food is sourced locally and sustainably whenever possible, and the wine list is divine.
Diablo Burger BURGERS $
(www.diabloburger.com; 120 N Leroux St; mains under $12; 11am-9pm Mon-Wed, 11am-10pm Thu-Sat) The beef maestros at this gourmet burger joint are so proud of their creations they sear the DB brand onto the English-muffin bun. The cheddar-topped Blake gives a nod to New Mexico with Hatch chile mayo and roasted green chiles. Diablo uses locally produced ingredients and includes a 'terroir-ist's manifesto' on the menu. The place is tiny, four tables inside and a few bar seats (they serve microbrews, wine and milkshakes), so come early. Cash only.
Beaver Street Brewery BREWPUB $$
(www.beaverstreetbrewery.com; 11 S Beaver St; lunch $8-10, dinner $10-12; 11am-11pm Sun-Thu, 11am-midnight Fri & Sat) This place packs them all in – families, river guides, ski bums and businesspeople. The menu is typical brewpub fare, with delicious pizzas, burgers and salads, and there's usually five handmade beers on tap, like its Railhead Red Ale or R&R Oatmeal Stout, plus some seasonal brews. Serious drinkers can walk next door to play pool at the 21-and-over Brews & Cues. Nightly dinner specials run between $13 and $16.
Macy's CAFE $
(www.macyscoffee.net; 14 S Beaver St; mains $3-7; 6am-8pm Mon-Wed, to 10pm Thu-Sun; ) The delicious house-roasted coffee at this Flagstaff institution has kept the city buzzing for over 30 years now. The vegetarian menu includes many vegan choices, along with traditional cafe grub like pastries, steamed eggs, bagels, yogurt and granola. A coin laundry is sandwiched between here and La Bellavia, so you can pop in a load and relax with your latte and book. Macy's is cash only.
Pato Thai Cuisine THAI $$
( 928-213-1825; www.patothai.com; 104 N San Francisco St; mains $7-14; 11am-9:30pm Mon-Sat, noon-8:30pm Sun) Pato Thai welcomes guests into a warmly-hued dining room redolent with galangal, Thai basil and lemongrass. The attractive environs are matched by well-executed, authentic Thai cuisine with a few Chinese dishes thrown in for good measure. The spiciness level is adjusted to your taste (err on the mild side).
Fratelli Pizza PIZZERIA $$
(www.fratellipizza.net; 119 W Phoenix;mains $10-20, slices $2.50; 10:30am-9pm Sun-Thu, to midnight Fri & Sat) Consistently voted Flagstaff's best pizza joint, Fratelli still pulls them in with its handmade, stone oven-baked pizza. Sauce choices include red, BBQ, pesto and white, and toppings range from standard pepperoni to grilled chicken, walnuts, artichoke hearts and cucumber.
MartAnne's Burrito Palace MEXICAN $
(10 N San Francisco St; mains $7-10; 7:30am-2pm Mon-Fri, 8:30am-1pm Sun) For those about to diet, we salute you. For those about to dig into a _fratelliquile_ , a pork-and-scrambled-eggs burrito smothered in green chile, green onions and cheese, we embrace you and call you friend. For we, too, understand the power of its goodness. MartAnne's, a snug hole-in-the-wall with sassy Day of the Dead decor, checkered floors and bright coffee mugs, is locally beloved. Cash only.
La Bellavia BREAKFAST $
(18 S Beaver St; mains $4-9; 6:30am-2pm) Be prepared to wait in line at this popular, cash-only breakfast spot. The seven-grain French toast with bananas, apples or blueberries is excellent; or try one of their egg dishes, such as eggs sardo, with sautéed spinach and artichoke hearts. Lunch includes a grilled portobello-mushroom sandwich and a grilled salmon salad, as well as standard options like grilled cheese, burgers and a tuna melt.
Brix AMERICAN $$$
( 928-213-1021; www.brixflagstaff.com; 413 N San Francisco St; mains $23-34; 11am-2pm & 5-9pm Mon-Fri, 5-9pm Sat) Situated in a renovated brick carriage house, Brix brings a breath of fresh, unpretentious sophistication to Flagstaff's dining scene. The menu varies seasonally, usingto delicious advantage what is fresh and ripe, and sometimes organic, for classics like salade Niçoise and roasted rack of lamb. Reservations are highly recommended.
Café Olé MEXICAN $-$$
( 928-774-8272; 119 S San Francisco St; mains $6-12; 11am-3pm & 5-8pm Tue-Sat; ) Food at this bright and friendly family-run place veers towards New Mexican-style, featuring green and red chile sauce.
Mountain Oasis INTERNATIONAL $$
( 928-214-9270; 11 E Aspen; mains $9-19; 11am-9pm; ) Vegetarians and vegans will find a bunch of options on this internationally spiced menu. Tasty specialties include the TBLT (tempeh bacon, lettuce and tomato), and Thai veggies and tofu with peanut sauce and brown rice. Steak and chicken are also featured on the menu at this relaxed, plant-filled oasis.
For groceries, Bashas' ( 928-774-3882; www.bashas.com; 2700 S Woodlands Village Blvd; 5am-11pm) is a good local chain supermarket with a respectable selection of organic foods. Our favorite health-food market is New Frontiers Natural Marketplace ( 928-774-5747; 320 S Cambridge Lane; mains $4-10; 8am-9pm Mon-Sat, 8am-8pm Sun; ) good for cobbling together healthy picnics.
#### Drinking
Pay 'n Take BAR
(www.payntake.com; 12 W Aspen Ave; 7am-10pm Mon-Wed, 7am-1am Thu-Sat, 9am-10pm Sun; ) This kickback spot has a great bar where you can enjoy a beer or a coffee. Help yourself to whatever you'd like from the wall refrigerators, and take it to one of the small tables inside or on the back patio. You can even have pizza delivered or bring takeout. Free wi-fi.
Cuvee 928 WINE BAR
( 928-214-9463; www.cuvee928winebar.com; 6 W Aspen Ave, Suite 110; 11:30am-9pm Mon-Tue, to 10pm Wed-Sat) This wine bar on Heritage Square makes a pleasant venue for people-watching as well as wine tasting. It has a relaxed but upscale ambience, well-rounded menu and full bar.
Late for the Train COFFEE SHOP
(www.lateforthetrain.com; 107 N San Francisco St; mains $2-6; 6am-6pm Sun-Thu, 6am-9pm Fri & Sat; ) Beans are roasted in-house, so the coffee and espresso drinks are some of the best in town. But on those really frigid winter days, try the habanero hot cocoa.
#### Entertainment
Flagstaff hosts all sorts of festivals and music programs; call the visitor center or log on to its website for details. On summer weekends, people gather on blankets for fun evenings at Heritage Square. Live music starts at 6:30pm, followed at 9pm by a kid-friendly movie projected on an adjacent building.
Pick up free local rag _Flagstaff Live!_ or check out www.flaglive.com for current shows and happenings around town.
Charly's Pub & Grill LIVE MUSIC
( 928-779-1919; www.weatherfordhotel.com; 23 N Leroux St; 8am-10pm) This restaurant at the Weatherford Hotel has regular live music. Its fireplace and brick walls provide a cozy setting for the blues, jazz and folk played here. Head upstairs to stroll the wraparound verandah outside the popular third-floor Zane Grey Ballroom, which overlooks the historic district. Inside, check out the 1882 bar, fireplace and original Thomas Moran painting.
Monte Vista Cocktail Lounge MUSIC
( 928-779-6971; www.hotelmontevista.com; Hotel Monte Vista, 100 N San Francisco St; from 4pm) In the Hotel Monte Vista; this hopping lounge hosts DJs most nights, and on weekends welcomes diverse bands, from country to hip-hop to rock.
Museum Club BAR
( 928-526-9434; www.themuseumclub.com; 3404 E Rte 66; 11am-2am Mon-Sat, to 9pm Sun) Housed in a 1931 taxidermy museum (hence its nickname, 'the zoo'), this log cabin-style club has been a roadhouse since 1936. Today, its Route 66 vibe, countrymusic and spacious wooden dance floor attract a lively crowd.
#### Information
Coconino National Forest Supervisor's Office ( 928-527-3600; www.fs.fed.us/r3/coconino; 1824 S Thompson St; 8am-4:30pm Mon-Fri) For information on hiking, biking and camping in the surrounding national forest.
Flagstaff Medical Center ( 928-779-3366; www.flagstaffmedicalcenter.com; 1200 N Beaver St; emergency 24hr)
Police station ( 928-779-3646; 911 E Sawmill Rd; emergency 24hr)
Post office ( 928-714-9302; 104 N Agassiz St; 9am-5pm Mon-Fri, to 1pm Sat)
USFS Flagstaff Ranger Station ( 928-526-0866; 5075 N Hwy 89; 8am-4:30pm Mon-Fri) Provides information on the Mt Elden, Humphreys Peak and O'Leary Peak areas north of Flagstaff.
Visitor center ( 928-774-9541, 800-379-0065; www.flagstaffarizona.org; 1 E Rte 66; 8am-5pm Mon-Sat, 9am-4pm Sun) Inside the Amtrak station, the visitor center has a great Flagstaff Discovery map and tons of information on things to do.
#### Getting There & Away
Flagstaff Pulliam Airport is 4 miles south of town off I-17. US Airways ( 800-428-4322; www.usairways.com) offers several daily flights from Phoenix Sky Harbor International Airport. Greyhound ( 928-774-4573, 800-231-2222; www.greyhound.com; 399 S Malpais Ln) stops in Flagstaffen route to/from Albuquerque, Las Vegas, Los Angeles and Phoenix. Arizona Shuttle ( 928-226-8060, 877-226-8060; www.arizonashuttle.com) has shuttles that run to the park, Williams and Phoenix Sky Harbor Airport.
Operated by Amtrak ( 928-774-8679, 800-872-7245; www.amtrak.com; 1 E Rte 66; 3am-10:45pm), the Southwest Chief stops at Flagstaff on its daily run between Chicago and Los Angeles.
#### Getting Around
Mountain Line Transit ( 928-779-6624; www.mountainline.az.gov; adult/child $1.25/0.60) services six fixed bus routes daily; pick up a user-friendly map at the visitor center. Those with disabilities can use the company's on-call VanGo service.
If you need a taxi, call A Friendly Cab ( 928-774-4444) or Sun Taxi ( 928-779-1111). Several major car-rental agencies operate from the airport and downtown; see Click here.
### Around Flagstaff
##### CAMERON
A tiny, windswept community 32 miles east of the park's East Entrance and 54 miles north of Flagstaff, Cameron sits on the western edge of the Navajo Reservation. There's not much to it; in fact, the town basically comprises just the Cameron Trading Post & Motel ( 928-679-2231; www.camerontradingpost.com; RV sites $15, r $99-109, ste $149-179; ). In the early 1900s Hopis and Navajos came to the trading post to barter wool, blankets and livestock for flour, sugar and other goods. Today visitors can browse a large selection of quality Native American crafts, including Navajo rugs, basketry, jewelry and pottery, and plenty of kitschy knickknacks.
Spacious rooms, many with balconies, feature hand-carved furniture and a Southwestern motif. RV sites offer hookups, and you can dine at Cameron Trading Post Dining Room ( 928-679-2231; mains $9-23; 6am-10pm), a good place to try the Navajo taco (fried dough with whole beans, ground beef, chile and cheese).
##### SUNSET CRATER VOLCANO NATIONAL MONUMENT
Covered by a single $5 entrance fee (valid for seven days), both Sunset Crater Volcano and Wupatki National Monument lie along Park Loop Rd 545, a well-marked 36-mile loop that heads east off Hwy 89 about 12 miles north of Flagstaff, then rejoins the highway 26 miles north of Flagstaff.
In AD 1064 a volcano erupted on this spot, spewing ash over 800 sq miles, spawning the Kana-A lava flow and leaving behind 8029ft Sunset Crater. The eruption forced farmers to vacate lands they had cultivated for 400 years; subsequent eruptions continued for more than 200 years. The visitor center ( 928-526-0502; www.nps.gov/sucr; admission $5; visitor center 8am-5pm May-Oct, 9am-5pm Nov-Apr, monument sunrise-sunset) houses a seismograph and other exhibits pertaining to volcanology, while viewpoints and a 1-mile interpretive trail through the Bonito lava flow (formed c 1180) grant visitors a firsthand look at volcanic features; a shorter 0.3-mile loop is wheelchair accessible. You can also climb Lenox Crater (7024ft), a 1-mile round-trip that climbs 300ft. More ambitious hikers and mountain-bikers can ascend O'Leary Peak (8965ft; 8 miles round-trip), the only way to peer down into Sunset Crater (aside from scenic flights).
Across from the visitor center, the USFS-run Bonito Campground ( 928-526-0866; tent & RV sites $18; May–mid-Oct) provides running water and restrooms but no showers or hookups.
##### WUPATKI NATIONAL MONUMENT
The first eruptions here enriched the surrounding soil, and ancestors of today's Hopi, Zuni and Navajo people returned to farm the land in the early 1100s. By 1180 thousands were living here in advanced multistory buildings, but by 1250 their pueblos stood abandoned. About 2700 of these structures lie within Wupatki National Monument ( 928-679-2365; www.nps.gov/wupa; admission $5; 9am-5pm), though only a few are open to the public. A short self-guided tour of the largest dwelling, Wupatki Pueblo, begins behind the visitor center. Lamaki, Citadel and Nalakihu Pueblos sit within a half-mile of the loop road just north of the visitor center, and a 2.5-mile road veers west from the center to Wukoki Pueblo, the best preserved of the buildings. In April and October rangers lead visitors on a 16-mile round-trip weekend backpacking tour ($50; supply your own food and gear) of Crack-in-Rock Pueblo and nearby petroglyphs. Chosen by lottery, only 13 people may join each tour; apply two months in advance via the website or in writing.
##### WALNUT CANYON NATIONAL MONUMENT
The Sinagua cliff dwellings at Walnut Canyon ( 928-526-3367; www.nps.gov/waca; admission $5, valid for 7 days; 8am-5pm May-Oct, 9am-5pm Nov-Apr) are set in the nearly vertical walls of a small limestone butte amid this forested canyon. The mile-long Island Trail steeply descends 185ft (more than 200 stairs), passing 25 rooms built under the natural overhangs of the curvaceous butte. A shorter, wheelchair-accessible Rim Trail affords several views of the cliff dwelling from across the canyon. Even if you're not all that interested in the mysterious Sinagua people, whose origins are unknown and whose site abandonments are still not understood today, Walnut Canyon itself is a beautiful place to visit, not so far from Flagstaff.
## GRAND CANYON REGION
No matter how much you read about the Grand Canyon or how many photographs you've seen, nothing really prepares you for the sight of it. One of the world's seven natural wonders, it's so startlingly familiar and iconic you can't take your eyes off it. The canyon's immensity, the sheer intensity of light and shadow at sunrise or sunset, even its very age, scream for superlatives.
At about two billion years old – half of Earth's total life span – the layer of Vishnu Schist at the bottom of the canyon is some of the oldest exposed rock on the planet. And the means by which it was exposed is of course the living, mighty Colorado River, which continues to carve its way 277 miles through the canyon as it has for the past six million years.
The three rims of the Grand Canyon offer quite different experiences and, as they lie hundreds of miles and hours of driving apart, they're rarely visited on the same trip. Summer is when most of the visitors arrive (4.38 million in 2010), and 90% of them only visit the South Rim, which offers easy-access viewpoints, historic buildings, Native American ruins and excellent infrastructure.
If it's solitude you seek, make a beeline for the remote North Rim (Click here). Though it has fewer and less-dramatic viewpoints, its charms are no less abundant: at 8200ft elevation (1000ft higher than the South Rim), its cooler temperatures support wildflower meadows and tall, thick stands of aspen and spruce.
Run by the Hualapai Nation and not part of Grand Canyon National Park, Grand Canyon West (Click here) is famous for its Skywalk, the controversial glass bridge jutting out over the rim that debuted in 2007. Critics consider the Skywalk sacrilege and a harbinger of unwise development on the fragile West Rim, but most agree that its construction will be a much needed financial shot in the arm for the casino-less Hualapai Nation to keep their tribe afloat.
### Grand Canyon National Park – South Rim
If you don't mind bumping elbows with other travelers, you'll be fine on the South Rim. This is particularly true in summer when camera-toting day-trippers converge en masse, clogging its roads and easiest trails. Why is this rim so popular? Easy access is the most obvious reason: it's a mere 60 miles north of the I-40. Abundant infrastructure is another. This is where you'll find an entire village worth of lodging, restaurants, bookstores, libraries, a supermarket and a deli. Shuttles ply two scenic drives, and the flat and paved Rim Trail allows the mobility-impaired and stroller-pushing parents to take in the dramatic, sweeping canyon views.
If you want to venture into the inner gorge you'll have several trails to choose from – or you can just let a mule do the walking. Several museums and historic stone buildings illuminate the park's human history, and rangers lead a host of daily programs on subjects from geology to resurgent condors.
Though the accessibility of the South Rim means sharing your experience with others, there are many ways to commune with the canyon and its wildlife, and enjoy its sublime beauty, one on one. Escaping the crowds can be as easy as taking a day hike below the rim or merely tramping a hundred yards away from a scenic overlook.
Most visitors arrive via the South Entrance, 80 miles northwest of Flagstaff on Hwy 64/180. Avoid summer wait times of 30 minutes or more by prepaying your park ticket at the National Geographic Visitor Center in Tusayan (Click here), which allows you to cruise smugly through in a special lane. Or arrive at the East Entrance instead. In summer, if you've bought your ticket or have a park pass, you can now hop on the park's Tusayan shuttle at the IMAX Theater in Tusayan and disembark at the Grand Canyon Visitor Center.
A few miles north of the South Entrance, Grand Canyon Village (or simply the Village) is the primary hub of activity. Here you'll find lodges, restaurants, two of thethree developed campgrounds, backcountry office, visitor center, medical clinic, bank, grocery store, shuttles and other services. Coin-operated showers and laundry facilities are located next to Mather Campground.
West of the Village, Hermit Rd follows the rim for 8 miles, ending at Hermit's Rest. Seven pullouts along the way offer spectacular views; from those at Mohave and Hopi Points you can spot three Colorado River rapids. Interpretive signs explain the canyon's features and geology. From March to November the road is closed to private vehicles and accessible only by tour or free shuttle bus.
In the opposite direction, Desert View Dr meanders 25 miles to the East Entrance on Hwy 64, passing some of the park's finest viewpoints, picnic areas, the Tusayan Ruin & Museum and the Watchtower. A campground, snack bar, small information center and general store are in Desert View, right by the entrance. Also here is the park's only gas station, which offers 24-hour pay-at-the-pump service from April to September. Gas stations in Tusayan are closer to the Village and open year-round.
###### Climate
On average, temperatures are 20°F (about 11°C) cooler on the South Rim than at the bottom of the Grand Canyon. In summer, expect highs in the 80s and lows around 50°F (highs in the 30s and lows around 10°C). Weather is cooler and more changeable in fall, and snow and freezing overnight temperatures are likely by November. January has average overnight lows in the teens (-10°C to -7°C) and daytime highs around 40°F (4°C) Winter weather can be beautifully clear, but be prepared for snowstorms that can cause havoc.
### GETTING STARTED
Park admission is $25 per vehicle, or $12 per person if arriving on foot or by bicycle; it's valid for seven days at both rims. Bus and train passengers may pay a lesser fee or have it included in the tour price. Upon entering, you'll be given a map and _The Guide,_ an incredibly useful newspaper thick with additional maps, the latest park news and information on ranger programs, hikes and park services. It also lists current opening hours of restaurants and businesses.
The Grand Canyon Visitor Center should be your first stop. Recently remodeled, it offers a number of new interpretive exhibits inside the main visitor center building and on the adjacent plaza. In the attached theater, watch the new film _Grand Canyon: Journey of Wonder_ , a 20-minute introduction to the park's geology, history and plant and animal life. Take note that you can no longer pull over on the side of the road after entering the park and dash to Mather Point. Traffic is directed away from the rim, passing several new parking lots on its way into Grand Canyon Village. Instead, walk on the new plaza out to Mather Point – where the views are still as amazing.
Likewise, head to Lonely Planet (www.lonelyplanet.com/usa/grand-canyon-national-park) for planning advice, author recommendations, traveler reviews and insider tips.
The inner canyon is much drier, with about eight inches of rain annually, around half that of the South Rim. During summer, temperatures inside the canyon soar above 100°F (40°C) almost daily, often accompanied by strong hot winds. Even in midwinter, the mercury rarely drops to freezing, with average temperatures hovering between 37°F and 58°F (3°C and 14°C).
### GRAND CANYON SOUTH RIM IN...
#### One Day
Catch a predawn shuttle to see the sun come up at Yaki Point, then head back to the Village for coffee and pastries at the Deli at Marketplace. Swing by the Grand Canyon Visitor Center, stroll the Rim Trail from Mather Point to Yavapai Observation Station and the Trail of Time exhibit, then make a beeline to El Tovar Dining Room to beat the lunchtime crowds. In the afternoon, catch the shuttle to Hermit's Rest and hike about 10 minutes down the Hermit Trail to look for ancient fossil beds, then catch the sunset at Hopi Point.
#### Two Days
Follow the one-day itinerary, capping the day with dinner in the elegant Arizona Room and an overnight stay in the Village (book well ahead). The morning of day two, hike into the canyon on the South Kaibab Trail, stopping at Cedar Ridge for a picnic. Wrap up your Grand Canyon adventure with a drive east along Desert View Dr, stopping at viewpoints, the Tusayan Ruin & Museum and the Watchtower.
#### Sights
The Grand Canyon's natural splendor is of course the prime draw, but to enrich your trip it pays to visit the park's cultural and architectural sites. Some of the most important buildings were designed by noted architect Mary Jane Colter to complement the landscape and reflect the local culture. Unless otherwise noted, sights are in the Village and they are free.
Yavapai Geology Museum & Observation Station MUSEUM
( 8am-7pm) Views don't get much better than those unfolding behind the plate-glass windows of this little stone building at Yavapai Point, where handy panels identify and explain the variousformations before you. Another reason to swing by is the superb geology display that'll deepen your understanding of the canyon's multilayered geological palimpsest. From here, check out the new Trail of Time exhibit just west of the Rim Trail. This interpretative display traces the history of the canyon's formation, and every meter equals one million years of geologic history.
Kolb Studio GALLERY
( 8am-7pm) Photographers Ellsworth and Emery Kolb arrived at the Grand Canyon from Pennsylvania in 1902 and made a living photographing parties going down the Bright Angel Trail. Because there was not enough water on the rim to process the film, they had to run 4.5 miles down the trail to a spring at Indian Garden, develop the film and race back up in order to have the pictures ready when the party returned. Eventually, they built a small studio on the edge of the rim, which has since been expanded and now holds a small bookstore and an art gallery with changing exhibits.
Lookout Studio HISTORIC BUILDING
( 8am-sunset) Like Mary Colter's other canyon buildings, Lookout Studio was modeled after stone dwellings of the Southwest Pueblo Native Americans. Made of rough-cut Kaibab limestone, with a roof that mirrors the lines of the rim, the studio blends into its natural surroundings. Inside, you'll find a small souvenir shop and a tiny back porch that offers spectacular canyon views. There's also a stone stairway snaking below Lookout Studio towards another terrace, which is the site of the popular ranger-led Condor Talks.
Hopi House ARCHITECTURE
( 8am-8pm) A beautiful Colter-designed stone building, Hopi House has been offering high-quality Native Americanjewelry, basketwork, pottery and other craftssince its 1904 opening. The structure was built by the Hopi from native stone and wood, inspired by traditional dwellings on their reservation.
Tusayan Ruin & Museum MUSEUM
( 9am-5pm) Near the East Entrance, 22 miles east of the Village, you'll come across what's left of the nearly 900-year-old Ancestral Puebloan settlement of Tusayan. Only partially excavated to minimize erosion damage, it's less impressive than other such ruins in the Southwest but still interesting and worth a look. A small musuem displays pottery, jewelry and 4000-year-old twig animal figurines.
Watchtower ARCHITECTURE
Scramble to the top of Colter's stone tower at Desert View and pat yourself on the back for having reached the highest spot on the rim (7522ft). Unparalleled views take in not only the canyon and the Colorado River but also the San Francisco Peaks, the Navajo Reservation and the Painted Desert. The Hopi Room has festive murals depicting the snake legend, a Hopi wedding and other scenes.
#### Activities
###### Hiking
To truly experience the majesty of the canyon, hit the trail. It may look daunting, but there are options for all levels of skill and fitness. Though summer is the most popular season for day hikes – despite oppressively hot 100°F (40°C) plus temperatures below the rim – experienced canyon hikers know that it's much more pleasant to hike in the spring and fall, when there are also significantly fewer visitors.
The easiest and most popular is the Rim Trail, which is quite literally a walk in the park. It connects a series of scenic points and historical sights over 13 miles from Pipe Creek Vista to Hermit's Rest. The section of the Rim Trail between Pipe Creek Vista and Maricopa Point is paved, and mostly wheelchair accessible. It's possible to catch a shuttle bus to a viewpoint, walk a stretch, then catch the next shuttle back or onward. The 3 miles or so winding through the Village are usually packed, but crowds thin out further west.
Heading down into the canyon means negotiating supersteep switchbacks. The most popular is the Bright Angel Trail, which is wide, well graded and easy to follow. Starting in the Village, right by Kolb Studio, it's a heavily trafficked route that's equally attractive to first-time canyon hikers,seasoned pros and mule trains. But the din doesn't lessen the sheer beauty. The steep and scenic 7.8-mile descent to the Colorado River is punctuated with four logical turnaround spots, including two resthouses offering shade and water. The first resthouse is about 1.5 miles down the trail, the second is 3 miles. Day hikers and first-timers should strongly consider turning around at one of them or otherwise hitting the trail at dawn to safely make the longer hikes to Indian Garden or Plateau Point (9.2 and 12.2 miles round-trip, respectively). Hiking to the Colorado River for the day is not an option.
One of the park's prettiest trails, the South Kaibab Trail combines stunning scenery and adventurous hiking with everystep. The only corridor trail to follow a ridgeline, the red-dirt path allows for unobstructed 360-degree views. It's steep, rough and wholly exposed, which is why rangersdiscourage all but the shortest of day hikes during summer. A good place to turn around is Cedar Ridge, reached after about an hour. It's a dazzling spot, particularly at sunrise, when the deep ruddy umbers and reds of each canyon fold seem to glow from within. During the rest of the year, the trek to Skeleton Point, 1.5 miles beyond CedarRidge, makes for a fine hike – though the climb back up is a beast in any season. The South Kaibab Trailhead is 4.5 miles east of the Village on Yaki Point Rd and can only be reached by shuttle or the Hikers' Express leaving from Bright Angel Lodge around dawn (stopping at the Backcountry Information Center).
One of the steepest trails in the park, dropping 1200ft in the first 0.75 miles, Grandview Trail is also one of the finest and most popular hikes. The payoff is an up-close look at one of the inner canyon's sagebrush-tufted mesas and a spectacular sense of solitude. While rangers don't recommend the trek to Horseshoe Mesa (3 miles, four to six hours) in summer (there's no water on the very exposed trail, and the climb out is a doozy), it's not overly long and certainly doable for strong hikers strapped with a hydration system and hiking early or late inthe day. For a shorter but still rewarding option, hike as far as Coconino Saddle. Though it's only 1.5 miles round-trip, it packs a quick and precipitous punch as you plunge 1600ft in less than a mile. With the exception of a few short level sections, the Grandview is a rugged, narrow and rocky trail. The trailhead is at Grandview Point, 12 miles east of the Village on Desert View Dr.
The wild Hermit Trail descends into pretty Hermit Canyon via a cool spring. It's a rocky trip down, but if you set out early and take it slow, it offers a wonderfully serene hike and glimpses into secluded corners. Day hikers should steer towards Santa Maria Spring (5 miles round-trip) or to Dripping Springs via a spur trail (6.5 miles round-trip). The upper section of the Hermit is well shaded in the morning, making it a cool option in summer. The trailhead is at the end of its namesake road, 8 miles west of the Village. Although the road is only accessible via shuttle bus during the summer peak season, overnight backpackers are permitted to park near the trailhead year-round.
Grand Canyon Village
Top Sights
Hopi House B2
Kolb Studio A2
Yavapai Geology Museum & Observation Station 0 E1
Sights
1Lookout Studio A2
2Trail of Time D1
Activities, Courses & Tours
3Bright Angel Bicycles E2
4Bright Angel Trailhead A2
Sleeping
5Bright Angel Lodge & Cabins B2
6El Tovar B2
7Kachina Lodge B2
8Maswik Lodge A3
9Mather Campground E4
10Thunderbird Lodge B2
11Trailer Village E3
12Yavapai Lodge D3
Eating
Arizona Room (see 5)
Bright Angel Fountain (see 5)
Bright Angel Restaurant (see 5)
Canyon Café (see 12)
El Tovar Dining Room (see 6)
Maswik Cafeteria (see 8)
Shopping
13Books & More Store F2
Canyon View Deli (see 14)
Canyon Village Marketplace (see 14)
14Market Plaza D3
###### Biking
Cyclists have limited options inside the park, as bicycles are only allowed on paved roads and the Greenway Trail. The multi-use Greenway Trail, open to cyclists as well as pedestrians and wheelchairs, stretches about 13 miles from Hermit's Rest all the way to the South Kaibab Trailhead.
Hermit Rd offers a scenic ride west to Hermit's Rest, about 16 miles round-trip from the village. Shuttles ply this road every10 to 15 minutes between March and November (the rest of the year, traffic is minimal). They are not permitted to pass cyclists, so for the first 4 miles you'll have to pull over each time one drives by. However, starting from the Abyss, a completed section of the Greenway Trail diverges from the road and continues separately all the way to Hermit's Rest.
Alternatively, you could ride out to the East Entrance along Desert View Dr, a 50-mile round-trip from the village. The route is largely shuttle-free but sees a lot of car traffic in summer. Just off Desert View Dr, the 1-mile dirt road to Shoshone Point is an easy, nearly level ride that ends at this secluded panoramic vista, one of the few places to escape South Rim crowds.
Bright Angel Bicycles BICYCLE RENTAL
( 928-814-8704; www.bikegrandcanyon.com; full-day adult/child $35/25; 8am-6pm May-Sep, 10am-4:30pm Mar-Apr & Oct-Nov, weather permitting) Renting 'comfort cruiser' bikes on the South Rim, the friendly folks here custom-fit each bike to the individual. Rates include helmet and bicycle-lock rental; child trailers also available.
###### Mule Rides
Due to erosion concerns, the National Park Service (NPS) has limited inner-canyon mule rides to those traveling all the way to Phantom Ranch. Rather than going below the rim, three-hour day trips ($119) now take riders along the rim, through the ponderosa and piñon-and-juniper forest to the Abyss overlook. Riders dismount to enjoy the view and a snack before heading back to the village.
### TOP FIVE OVERLOOKS
Mohave Point For a look at the river and three rapids.
Hopi Point Catch huge sunset views.
Lipan Point Creeks, palisades, rapids and sunrises.
Desert View Climb to the top of the Watchtower and wave down at the river.
Yaki Point A favorite point to watch the sunrise warm the canyon's features.
Overnight trips (one/two people $482/850) and two-night trips (one/two people $701/1170) still follow the Bright Angel Trail to the river, travel east on the River Trail and cross the river on the Kaibab Suspension Bridge. Riders spend the night at Phantom Ranch. It's a 5½-hour, 10-mile trip to Phantom Ranch, but the return trip up the 8-mile South Kaibab Trail is an hour shorter. Overnight trips include dorm accommodations and all meals at Phantom.
Riders must be at least 4ft 7in tall, speak fluent English and weigh no more than 200lbs fully clothed. Personal backpacks, waist packs, purses or bags of any kind are not allowed on the mules. Anything that could possibly fall off and injuresomeone in the canyon below will be kept for you until you return. For complete regulations and more information, consult the Xanterra website below.
Mule trips are popular and fill up quickly; to book a trip more than 24 hours and up to 13 months in advance, call Xanterra ( 888-297-2757, 303-297-2757; www.grandcanyonlodges.com/mule-rides-716.html). If you arrive at the park and want to join a mule trip the following day, ask about availability at the transportation desk at Bright Angel Lodge (your chances are much better during the off season). If the trips are booked, join a waiting list, cross your fingers and show up at the lodge at 6:15am on the day of the trip and hope there's been a cancellation. Or make tracks to the other side of the canyon: mule rides on the North Rim (Click here) are usually available the day before the trip.
If you're not planning a mule trip, just watching the wranglers prepare the mules can be fun, particularly for young children. In summer stop by the mule corral at 8am; in winter they get going about an hour later.
###### White-Water Rafting
Rafting the Colorado – the King Kong of North American rivers – is an epic, adrenaline-pumping adventure. The biggest single drop at Lava Falls plummets 37stomach-churning feet in just 300yd. But roller-coaster thrills are only the beginning. The canyon's true grandeur is best grasped looking up from the river, not down from the rim. Its human history comes alive in ruins, wrecks and rock art. You can hike to mystical grottos and waterfalls, explore ethereally lit slot canyons and view wildlife in its native habitat.
Commercial trips vary in length from three days to three weeks and in the type of watercraft used. Motorized pontoon rafts are the most stable and generally the least scary option. The huge inflatable boats seat eight to 16 passengers and go twice as fast as oar or paddle boats. Oar boats are more common, and more exciting. Rowed by an experienced guide, they provide good stability but feel more like a raft.
A fun and intimate alternative is to float in a river dory, a small, elegant hard-shelled rowboat for four passengers that's a lot speedier than a raft. Still, if it's thrills you're after, book a trip in an inflatable raft, which has you, your raft-rat shipmates and a guide paddling all at once.
At night you'll be camping under stars on sandy beaches (gear provided). It's not as primitive as it sounds – guides are legendary not only for their white-water acumen but also for their culinary skills.
It takes about two or three weeks to run the entire 279 miles of river through the canyon. Shorter sections of around 100 miles take four to nine days. Prices listed here are just a sampling of what each company offers.
Arizona Raft Adventures RAFTING
( 928-786-7238, 800-786-7238; www.azraft.com;6-day Upper Canyon hybrid trips/paddle trips $1940/2040, 10-day Full Canyon motor trips $2830) This multigenerational family-run outfit offers paddle, oar, hybrid (with opportunities for both paddling and floating) and motor trips.
Arizona River Runners RAFTING
( 602-867-4866, 800-477-7238; www.raftarizona.com; 6-day Upper Canyon oar trips $1795, 12-day Full Canyon motor trips $2695) Have been at their game since 1970, offering oar-powered and motorized trips.
SOARS RAFTING
( 209-736-4677, 800-346-6277; www.oars.com; 6-day Upper Canyon oar trips $2608, 15-day Full Canyon dory trips $5010) One of the best outfitters out there, OARS offers oar, paddle and dory trips, and offers the option of carbon-offsetting your trip.
Wilderness River Adventures RAFTING
( 928-645-3296, 800-992-8022; www.riveradventures.com; 6-day Full Canyon motor trips $2135, 12-day Full Canyon oar trips $3520) Also offers hybrid trips that give rafters the chance to paddle or float as on an oar-powered trip.
###### Ranger-Led Activities
Rangers are fonts of information, which they happily share in free programs. Their talks cover everything from fossils to birds to Native Americans, while their hikes deepen your understanding of the canyon's geologyand history. _The Guide_ newspaper and the displays outside Grand Canyon Visitor Center list the latest offerings.
#### Tours
###### Coach Tours
First-time visitors can keep the overwhelm factor at bay by joining a narrated bus tour. Tours travel west to Hermit's Rest (two hours, $26) and east to Desert View (about four hours, $45; combination tour $58), stopping at key viewpoints. Sunrise and sunset tours are also available. Stop by the transportation desk at any lodge, or ask the El Tovar concierge for the latest schedule and tickets. Kids under 16 ride for free.
### BACKCOUNTRY ACCESS
Most overnight backpacking trips go from the South Rim to the river and then return, because South Rim-to-North Rim trips involve a tedious four- to five-hour shuttle ride. Most people spend two nights below the rim – either two nights at Bright Angel Campground or Indian Garden Campground, or one night at each. If you do arrange a shuttle you could add a night at Cottonwood Campground on the way up to the North Rim. If your time is limited, a one-night trip is also rewarding. If you prefer a bed to a sleeping bag, make reservations at the canyon-bottom Phantom Ranch (Click here) at least a year in advance.
Overnight hikes require a backcountry permit. The park issued 13,616 backcountry permits in 2009, but demand far exceeds available slots. If you're caught camping in the backcountry without a permit, expect a hefty fine and possible court appearance.
Permits cost $10, plus an additional $5 per person per night, and are required for all backcountry use unless you've got a reservation at Phantom Ranch. The fee is nonrefundable and payable by check or credit card. Reservations are accepted in person or by mail or fax ( 928-638-2125) beginning the first day of the month, four months prior to the planned trip (ie on May 1, request a date in September). Permits faxed on the first day of the month before 5pm are considered first when assigning permits, though not necessarily in the order received (they are randomly assigned a computer-generated number). Be sure to list your second and third choices on the form to improve your odds of snagging a spot. Backcountry rangers read all notes on the forms and will try to meet your order of preference. Faxing your request is the best way to go. You cannot email your permit request.
For detailed instructions and to download the permit request form, go to the park's website (www.nps.gov/grca/planyourvisit/backcountry.htm) and click on the Backcountry Permit Quicklink. Alternatively, contact the Backcountry Information Center ( 928-638-7875; fax 928-638-2125; 8am-noon & 1-5pm Mon-Fri) and ask them to mail you the form. If you arrive without a permit, hightail it to the center, near Maswik Lodge, and get on the waiting list. You must show up daily at 8am to remain on the list, but you'll likely hear your name called in one to four days, depending on the season and itinerary. For safety reasons, you will not be granted a permit for the day you show up at the office; the earliest would be for the next day.
###### Flyovers
At press time, more than 300 flyovers of the Grand Canyon were departing daily from Tusayan and Las Vegas. However, the NPS and the Federal Aviation Administration were inviting public comments on a draft environmental impact report in June 2011, which may have implications for the number or existence of scenic flyovers at Grand Canyon National Park. Flights have already been restricted in number, altitude and routes to reduce noise pollution affecting the experience of other visitors and wildlife.
Contact the following companies for specific rates, as each offers several options.
Grand Canyon Airlines ( 866-235-9422, 928-638-2359; www.grandcanyonairlines.com)
Grand Canyon Helicopters ( 928-638-2764, 702-835-8477; www.grandcanyonhelicoptersaz.com)
Maverick Helicopters ( 888-261-4414; www.maverickhelicopter.com)
Papillon Grand Canyon Helicopters ( 888-635-7272, 702-736-7243; www.papillon.com)
Scenic Airlines ( 866-235-9422; www.scenic.com)
#### Sleeping
Pitch a tent in one of three campgrounds or enjoy a solid roof in one of the six hotels ranging from no-frill motels to luxurious lodges. Xanterra ( 303-297-2757, 888-297-2757; www.grandcanyonlodges.com) operates all park lodges, as well as Trailer Village. Reservations are accepted up to 13 months in advance and should be made as early as possible. For same-day bookings call the South Rim Switchboard ( 928-638-2631). Summer rates we've quoted below usually drop by 10% or 20% in winter. Children under 16 stay free, but cribs and cots are $10 per day.
If everything in the park is booked up, consider Tusayan (7 miles south; Click here), Valle (30 miles south; Click here) or Williams (60 miles south; Click here). Campers can pitch a tent for free in the surrounding Kaibab National Forest (Click hereAntelope Canyon).
###### Camping
The National Park Service ( 877-444-6777, international 518-885-3639; www.recreation.gov)operates Mather and Desert View Campgrounds. Reservations for Mather are accepted up to six months in advance, up until the day before your arrival. From mid-November through February sites at Mather Campground are first-come, first-served.
Desert View Campground CAMPGROUND $
(campsites $12; May–mid-Oct) In a piñon-juniper forest near the East Entrance, this first-come, first-served campground is quieter than Mather Campground in the Village, with nicely spread-out sites that ensure a bit of privacy. The best time to secure a spot is midmorning, when people are breaking camp. Facilities include toiletsand drinking water, but no showers or hookups.
Mather Campground CAMPGROUND $
(www.recreation.gov; Grand Canyon Village; campsites $18; year-round) Sites are shaded and fairly well dispersed, and the flat ground offers a comfy platform for your tent. You'll find pay showers, laundry facilities, drinking water, toilets, grills and a small general store; a full grocery store is a short walk away. Reservations are accepted from March through mid-November; the rest of the year it's first-come, first-served. Walk or bike in for $6 sites. No hookups.
Trailer Village CAMPGROUND $
( 888-297-2757, same-day reservations 928-638-2631; www.xanterra.com; Grand Canyon Village; campsites $32; year-round) As the name implies, this is basically a trailer park with RVs lined up tightly at paved pull-through sites amid a rather barren, dry patch of ground. Check for spots with trees on the far north side. You'll find picnic tables and barbecue grills, but showers are a quarter-mile away at Mather Campground.
Stays at any of the three campgrounds below the rim require a backcountry overnight permit (see Click here). Indian Garden Campground has 15 sites and is 4.6 miles down the Bright Angel Trail, while Bright Angel Campground is on the canyon floor near Phantom Ranch, some 9.3 miles via the Bright Angel Trail. Both are ranger-staffed and have water and toilets. Cottonwood Campground is halfway up the North Kaibab Trail to the North Rim, about 16.6 miles from the South Rim; see Click here.
###### Lodges
With the exception of Phantom Ranch, which sits on the canyon floor, all of the lodges listed below are located in Grand Canyon Village. All lodges are booked through Xanterra ( 303-297-2757, 888-297-2757; www.grandcanyonlodges.com). Advance reservations are highly recommended. For same-day reservations or to reach any lodge, call the South Rim Switchboard ( 928-638-2631).
El Tovar LODGE $$-$$$
(d $178-273, ste $335-426; year-round; ) Yup, Albert Einstein slept here and so did Teddy Roosevelt, and despite a recent renovation, this rambling 1905 wooden lodge hasn't lost a lick of its genteel historic patina. Even if you're not checking into one of the 78 rooms, swing by the hotel for its replica Remington bronzes, stained glass and exposed beams or to admire the stunning canyon views from its wide porches, martini in hand. Standard rooms are on the small side, so those in need of elbow room should go for the deluxe.
Phantom Ranch CABIN $
(dm $43; year-round; ) It ain't luxury, but after a day on the trail, even a bunk is likely to feel heavenly. These are spread across cozy private cabins sleeping four to 10, and single-sex dorms outfitted for 10 people. Rates include bedding, soap, shampoo and towels, but meals are extra (breakfast/dinner from $21/27) and must be reserved when booking your bunk. You're free to bring your own food and stove. Snacks, limited supplies, beer and wine are also sold. Without a reservation, try showing up at the Bright Angel Lodge transportation desk before 6am and hope to snag a canceled bunk.
Bright Angel Lodge & Cabins LODGE $$
(d without/with private bath $81/92, cabins $113-178; year-round; ) This 1935 log-and-stone lodge on the ledge delivers historic charm by the bucketload and has the nicest rooms on the South Rim (except for those at El Tovar). Public spaces, though, are busy and less elegant. If you're economizing, get a basic double (no TV – just a bed, desk and sink) with shared bathrooms down the hall. Cabins are brighter, airier and have tasteful Western character; the most expensive have rim views.
Maswik Lodge LODGE $$
(d South/North $92/173, cabins $92; year-round; ) Maswik is comprised of 16 modern two-story buildings set in the woods; rooms are of the standard motel variety. Rooms at Maswik North feature private patios, air-con, cable TV, high ceilings and forest views, while those at Maswik South are smaller, with fewer amenities and more forgettable views. The cramped cabins are available only in the summer.
Kachina & Thunderbird Lodges LODGE $$
(d streetside/rimside $173/184; year-round; ) Beside the Rim Trail between El Tovar and Bright Angel, these institutional-looking lodges offer standard motel-style rooms with two queen beds, full bath and TV. It's worth spending up a little for the rimside rooms, some with partial canyon views.
### GRAND CANYON FOR CHILDREN
The Junior Ranger program for kids from four to 14 is popular. Pick up an activity book at the visitor center, fulfill the requirements and attend a ranger program – then get sworn in as a junior ranger and receive a certificate and badge.
Aspiring naturalists aged nine to 14 can borrow a Discovery Pack containing binoculars, a magnifying glass, field guides and other tools. Kids attend a 90-minute ranger-led program before heading off with their families to complete the activities in their field journal. Completion earns a Discovery Pack patch.
Active types can earn the Dynamic Earth patch by joining a ranger-led Adventure Hike, either down the Hermit Trail for close-ups of fossils or to Pima Point to learn about the canyon's geological mysteries.
In the Way Cool Stuff for Kids and Kids Rock! programs, which are geared to kids aged six to 12, rangers use hands-on activities to teach kids about ecology and wildlife. For example, the ranger builds a forest with the children, who pretend to be trees, grasses, bees and other plants and animals.
Little ones get in on the fun during Story Time Adventure held on the rim-facing porch of El Tovar.
Yavapai Lodge LODGE $$
(d West/East $114/163; Apr-Oct; ) Yavapai Lodge lies more than a mile from the traffic and chaos of the central village, but is still within walking distance of the grocery store, post office and bank in Market Plaza. The lodgings are stretched out amid a peaceful piñon and juniper forest, yet you can pull your car right up to your door. Rooms in Yavapai East are in six air-conditioned, two-story buildings, while rooms in Yavapai West are spread out in 10 single-story buildings without air-conditioning. These are basic, clean motel rooms with tubs, showers and TVs.
#### Eating & Drinking
Grand Canyon Village has all the eating options you need, whether it's picking up picnic parts at Canyon Village Marketplace, an après-hike ice cream cone at Bright Angel Fountain, or a sit-down celebratory dinner at El Tovar Dining Room. Hours listed here are for the summer and may vary in slower seasons.
All South Rim bars close at 11pm, and drinks are prohibited along the rim itself.
El Tovar Dining Room INTERNATIONAL $$-$$$
(El Tovar; 928-638-2631, ext 6432; mains $18-31; 6:30-11am, 11:30am-2pm & 5-10pm) The memorable surroundings feature dark-wood tables set with china and white linen, and huge picture windows with views of the rim and canyon beyond. The service is excellent, the menu creative, the portions big and the food very good. Breakfast options include fresh-squeezed orange juice, El Tovar's pancake trio (buttermilk, blue cornmeal and buckwheat pancakes with pine nut butter and prickly pear syrup) and cornmeal-encrusted trout with two eggs. Lunch and dinner menus are equally creative.
Reservations are required for dinner. To avoid lunchtime crowds, eat before the Grand Canyon Railway train arrives at 12:15pm. The adjacent cocktail lounge is busy for afternoon cocktails and after-dinner drinks.
Arizona Room AMERICAN $$-$$$
(Bright Angel Lodge; mains $8-28; 11:30am-3pm Mar-Oct & 4:30-10pm Mar-Dec) Antler chandeliers hang from the ceiling and picture windows overlook a small lawn, the rim walk and the canyon. Try to get on the waitlist when doors open at 4:30pm, because by 4:40pm you may have an hour's wait – reservations are not accepted. Mains include steak, chicken and fish dishes, while appetizers include such creative options as pulled pork quesadillas.
Phantom Ranch Canteen AMERICAN $$$
(Phantom Ranch; mains $27-42; 5am & 6.:30am breakfast seatings, 5pm & 6:30pm dinner seatings) On the canyon floor, Phantom Ranch offers family-style meals on a set menu: hearty stew, steaks and vegetarian chili, as well as hearty breakfasts and sack lunches for the trail. You must make meal reservations before your descent, ideally when you reserve your accommodations. The canteen is open to the public for cold lemonade and packaged snacks between 8am and 4pm, and for beer, wine and hot drinks from 8pm to 10pm.
Bright Angel Restaurant AMERICAN $$
(Bright Angel Lodge; mains $10-26; 6:30am-10pm; ) Menu offerings include burgers, fajitas, salads and pasta. Families with small children gravitate here so it can get loud, and the harried staff provide the most perfunctory service of the three waitstaffed restaurants on the South Rim. Reservations not accepted.
The dark, windowless bar off the hallway doesn't offer much in the way of character, but it's a cozy spot for a beer or espresso.
Canyon View Deli CAFETERIA $
( 928-631-2262; Market Plaza; mains $4-7; 7am-8pm) This counter in the village grocery store is the best place to find fresh-made sandwiches and premade salads. Breakfast burritos, doughnuts and coffee are available in the morning.
Maswik Cafeteria CAFETERIA $
(Maswik Lodge; mains $4-10; 6am-10pm) Though fairly predictable, the food encompasses a nice variety and isn't too greasy. The various food stations serve burgers, sandwiches, fried chicken, Mexican food and even Vietnamese _pho_. The adjoining Maswik Pizza Pub serves beer and shows sporting events on TV.
Canyon Café CAFETERIA $
(Yavapai Lodge; mains $4-10; 6am-10pm) At Yavapai Lodge, this cafe has the same sort of food and setup as at Maswik Cafeteria, and you can get boxed lunches to go. Hours vary seasonally.
Bright Angel Fountain FAST FOOD $
( 928-638-2631; Bright Angel Lodge; mains $2-5; 10am-8pm) On the rim at Bright Angel Lodge, this cafeteria-style fountain serves hot dogs, premade sandwiches, ice cream, fruit, juice and bottled water. Cash only.
Hermit's Rest Snack Bar FAST FOOD $
( 928-638-2351; Hermit's Rest; mains $2-5; 9am-5pm) This walk-up window outside Hermit's Rest is basically a human-powered vending machine, and is cash-only.
#### Shopping
Books & More BOOKS
( 8am-8pm Jun-Aug, vary rest of the year) Located across the plaza from the Grand Canyon Visitor Center, Books & More has an extensive collection of books about the canyon. You'll also find canyon prints and T-shirts.
Canyon Village Marketplace MARKET
( 928-631-2262; Market Plaza; 8am-8pm) The biggest source for supplies on either rim, this market offers everything you'd expect from your local grocery store, including a fair selection of organic items and over-the-counter medications. Prices and selection are better outside the park.
Desert View Marketplace MARKET
( 928-638-2393; Desert View; 9am-5pm) At the East Entrance, this general store sells simple groceries and souvenirs. There's also a snack bar nearby.
#### Information
Almost all services on the South Rim are in Grand Canyon Village, easily accessible via the blue Village Route shuttles. On the east side, Market Plaza includes the grocery/deli/outdoor shop Canyon Village Marketplace ( 928-631-2262; 8am-8pm), Chase Bank ( 928-638-2437; 9am-5pm Mon-Thu, 9am-6pm Fri) with a 24-hour ATM, and a post office ( 928-638-2512; 9am-4:30pm Mon-Fri, 11am-1pm Sat) where stamps are available via a vending machine from 5am to 10pm. The main visitor center is Grand Canyon Visitor Center ( 928-638-7644; 7:30am-6:30pm), just behind Mather Point.
Limited hours go into effect between October and March. If you have questions, NPS rangers and the people who staff the hotels, restaurants and services are typically helpful and friendly.
###### Internet Access
Grand Canyon Community Library ( 928-638-2718; per 50min $3; 10:30am-5pm Mon-Fri) Just behind the garage, this little brown building houses the community library and several terminals providing internet access; hours vary seasonally, so call ahead.
Park Headquarters Library ( 8am-noon & 1-4:30pm Mon-Thu & alternate Fri) At the back of the courtyard at Park Headquarters, the small library offers free internet access (when someone's staffing it).
###### Tourist Information
Backcountry Information Center ( fax 928-638-7875; 8am-noon & 1-5pm) Located near Maswik Lodge, this is the place to get waitlisted for a backcountry permit if you haven't reserved one ahead of time.
Bright Angel, Yavapai & Maswik Transportation Desks ( 928-638-2631, ext 6015; 8am-5pm) In the lobbies of Bright Angel, Yavapai and Maswik Lodges, these service desks can book bus tours and same- or next-day mule trips. They can also answer questions about horseback rides, scenic flights and smooth-water float trips. Bright Angel can arrange last-minute lodgings at Phantom Ranch, if available.
Desert View Information Center ( 928-638-7893; 9am-5pm) This staffed information center also offers books and maps.
El Tovar ( 8am-5pm) This hotel's helpful concierge can answer questions, arrange same- or next-day bus tours and sell stamps.
Grand Canyon Visitor Center ( 928-638-7644; 8am-5pm) Three hundred yards behind Mather Point, this is the main visitor center, encompassing the theater and a bookstore. Outside the visitor center, bulletin boards and kiosks display information on ranger programs, the weather, tours and hikes. Inside is a ranger-staffed information desk and a lecture hall, where rangers offer daily talks on a variety of subjects.
Tusayan Ruin & Museum ( 928-638-2305; 9am-5pm) Three miles west of Desert View, this museum features exhibits on the park's indigenous people and has a ranger-staffed information desk.
Verkamp's Visitor Center ( 8am-7pm) Next to Hopi House, also features a display about the building's history.
#### Getting Around
Though the park can seem overwhelming when you first arrive, it's actually quite easy to navigate, especially when you leave it to shuttle drivers. _The Guide_ contains a color-coded shuttle-route map in the centerfold.
###### Car
Note that from March through November, cars are not allowed on Hermit Rd, which heads west from the village to Hermit's Rest.
###### Shuttle
Free shuttle buses ply three routes along the South Rim. In the pre-dawn hours, shuttles run every half-hour or so and typically begin running about an hour before sunrise; check _The Guide_ for current sunrise and sunset information. From early morning until after sunset, buses run every 15 minutes.
The red Hermit's Rest Route runs west along Hermit Rd from March through November, during which time the road is closed to private vehicles.
The blue Village Route provides year-round transportation between the Grand Canyon Visitor Center, Yavapai Point, Market Plaza, the Backcountry Information Center, hotels, restaurants, campgrounds and parking lots.
The green Kaibab Trail Route provides service to and from the Yavapai Geology Museum, Mather Point, Grand Canyon Visitor Center, Pipe Creek Vista, South Kaibab Trailhead and Yaki Point. South Kaibab Trailhead and Yaki Point are on a spur road off Desert View Dr that is closed to cars year-round.
The early-bird Hikers' Express shuttle leaves daily from Bright Angel Lodge, stopping at the Backcountry Information Center before heading to the South Kaibab Trailhead. Check the guide for seasonal departure times.
The purple Tusayan Route (summer only) runs between Tusayan and the Grand Canyon Visitor Center. Stops include the airport and the IMAX Theater. You must purchase a park permit prior to boarding. Park permits are for sale in Tusayan at the National Geographic Visitor Center next to the IMAX.
###### Taxi
Grand Canyon South Rim Taxi Service ( 928-638-2822) offers taxi service to and from Tusayan and within the park. Service is available 24 hours, but there are only a couple of taxis, so you may have to wait.
### Tusayan
The friendly little town of Tusayan, situated 1 mile south of the park's South Entrance along Hwy 64, is basically a half-mile strip of hotels and restaurants. The National Geographic Visitor Center & IMAX Theater is a good place to regroup– and buy your park tickets – before arriving at the South Entrance. In summer, you can catch the Tusayan shuttle from here into the park .
As you drive into Tusayan from the south, you'll pass the airport. The southernmost hotels are the Best Western Grand Canyon Squire Inn on your left and the Grand Hotel on your right. In quick succession are Seven Mile Lodge, Red Feather Lodge and the National Geographic Visitor Center & IMAX Theater, all bordering the west side of Hwy 64. We Cook Pizza & Pasta and Sophie's Mexican Kitchen are across Hwy 64, just south of Grand Canyon Camper Village.
#### Sleeping
Some of these motels offer a touch more character than you'd find at most other American roadside motels, but don't expect anything particularly memorable.
Grand Hotel HOTEL $$-$$$
( 928-638-3333; www.grandcanyongrandhotel.com; d $190-220; ) The distinct Western motif in this hotel's open public spaces gives this newish hotel an old look, and it works. Relatively large, comfortable rooms are filled with pleasing Mission-style furniture, and the ones in back face the woods. You may catch Navajo dance performances in the evening (schedule varies), and nightly live country music draws locals and visitors from around 10:30pm.
Ten-X Campground CAMPGROUND $
( 928-638-7851; sites per vehicle $10; May-Sep) Woodsy and peaceful, this first-come, first-served USFS campground 2 miles south of Tusayan has 70 sites and can fill up early in the summer. You'll find large sites, picnic tables, fire rings and BBQ grills (the campground host sells firewood), water and toilets, but no showers.
Seven Mile Lodge MOTEL $
( 928-638-2291; d $90; ) This simple, friendly motel doesn't take reservations, but you can show up as early as 9am to see if there are any vacancies; rooms are usually filled by early afternoon in the summer.
Best Western Grand Canyon
Squire Inn HOTEL $$$
( 928-638-2681; www.grandcanyonsquire.com; d $260; ) Rooms range from standard doubles in a two-story 1973 annex, sans elevator, to spacious interior rooms in the main hotel, with elevator. Amenities include a restaurant, popular sports bar, bowling alley, pool tables, fitness center, coin laundry and seasonal outdoor pool.
Red Feather Lodge MOTEL $$-$$$
( 928-638-2414; www.redfeatherlodge.com; d $140-170; ) This motel offers well-kept rooms in two buildings, as well as a fitness center and an outdoor pool. The three-story hotel features elevators and interior doors; the older two-story motor lodge offers outside entrances and stairs.
Grand Canyon Camper Village CAMPGROUND $
( 928-638-2887; www.grandcanyoncampervillage.com; tent sites $25, RV sites $35-50; ) A mile south of the park on Hwy 67, this private campground has a ton of sites, many with no shade or natural surroundings, but there are toilets and pay showers. Full hookups are available.
#### Eating
Considering the number of annual tourists that pass through Tusayan, the village manages to retain a sort of old-fashioned, roadside-hub pace. There's an OK variety of eateries to choose from, but as yet no one has established a notable culinary presence.
Sophie's Mexican Kitchen MEXICAN $$
( 928-638-1105; mains $10-16; 11am-9pm; ) Festooned with colorful _papel picado_ (cut paper banners), this cheery restaurant offers Mexican food like street-style tacos, fajitas and a few vegetarian options.
RP's Stage Stop CAFE $
(mains $3-7; 7am-8pm; ) The only place in Tusayan to grab an espresso drink and pick up a sandwich for your picnic lunch; also a good spot to find wi-fi if you don't have access where you're staying.
We Cook Pizza & Pasta PIZZERIA $$
( 928-638-2278; mains $10-29; 11am-10pm; ) This cavernous, busy pizza joint is the kind of place where you order, take a number, and unceremoniously chow down at one of the big tables. The pizza isn't particularly compelling, but it's good and no-nonsense, just like its name.
Coronado Room AMERICAN $$-$$$
( 928-638-2681; mains $13-30; 5-10pm; ) The Best Western Grand Squire Inn serves the classiest cuisine around. Wild game such as venison, elk and bison figure prominently, but tamer options like chicken and crab cakes are equally good.
### PARK PASSES
Park passes are available at the National Geographic Visitor Center when a ranger is on duty.
#### Entertainment
Nightlife in Tusayan is mostly limited to the popular sports bar in the Best WesternGrand Canyon Squire Inn, which also features live music nightly and Navajo dance performances on some weekend evenings.
National Geographic Visitor Center
& IMAX Theater THEATER
( 928-638-2468; www.explorethecanyon.com; adult/child $13/10; 8am-10pm Apr-Oct, 10am-8pm Nov-Mar) Hourly, on the half-hour, the IMAX theater here screens the terrific 34-minute film _Grand Canyon – The Hidden Secrets_. With exhilarating river-running scenes and virtual-reality drops off canyon rims, the film plunges you into the history and geology of the canyon through the eyes of ancient Native Americans, John Wesley Powell and a soaring eagle.
The IMAX experience affords you a safer, cheaper alternative to a canyon flyover, but if you do have your heart set on a helicopter ride, you'll also find Grand Canyon National Park Airport conveniently located in Tusayan.
### Valle
About 25 miles south of the park, Valle marks the intersection of Hwy 64 to Williams and Hwy 180 to Flagstaff. There isn't much to it apart from a couple of curiosities, as well as a gas station, minimart and rooms next door at the Grand Canyon Inn ( 800-635-9203, 928-635-9203; www.grand-canyon-inn.com; d $120; ). This family-run motel offers standard motel rooms, a restaurant (open 7:30am to 2pm and 6pm to 9pm) and a heated outdoor pool.
Flintstones Bedrock City AMUSEMENT PARK
( 928-635-2600; admission $6; 7am-9pm Mar-Oct) You probably won't want to stay at the barren windswept campground (tent/RV sites $12/16), but kids and fans of camp (the kitsch kind) will love this slightly spooky, well-worn roadside attraction. Built in 1972, it features a constant loop of Flintstones episodes in the tiny concrete movie theater, a Flintmobile that circles a volcano and a clutch of Bedrock-style buildings. The gift shop and basic diner are straight out of a David Lynch film.
Planes of Fame Air Museum MUSEUM
( 928-635-1000; www.planesoffame.org; cnr Hwys 64 & 180; adult/child/under 5 $6.95/1.95/free; 9am-5pm) This air museum has a collection of over 150 vintage airplanes on display, most of them fully functional and in immaculate condition. Aviation enthusiasts will find it fascinating.
### Kaibab National Forest
No canyon views, but no crowds either. Divided by the Grand Canyon into two distinct ecosystems, this 1.6-million-acre forest (www.fs.fed.us/r3/kai) offers a peaceful escape from the park madness. Thick stands of ponderosa dominate the higher elevations, while piñon and juniper create a fragrant backdrop further down. Sightings of elk, mule, deer, turkeys, coyotes and even mountain lions and black bears are all possible.
Hwy 64/180 slices through 60 miles of forest between the South Rim and Williams, offering access to outdoor recreation at its finest. There's a ranger station in Tusayan ( 928-638-2443), but the best place to pick up maps and information is at the visitor center in Williams.
There are literally hundreds of miles of hiking trails to explore, and dogs are allowed off-leash as long as they don't bother anyone. Mountain biking is possible after the snowmelt, roughly between April and November. A popular, moderate ride is along the Tusayan Bike Trail, actually an old logging road. The trailhead is 0.3 miles north of Tusayan on the west side of Hwy 64/180. It's 16 miles from the trailhead to the Grandview Lookout Tower,an 80ft-high fire tower with fabulous views. If you don't want to ride all that way, three interconnected loops offer 3-, 8- and 9-mile round-trips. From the lookout you can continue on the easy and still-evolving 24-mile Arizona Trail. In the winter the USFS maintains 21 miles of cross-country skiing trails.
Apache Stables ( 928-638-2891; www.apachestables.com; Moqui Dr/Forest Service Rd 328; 1/2hr ride $49/89, trail & wagon ride $59) offers horseback rides through the forest (no canyon views). You can also ride your pony on a one-hour evening trek to a campfire and return by wagon or go both ways by wagon. Either way, you must bring your own food (think hot dogs and marshmallows) and drinks. The stables are about 1 mile north of Tusayan on Moqui Dr (Forest Service Rd 328) off Hwy 64/180.
There's free backcountry camping throughout the forest as well as seven first-come, first-served developed campgrounds, including Ten X Campground.
### Williams
A pretty slow spot by day, Williams comes to life in the evening when the Grand Canyon Railway train returns with passengers from the South Rim... and then closes down again on the early side. It's a friendly town and caters to canyon tourists. Route 66 passes through the main historic district as a one-way street headed east; Railroad Ave parallels the tracks and Route 66, and heads one-way west.
#### Sights & Activities
There are plenty of opportunities for hiking and biking in nearby Kaibab, Coconino and Prescott National Forests.
Grand Canyon Railway HISTORIC RAILWAY
( 800-843-8724; www.thetrain.com; Railway Depot, 233 N Grand Canyon Blvd, round-trip adult/child from $70/40; ) Following a 9:30am Wild West show by the tracks, this historic train departs for its two-hour ride to the South Rim. If you're only visiting the rim for the day, this is a fun and hassle-free way to travel. You can leave the car behind and enjoy the park by foot, shuttle or tour bus.
BearizonaWILDLIFE PARK
( 928-635-2289; www.bearizona.com; 1500 E Rte 66; adult/child/under 4 $16/8/free; 8am-5pm Mar-Nov) Established in 2010, this awesomely named drive-through wildlife park is inhabited by indigenous North American fauna. Visitors drive themselves along a road that winds through various fenced enclosures over 160 acres, where they can see roaming gray wolves, bison, bighorn sheep and black bears up close.
#### Sleeping
###### Camping
Free dispersed camping is allowed in the national forest provided you refrain from camping in meadows, within a quarter-mile of the highway or any surface water, or within a half-mile of any developed campground.
Three pleasant USFS campgrounds near Williams offer year-round camping without hookups. Swimming is not allowed in any of the lakes. Contact the visitor center or the Williams Ranger Station for information.
Kaibab Lake CampgroundCAMPGROUND $
(tent & RV sites $18-30) Four miles northeast of town; take exit 165 off I-40 and go north 2 miles on Hwy 64.
Circle Pines KOA CAMPGROUND $
( 928-635-2626, 800-562-9379; www.circlepineskoa.com; 1000 Circle Pines Rd; tent/RV sites $26/45, cabins $52-228; ) Amid 27 acres of ponderosa-pine forest, a half-mile north of I-40 (take exit 167), Circle Pines is open year-round and offers plenty of activities for children and adults alike.
###### Lodging
Red Garter Bed & Bakery B&B $$
( 928-635-1484; www.redgarter.com; 137 W Railroad Ave; d $120-145; ) Up until the 1940s, gambling and girls were the draw at this 1897 bordello-turned-B&B across from the tracks. Nowadays, the place trades on its historic charm and reputation for hauntings. Of the four restored rooms, the suite was once reserved for the house's 'best gals,' who would lean out the window to flag down customers. Rates include a 'continental-plus' breakfast with freshly-baked pastries. Sociable innkeeper John Holst knows the area well and is happy to get out a map.
Grand Canyon Hotel BOUTIQUE HOTEL $
( 928-635-1419; www.thegrandcanyonhotel.com; 145 W Rte 66; dm $28, d with shared bath $60, d with private bath $70-125; ) This charming spot is just what the town needed – a European-style hotel in a historic 1889 building right on Route 66. There's air-con in interior rooms, but in the exterior rooms you can get a good breeze going with the window open and ceiling fan whirring. Private rooms are individually themed and decorated.
Lodge on Route 66 MOTEL $$-$$$
( 928-635-4534; www.thelodgeonroute66.com; 200 E Rte 66; r $85-100, ste $135-185; ) The Lodge is a beautifully designed blend of a Route 66 motel with low-key Southwestern style (ie no Kokopelli motif). Sturdy dark-wood furniture and wrought-iron accents give an elegant feel to this upmarket motel. Standard rooms are on the cramped side, with the big beds and little else taking up most of the available space, but roomier suites feature kitchenettes. Continental breakfast included.
Canyon Motel & RV Park MOTEL $-$$
( 928-635-9371; www.thecanyonmotel.com; 1900 E Rodeo Rd; RV sites $35-38, cottages $74-78, train cars $78-160; ) Stone cottages and rooms in two railroad cabooses and a former Grand Canyon Railway coach car offer a quirky alternative to a standard motel. Kids love the cozy train cars, which sport bunk beds and private decks. Cottages feature wood floors and kitchenettes.
FireLight B&B B&B $$-$$$
( 928-635-0200; www.firelightbedandbreakfast.com; 175 W Meade Ave; r $160-175, ste $250; ) Four well-appointed and tastefully decorated rooms in this Tudor-style house have their own fireplaces. A gourmet breakfast is served every morning by your hosts Debi (the interior designer) and Eric; this romantic spot is adults only.
Grand Canyon Railway Hotel HOTEL $$
( 928-635-4010; www.thetrain.com; 235 N Grand Canyon Blvd; d $190; ) This sprawling hotel caters primarily to Grand Canyon Railway passengers (railway packages also available). The Southwestern-style rooms are what you'd expect at any standard hotel. A restaurant, lounge and coffee house cover the dining and drinking bases.
#### Eating & Drinking
American Flyer Coffee Company CAFE $
(www.americanflyercoffeeco.com; 326 W Rte 66; mains $2-6; 7am-2pm Sun-Thu & 7am-6pm Fri &Sat; ) This extremely friendly cafe/bike-repair shop offers wi-fi access, freshly-baked pastries and healthy items like salads and wraps along with its excellent house-roasted coffee.
Pancho McGillicuddy's
Mexican Cantina MEXICAN $
( 928-635-4150; www.vivapanchos.com; 141 W Railroad Ave; mains $9-10; 11am-10pm) This bustling place serves up perfectly decent Mexican food to hungry passengers. The restaurant is housed in an 1893 tavern and has a lively bar serving local microbrews on tap.
Pine Country Restaurant AMERICAN $
( 928-635-9718; www.pinecountryrestaurant.com; 107 N Grand Canyon Blvd; mains $9-22; 6am-9pm) This family restaurant offers reasonably priced American basics and gigantic pies. Though the menu offers few surprises, the price is right. Just across the street from the visitor center, it has wide windows and plenty of room to relax in a home-style setting.
Dara Thai Cafe THAI $
( 928-635-2201; 145 W Rte 66, Suite C; mains $8-12; 11am-2pm & 5-9pm Mon-Sat; ) Dara Thai offers a lighter alternative to meat-heavy menus elsewhere in town. Lots of choice for vegetarians, and all dishes are prepared to your specified spiciness. Despite its address, the front door is found along S 2nd St.
Red Raven Restaurant AMERICAN $$
( 928-635-4980; www.redravenrestaurant.com; 135 W Rte 66; mains $10-22; 11am-2pm & 5-9pm Tue-Sun) White tablecloths and candlelight set the mood at the family-run Red Raven, delivering the most upscale dining experience you'll find in Williams.
Cruisers Café 66 AMERICAN $$
(www.cruisers66.com; 233 W Rte 66; mains $10-20; 3-10pm) Housed in an old Route 66 gas tation and decorated with vintage gas pumps and old-fashioned Coke ads, this cafe is a fun place for kids. Expect barbecue fare, such as burgers, spicy wings, pulled-pork sandwiches and mesquite-grilled ribs (cooked on the outdoor patio).
World Famous Sultana Bar BAR $
(301 W Rte 66; 10-2am) Expect the once-over when you walk in, as this place seems to spook most tourists. But if you like the sort of bar that's kitted out with dusty taxidermied animals, crusty locals and a jukebox, stop by for a beer and a game of pool.
#### Information
Police station ( 928-635-4461; 501 W Rte 66; 9am-5pm Mon-Fri)
Post office ( 928-635-4572; 120 S 1st St; 9am-5pm Mon-Fri, to noon Sat)
Visitor center ( 928-635-4061, 800-863-0546; www.williamschamber.com; 200 W Railroad Ave; 8am-5pm) Inside the historic train depot; offers a small bookstore with titles on the canyon, Kaibab National Forest and other areas of interest.
Williams Health Care Center ( 928-635-4441; 301 S 7th St; 8am-8pm)
Williams Ranger Station ( 928-635-5600; 742 S Clover Rd; 8am-4pm Mon-Fri) You'll find USFS rangers at both the visitor center and here.
#### Getting There & Around
Amtrak ( 800-872-7245; www.amtrak.com; 233 N Grand Canyon Blvd) Trains stop at Grand Canyon Railway Depot.
Arizona Shuttle ( 928-225-2290, 800-563-1980; www.arizonashuttle.com) Offers three shuttles a day to the canyon (per person $22) and to Flagstaff (per person $19).
### Havasupai Reservation
One of the Grand Canyon's true treasures is Havasu Canyon, a hidden valley with four stunning, spring-fed waterfalls and inviting azure swimming holes in the heart of the 185,000-acre Havasupai Reservation. Parts of the canyon floor, as well as the rock underneath the waterfalls and pools, are made up of limestone deposited by flowing water. These limestone deposits are known as travertine, which gives the famous blue-green water its otherworldly hue.
Because the falls lie 10 miles below the rim, most trips are combined with a stay at either Havasupai Lodge in Supai or at the nearby campground. Supai is the only village within the Grand Canyon, situated 8 miles below the rim. The Havasupai Reservation lies south of the Colorado River and west of the park's South Rim. From Hualapai Hilltop, a three- to four-hour drive from the South Rim, a well-maintained trail leads to Supai, waterfalls and the Colorado River. For detailed information on traveling into Havasu Canyon, see www.havasupai-nsn.gov/tourism.html.
Before heading down to Supai, you _must_ have reservations to camp or stay in the lodge. Do not try to hike down and back in one day – not only is it dangerous, but it doesn't allow enough time to see the waterfalls.
About a mile beyond Supai are the newly-formed (and as yet unofficially-named) New Navajo Falls and Rock Falls and their blue pools below. The new falls developed above the former Navajo Falls, which was completely destroyed in a major flash flood in 2008. After crossing two bridges, you will reach beautiful Havasu Falls; this waterfall drops 100ft into a sparkling blue pool surrounded by cottonwoods and is a popular swimming hole. Havasu Campground sits a quarter-mile beyond Havasu Falls. Just beyond the campground, the trail passes Mooney Falls, which tumbles 200ft down into another blue-green swimming hole. To get to the swimming hole, you must climb through two tunnels and descend a very steep trail – chains provide welcome handholds, but this trail is not for the faint of heart. Carefully pick your way down, keeping in mind that these falls were named for prospector DW James Mooney, who fell to his death here. After a picnic and a swim, continue about 2 miles to Beaver Falls. The Colorado River is 5 miles beyond. It's generally recommended that you don't attempt to hike to the river and, in fact, the reservation actively discourages this.
#### Sleeping & Eating
It is essential that you make reservations in advance; if you hike in without a reservation, you will not be allowed to stay in Supai and will have to hike 8 miles back up to your car at Hualapai Hilltop.
Havasu Campground CAMPGROUND $
( 928-448-2121, 928-448-2141, 928-448-2180; Havasupai Tourist Enterprise, PO Box 160, Supai, AZ 86435; per night per person $17) Two miles past Supai, the campground stretches three-quarters of a mile along the creek between Havasu and Mooney Falls. Sites have picnic tables and the campground features several composting toilets, as well as drinking water at Fern Spring. Fires are not permitted but gas stoves are allowed.
Havasupai Lodge LODGE $$
( 928-448-2111, 928-448-2101; PO Box 159, Supai, AZ 86435; r $145; ) The only lodging in Supai offers motel rooms, all with canyon views, two double beds, air-conditioning and private showers. There are no TVs or telephones. Reservations are essential.
The Sinyella Store ( 7am-7pm) is the first shop you'll see as you walk through the village. In Supai, the Havasupai Tribal Cafe ( 928-448-2981; 6am-6pm) serves breakfast, lunch and dinner daily, and the Havasupai Trading Post ( 928-448-2951; 6am-6pm) sells basic but expensive groceries and snacks.
#### Information
Havasupai Tourist Enterprise ( 928-448-2141, 928-448-2237; www.havasupai-nsn.gov; PO Box 160, Supai, AZ 86435; adult/child $35/free; 5:30am-7pm) Visitors pay an entry fee and $5 environmental care fee when they arrive in Supai.
The local post office is the only one in the country still delivering its mail by mule, and mail sent from here bears a special postmark to prove it.
There's also a small emergency clinic ( 928-448-2641) in Supai.
Liquor, recreational drugs, pets and nude swimming are not allowed, nor are trail bikes allowed below Hualapai Hilltop.
#### Getting There & Around
Seven miles east of Peach Springs on historic Route 66, a signed turnoff leads to the 62-mile paved road ending at Hualapai Hilltop. Here you'll find the parking area, stables and the trailhead into the canyon – but no services.
Don't let place names confuse you: Hualapai Hilltop is on the Havasupai Reservation, not the Hualapai Reservation, as one might think.
###### Helicopter
On Sunday, Monday, Thursday and Friday from mid-March through mid-October, a helicopter ($85 one way) shuttles between Hualapai Hilltop and Supai from 10am to 1pm. Advance reservations are not accepted; show up at the parking lot and sign up. However, service is prioritized for tribal members and those offering services and deliveries to the reservation. Call Havasupai Tourist Enterprise before you arrive to be sure the helicopter is running.
###### Horse & Mule
If you don't want to hike to Supai, you can ride a horse (round-trip to lodge/campground $120/187). It's about half that price if you hike in and ride out, or vice versa. You can also arrange for a packhorse or mule (round-trip $85) to carry your pack into and out of the canyon.
Horses and mules depart Hualapai Hilltop at 10am year-round. Call the lodge or campground (wherever you'll be staying) in advance to arrange a ride.
### Hualapai Reservation & Skywalk
Home to the much-hyped Skywalk, the Hualapai Reservation borders many miles of the Colorado River northeast of Kingman, covering the southwest rim of the canyon and bordering the Havasupai Reservation to the east and Lake Mead National Recreation Area to the west.
In 1988 the Hualapai Nation opened Grand Canyon West, which is _not_ part of Grand Canyon National Park. Though the views here are lovely, they're not as sublime as those on the South Rim – but the unveiling of the glass bridge known as the Grand Canyon Skywalk in 2007 added a completely novel way to view the canyon.
#### Sights & Activities
##### GRAND CANYON WEST
Nowadays, the only way to visit Grand Canyon West ( 928-769-2636, 888-868-9378; www.grandcanyonwest.com; per person $43-87; 7am-7pm Apr-Sep, 8am-5pm Oct-Mar), the section of the west rim overseen by the Hualapai Nation, is to purchase a package tour. A hop-on, hop-off shuttle travels the loop road to scenic points along the rim. Tours can include lunch, horse-drawn wagon rides from an ersatz Western town and informal Native American performances.
All but the cheapest packages include admission to the Grand Canyon Skywalk, the horseshoe-shaped glass bridge cantilevered 4000ft above the canyon floor. Jutting out almost 70ft over the canyon, the Skywalk allows visitors to see the canyon through the glass walkway. Would-be visitors to the Skywalk are required to purchase a package tour, which makes the experience a pricey prospect.
##### PEACH SPRINGS
The tribal capital of the Hualapai Reservation is tiny Peach Springs, also a jumping-off point for the only one-day rafting excursions on the Colorado River. Grand Canyon West is about 55 miles northwest of here via what locals have dubbed 'Buck-and-Doe-Rd.' It's beautiful, but don't even think about taking it without a 4WD.
If you plan to travel off Route 66 on the Hualapai Reservation, you need to buy a permit ($16 plus tax, per person) at the Hualapai Office of Tourism ( 928-769-2219) at the Hualapai Lodge. This is also where you arrange raft trips operated by Hualapai River Runners ( 928-769-2219; 928-769-2636; http://grandcanyonwest.com; Mar-Oct). Packages ($328) include transportation from the lodge to the river at Diamond Creek via a bone-jarring 22-mile track (the only road anywhere to the bottom of the canyon), the motorized-raft trip to Pierce Ferry landing, a helicopter ride out of the canyon and the bus ride back to Peach Springs.
The modern Hualapai Lodge ( 928-769-2230; 900 Rte 66; d $110; ) is the only place to stay in Peach Springs and, oddly, has a saltwater swimming pool and hot tub. The attached Diamond Creek Restaurant (mains $7-13; breakfast, lunch, dinner) serves American standards. Lodging/rafting packages are available.
#### Getting There & Around
At the time of writing, 12 of the 21 miles of Diamond Bar Rd to Grand Canyon West were paved, and the middle 9 miles were being graded regularly. Call the Hualapai Lodge to check road conditions before heading out, especially if it's been raining, as the road may be impassable. If you don't want to drive, use the park-and-ride service ( 702-260-6506; per person round-trip $15) that departs from Meadview, Arizona; advance reservations required.
To get to Grand Canyon West from Kingman, fill up your gas tank and drive north on Hwy 93 for approximately 26 miles. Then head northeast along the paved Pierce Ferry Rd for about another 30 miles, before turning onto Diamond Bar Rd for the final 21-mile stretch. Directions from other towns are detailed on the Grand Canyon West website: www.grandcanyonwest.com.
### Grand Canyon National Park – North Rim
On the Grand Canyon's North Rim, solitude reigns supreme. There are no shuttles or bus tours, no museums, shopping centers, schools or garages. In fact, there isn't much of anything here beyond a classic rimside national park lodge, a campground, a motel, a general store and miles of trails carving through sunny meadows thick with wildflowers, willowy aspen and towering ponderosa pines. Amid these forested roads and trails, what you'll find is peace, room to breathe and a less fettered Grand Canyon experience.
At 8200ft, the North Rim is about 10°F (6°C) cooler than the south – even on summer evenings you'll need a sweater. The lodge and all services are closed from mid-October through mid-May. Rambo types can cross-country ski in and stay at the campground (Click here).
Park admission is $25 per vehicle or $12 per person if arriving on foot or by bicycle; it's valid for seven days at both rims. Upon entering, you'll be given a map and _The Guide_. The entrance to the North Rim is 24 miles south of Jacob Lake on Hwy 67. From here, it's another 20 miles to the Grand Canyon Lodge
### GRAND CANYON NORTH RIM IN...
#### One Day
Arrive at the rim as early as possible and get your first eyeful of the canyon from Bright Angel Point. If you didn't bring a picnic, grab a sandwich at Deli in the Pines, then spend the rest of the morning hiking through meadows and aspen on the Widforss Trail. In the afternoon drive out to Point Imperial, soak up the view, then backtrack and head out on Cape Royal road. Return to Grand Canyon Lodge to relax in a rough-hewn rocker on the verandah before pointing the wheels back north.
#### Two Days
Follow the one-day itinerary, wrapping the day up with dinner and a good night's sleep at the Grand Canyon Lodge. On day two, hike down the North Kaibab Trail as far as Roaring Springs for a picnic with a side of stunning views. Chill your feet in a cool pool before making the trek back to the top. Don't have buns of steel? Let a mule do the walking.
#### Sights & Activities
###### Hiking & Backpacking
The short and easy paved trail (0.3 miles) to Bright Angel Point is a canyon must. Beginning from the back porch of the Grand Canyon Lodge, it goes to a narrow finger of an overlook with unfettered views of the mesas, buttes, spires and temples of Bright Angel Canyon. That's the South Rim, 11 miles away, and beyond it the San Francisco Peaks near Flagstaff.
The 1.5-mile Transept Trail, a rocky dirt path with moderate inclines, meanders north from the lodge through aspens to the North Rim Campground. The winding Widforss Trail follows the rim for five miles with views of canyon, meadows and woods, finishing at Widforss Point. The trailhead is 1 mile west of Hwy 67, or 2.7 miles north of the lodge.
The steep and difficult 14-mile North Kaibab Trail is the only maintained rim-to-river trail and connects with trails to the South Rim near Phantom Ranch. The trailhead is 2 miles north of Grand CanyonLodge. There's a parking lot, but it's often full soon after daylight. An informal hikers' shuttle departs around 5:45am and 7:10am, but you need to sign up the night before.
If you just want to get a taste of inner-canyon hiking, walk 0.75 miles down to Coconino Overlook or 2 miles to the Supai Tunnel. More ambitious day-hikers can continue another 2 miles to the waterfall of Roaring Springs, which is also a popular mule-ride destination. Take the short detour to the left, where you'll find picnic tables and a pool to cool your feet. Seasonal water is available at the restrooms.
If you wish to continue to the river, plan on camping overnight (backcountry permitrequired, see Click here) at Cottonwood Campground (Click here), some 2 miles beyond Roaring Springs. It's a beautiful spot with seasonal drinking water, pit toilets, a phone and a ranger station, but the 11 campsites are not shaded.
From the campground, it's a gentle downhill walk along Bright Angel Creek to the Colorado River. Phantom Ranch and the Bright Angel Campground are 7 and 7.5 miles respectively below Cottonwood.
Rangers suggest three nights as a minimum to enjoy a rim-to-river-to-rim hike, staying at Cottonwood on the first and third nights and Bright Angel on the second. Faster trips would be an endurance slog and not much fun.
Hiking from the North Rim to the South Rim requires a ride on the Trans-Canyon Shuttle to get you back.
###### Mule Rides
Canyon Trail Rides HORSEBACK RIDING
( 435-679-8665; www.canyonrides.com; mid-May–mid-Oct) You can make reservations anytime for the upcoming year but, unlike mule trips on the South Rim, you can usually book a trip upon your arrival at the park; just duck inside the lodge to the Mule Desk ( 928-638-9875; 7am-5pm). Mule rides from the North Rim don't go into the canyon as far as the Colorado River, but the half-day trip gives a taste of life below the rim.
One Hour Rim of the Grand Canyon (7 year age limit, 220lb weight limit; $40; several departures daily) Wooded ride to an overlook.
Half-Day Trip to Uncle Jim's Point (10 year age limit, 220lb weight limit; $75; 7:30am & 12:30pm) Follow the Ken Patrick Trail through the woods.
Half-Day Canyon Mule Trip to Supai Tunnel (10 year age limit, 200lb weight limit; $75; 7:30am & 12:30pm) Descend 1450ft into the canyon along the North Kaibab Trail.
###### Cross-Country Skiing
Once the first heavy snowfall closes Hwy 67 into the park (as early as late October or as late as January), you can cross-country ski the 44 miles to the rim and camp at the campground (no water, pit toilets). Camping is permitted elsewhere with a backcountry permit, available from rangers year-round. You can ski any of the rim trails, though none are groomed. The closest ski rental is in Flagstaff.
###### Scenic Drives
Driving on the North Rim involves miles of slow, twisty roads through dense stands of evergreens and aspen to get to the most spectacular overlooks. From Grand Canyon Lodge, drive north for about 3 miles, then take the signed turn east to Cape Royal and Point Imperial and continue for 5 miles to a fork in the road called the Y.
From the Y it's another 15 miles south to Cape Royal (7876ft) past overlooks, picnic tables and an Ancestral Puebloan site. A 0.6-mile paved path, lined with piñon, cliffrose and interpretive signs, leads from the parking lot to a natural arch and Cape Royal Point, arguably the best view from this side of the canyon.
Point Imperial, the park's highest overlook at 8803ft, is reached by following Point Imperial Rd from the Y for an easy 3 miles. Expansive views include Nankoweap Creek, the Vermilion Cliffs, the Painted Desert and the Little Colorado River.
The dirt roads to Point Sublime (34 miles round-trip; an appropriately named 270-degree overlook) and Toroweap (122 miles round-trip; a sheer-drop view of the Colorado River 3000ft below) are rough, require high-clearance vehicles and are not recommended for 2WDs. While they certainly offer amazing views, they require navigating treacherous roads and if your goal is absolute solitude, you might be disappointed. The dirt road to Point Sublime starts about 1 mile west of Hwy 67, 2.7 miles north of Grand Canyon Lodge (look for the Widforss Trail sign). It should take about two hours to drive the 17 miles each way. Toroweap is reached via BLM Rd 109, a rough dirt road heading south off Hwy 389, 9 miles west of Fredonia. The one-way trip is 61 miles and should take at least two hours.
#### Sleeping
Accommodations on the North Rim are limited to one lodge and one campground.
North Rim Campground CAMPGROUND $
( 877-444-6777, 928-638-7814; www.recreation.gov; sites $18-25; ) This campground, 1.5 miles north of the lodge, offers shaded sites on level ground blanketed in pine needles. Sites 11, 14, 15, 16 and 18 overlook the Transept (a side canyon) and cost $25. There's water, a store, a snack bar, coin-op showers and laundry facilities, but no hookups. Reservations are accepted up to six months in advance.
Grand Canyon Lodge LODGE $$
( 928-638-2611 for same-day reservation, 877-386-4383 for reservations up to 12 months in advance, 480-337-1320 for reservations from outside the USA; www.foreverlodging.com; r $116, cabins $121-187 for 2, $10 for each additional guest over 15; mid-May–mid-Oct; ) Walk through the front door of Grand Canyon Lodge into the lofty sunroom and there, framed by picture windows, is the canyon in all its glory. Rooms are not in the lodge itself, but in rustic cabins sleeping up to five people. The nicest are the bright and spacious Western cabins, made of logs and buffered by trees and grass. Reserve far in advance; children under 16 sleep free. About 0.5 miles up the road are 40 simple motel rooms, each with a queen bed.
If these two options are fully booked, try snagging a room at the Kaibab Lodge ( 928-638-2389; www.kaibablodge.com; Hwy 67, 18 miles north of North Rim; r $140-150, cabins $85-180; mid-May–mid-Oct; ), on Hwy 67 about 6 miles north of the park entrance; it also has a restaurant. Nearby is the first-come, first-served DeMotte Campground (Hwy 67, 16 miles north of North Rim; per site for first vehicle $17, for second $8; mid-May–mid-Oct; ) with 38 primitive sites. None have hookups. It usually fills up between noon and 3pm.
There's also free dispersed camping in the surrounding Kaibab National Forest. Otherwise, you'll find more options another 60 miles north in Kanab, Utah (Click here).
#### Eating & Drinking
Visitors can contact the restaurants through the North Rim Switchboard ( 928-638-2612, 928-638-2611). With a day's notice, the Lodge Dining Room will prepare a sack lunch ($11) ready for pick-up at 6:30am for those wanting to picnic on the trail.
Grand Canyon Lodge
Dining Room AMERICAN $$
( 928-645-6865, call btwn Jan 1 & Apr 15 for next season; mains $12-24; 6:30-10am, 11:30am-2:30pm, 4:45-9:45pm, mid-May–mid-Oct) Although seats beside the window are wonderful, views from the dining room are so huge, it really doesn't matter where you sit. While the solid menu includes buffalo steak and several vegetarian options, don't expect culinary memories. Make reservations in advance of your arrival to guarantee a spot for dinner (reservations are not accepted for breakfast or lunch).
Rough Rider Saloon BAR $
(snacks $2-5; 5:30-10:30am & 11:30am-11pm, mid-May–mid-Oct) If you're an early riser stop at this small saloon on the boardwalk beside the lodge for an espresso, a fresh-made cinnamon roll and a banana. Startingat 11:30am the saloon serves beer, wine and mixed drinks, as well as hot dogs and Anasazi chile. Teddy Roosevelt memorabilia lines the walls, honoring his role in the history of the park. This is the only bar in the lodge, so if you want to enjoy a cocktail on the sun porch or in your room, pick it up here.
Grand Canyon Cookout Experience AMERICAN $$
(adult $30-35, child $12-22, no charge for childrenunder 6; 6-7:45pm Jun-Sep; ) Chow down on barbecued meat, skillet cornbread and southwestern baked beans all served buffet style, with a side of Western songs and cheesy jokes.
Deli in the Pines CAFETERIA $
(mains $4-8; 7am-9pm, mid-May–mid-Oct) This small cafeteria adjacent to the Lodge serves surprisingly good food, although the menu is limited to sandwiches, pizza and other more simple items.
#### Information
At the Lodge you'll find a restaurant, deli, saloon, postal window and gift shop, as well as the North Rim Visitor Center ( 928-638-7864; www.nps.gov/grca; 8am-6pm). About a mile up the road, next to the campground, are laundry facilities, fee showers, a gas station, a general store ( 7am-7pm) and the North Rim Backcountry Office ( 928-638-7875; 1-5pm). To contact the Grand Canyon Lodge front desk, saloon, gift shop, gas station or general store, call the North Rim Switchboard ( 928-638-2612). The closest ATM is in Jacob Lake.
#### Getting There & Around
The only access road to the Grand Canyon North Rim is Hwy 67, which closes with the first snowfall and reopens in spring after the snowmelt (exact dates vary).
Although only 11 miles from the South Rim as the crow flies, it's a grueling 215-mile, four- to five-hour drive on winding desert roads between here and Grand Canyon Village. You can drive yourself or take the Trans-Canyon Shuttle ( 928-638-2820; one way/round-trip $70/130, no credit cards), which departs from Grand Canyon Lodge at 7am daily to arrive at the South Rim at 11:30am. Reserve at least two weeks in advance.
### Arizona Strip
Wedged between the Grand Canyon and Utah, the Arizona Strip is one of the state's most remote and sparsely populated regions. Only about 3000 people live here, in relative isolation, many of them members of the Fundamentalist Church of Latter-Day Saints (FLDS), who defy US law by practicing polygamy.
Only one major paved road – Hwy 89A –traverses the Arizona Strip. It crosses the Colorado River at Marble Canyon before getting sandwiched by the crimson-hued Vermilion Cliffs to the north and House Rock Valley to the south. Scan the skies for California condors, an endangered species recently reintroduced to the area. Desert scrub gives way to piñon and juniper as the highway climbs up the Kaibab Plateau to enter the Kaibab National Forest. At Jacob Lake, it meets with Hwy 67 to the Grand Canyon North Rim. Past Jacob Lake, as the road drops back down, you get stupendous views across southern Utah.
### PIPE SPRING NATIONAL MONUMENT
Fourteen miles southwest of Fredonia on Hwy 389, Pipe Spring ( 928-643-7105; www.nps.gov/pisp; adult/child $5/free; 7am-5pm Jun-Aug, 8am-5pm Sep-May) is quite literally an oasis in the desert. Visitors can experience the Old West amid cabins and corrals, an orchard, ponds and a garden. In summer, rangers and costumed volunteers re-enact various pioneer tasks. Tours (on the hour and half-hour) let you peek inside the stone Winsor Castle ( 8am-4:30pm Jun-Aug, 9am-4pm Sep-May), and there's also a small museum ( 7am-5pm Jun-Aug, 8am-5pm Sep-May) that examines the turbulent history of local Paiutes and Mormon settlers.
##### MARBLE CANYON & LEES FERRY
About 14 miles past the Hwy 89/89A fork, Hwy 89A crosses the Navajo Bridge over the Colorado River at Marble Canyon. Actually, there are two bridges: a modern one for motorists that opened in 1995, and a historical one from 1929. Walking across the latter you'll enjoy fabulous views down Marble Canyon to the northeast lip of the Grand Canyon. The Navajo Bridge Interpretive Center ( 9am-5pm, May–Oct) on the west bank has good background info about the bridges, as well as the area and its natural wonders. Keep an eye out for California condors!
Just past the bridge, a paved 6-mile road veers off to the fly-fishing mecca of Lees Ferry. Sitting on a sweeping bend of the Colorado River, it's in the far southwestern corner of Glen Canyon National Recreation Area (Click here) and a premier put-in spot for Grand Canyon rafters. Fishing here requires an Arizona fishing license, available at local fly shops and outfitters such as Marble Canyon Outfitters ( 928-645-2781; www.leesferryflyfishing.com; inside Marble Canyon Lodge, Alt 89).
Lees Ferry was named for John D Lee, the leader of the 1857 Mountain Meadows Massacre, in which 120 emigrants from Arkansas were brutally murdered by Mormon and Paiute forces. To escape prosecution, Lee moved his wives and children to this remote outpost, where they lived at the Lonely Dell Ranch and operated the only ferry service for many miles around. Lee was tracked down and executed in 1877, but the ferry service continued until the Navajo Bridge opened in 1929. You can walk around Lonely Dell Ranch and have a picnic amid the stone house and the log cabins.
On a small hill, Lees Ferry Campground (campsites $12) has 54 riverview sites along with drinking water and toilets, but no hookups. Public coin showers are available at Marble Canyon Lodge ( 928-355-2225; www.marblecanyoncompany.com; Alt89, Marble Canyon, 0.4 miles west of Navajo Bridge; s/d/apt $70/80/140; restaurant 6am-10pm; ), which has simple rooms, and deli sandwiches to go.
Another option is the rustic but comfortable Lees Ferry Lodge ( 928-355-2231; www.vermilioncliffs.com; Alt 89, Marble Canyon, 3.5 miles west of Navajo Bridge; s/d $64/74; 6:30am-9pm; ), which has 10 rooms plus a restaurant and bar with 100 international beers (unless somebody finished off a few brands the night before). It's one of those bars where you're never quite sure who's going to roar off the highway and stomp through the door – but they'll surely have an interesting story.
##### JACOB LAKE
From Marble Canyon, Hwy 89A climbs 5000ft over 40 miles to the Kaibab National Forest and the oddly lakeless outpost of Jacob Lake. All you find is a motel with a restaurant, a gas station and the USFS Kaibab Plateau Visitor Center ( 928-643-7298; intersection of Hwys 89A & 67; 8am-5pm, Jun–Sep). From here Hwy 67 runs south for 44 miles past meadows, aspen and ponderosa pine to the Grand Canyon North Rim. The only facilities between Jacob Lake and the rim are the Kaibab Lodge, North Rim Country Store and DeMotte Campground, about 18 miles south.
Camping is free in the national forest or you can try Jacob Lake Inn ( 928-643-7232; www.jacoblake.com; intersection of Hwys 89A & 67, 44 miles north of North Rim; r $119-138, cabins $89-103; 6:30am-9pm mid-May–mid-Oct, 8am-8pm mid-Oct–mid-May; ), which has no-frills cabins with tiny bathrooms, well-worn motel rooms and spacious doubles in the modern hotel-style building. There's also a restaurant ( 6:30am-9pm, varies seasonally) with a great bakery and ice cream counter. Try the Cookie in a Cloud, a cakey cookie topped with marshmallow and chocolate.
Kaibab Lodge Camper Village ( 928-643-7804; www.kaibabcampervillage.com; tent/RV sites $17/35; mid-May–mid-Oct), a mile south of Jacob's Lake, has more than 100 sites for tents and RVs.
### Page & Glen Canyon National Recreation Area
An enormous lake tucked into a landlocked swath of desert? You can guess how popular it is to play in the spangly waters of Lake Powell. The country's second-largest reservoir and part of the Glen Canyon National Recreation Area ( 928-608-6200; www.nps.gov/glca; 7-day pass per vehicle $15) was created by the construction of Glen Canyon Dam in 1963. To house the scores of workers an entire town was built from scratch near the dam. Now a modern town with hotels, restaurants and supermarkets, Page is a handy base for lake visitors.
Straddling the Utah-Arizona border, the 186-mile-long lake has 1960 miles of empty shoreline set amid striking red-rock formations, sharply cut canyons and dramatic desert scenery. Lake Powell is famous for its houseboating, which appeals to families and college students alike. Though hundreds of houseboats ply its waters at any given time, it's possible to explore its secluded inlets, bays, coves and beaches for days with hardly seeing anyone at all.
The gateway to Lake Powell is the small town of Page (population 6800), which sits right next to Glen Canyon Dam in the far southwest corner of the recreation area. Hwy 89 (called N Lake Powell Blvd in town) forms the main strip.
Aramark ( 800-528-6154; www.lakepowell.com) runs five of the lake's six marinas, including the often frenetic Wahweap Marina ( 928-645-2433), 6 miles north of Page. The only other marina on the Arizona side is the much more peaceful Antelope Point Marina ( 928-645-5900, ext 5), which opened in 2007 on the Navajo Reservation about 8 miles east of Page. Marinas have stores, restaurants and other services, and rent boats, kayaks, jet skis and water skis.
#### Sights
Antelope Canyon CANYON
(www.navajonationparks.org/htm/antelopecanyon.htm) Unearthly in its beauty, Antelope Canyon is a popular slot canyon on the Navajo Reservation a few miles east of Page and open to tourists by Navajo-led tour only. Wind and water have carved sandstone into an astonishingly sensuous temple of nature where light and shadow play hide and seek. Less than a city block long (about a quarter-mile), its symphony of shapes and textures are a photographer's dream. Lighting conditions are best around mid-morning between April and September, but the other months bring smaller crowds and a more intimate experience.
Four tour companies offer trips into upper Antelope Canyon; Antelope Slot Canyon Tours ( 928-645-5594; www.antelopeslotcanyon.com; 55 S Lake Powell Blvd), owned by Chief Tsotsie, is recommended. The 90-minute sightseeing tour costs $29, while the 2½-hour photographic tour is $46; both include the $6 Navajo Permit Fee. The company also offers tours to lesser-known Cathedral Canyon.
John Wesley Powell Museum MUSEUM
( 928-645-9496; www.powellmuseum.org; 64 NLake Powell Blvd; admission $5; 9am-5pm mid-Feb–mid-Dec) In 1869, one-armed John Wesley Powell led the first Colorado River expedition through the Grand Canyon. This small museum displays memorabilia of early river runners, including a model of Powell's boat, with photos and illustrations of his excursions.
Glen Canyon Dam DAM
At 710ft tall, Glen Canyon Dam is the nation's second-highest concrete arch dam – only Hoover Dam is higher, by 16ft. Guided 45-minute tours departing from the Carl Hayden Visitor Center ( 928-608-6404; tours adult/child $5/2.50; 8am-5pm Mar–mid-May, Sep & Oct, 8am-6pm mid-May–Aug) take you deep inside the dam via elevators. Tours run every half-hour from 8:30am to 4pm in summer (less frequently the rest of the year). Displays and videos in the visitor center tell the story of the dam's construction and offer technical facts on water flow, generator output etc.
Rainbow Bridge National Monument PARK
( 928-608-6404; www.nps.gov/rabr; admission $4) On the south shore of Lake Powell, about 50 miles by water from Wahweap Marina, Rainbow Bridge is the largest natural bridge in the world, at 290ft high and 275ft wide. A sacred Navajo site, it resembles the graceful arc of a rainbow. Most visitors arrive by boat, but experienced backpackers can also drive along dirt roads to access two unmaintained trails (each 28 miles round-trip) on the Navajo Reservation. Tribal permits are required. Check with the Navajo Parks & Recreation Department ( 928-871-6647; www.navajonationparks.org) on how to obtain one.
### NEED A LIFT?
The main town in the Arizona Strip is postage-stamp-sized Fredonia, some 30 miles northwest of Jacob Lake. Fredonia has the Kaibab National Forest District Headquarters ( 928-643-7395; 430 S Main St; 8am-5pm Mon-Fri), where you can pick up info on hiking and camping in the forest. Fredonia also has a service station, Judd Auto Service ( 928-643-7726, 623 S Main St; seasonal variation), which provides towing as well as tire repair and simple mechanical work.
#### Activities
###### Boating & Cruises
Marinas rent kayaks (in peak season, June to August, per day single/double $26/32), 19ft powerboats ($375), wakeboards ($41), kneeboards ($27) and other toys. From Wahweap Marina, Aramark ( 800-528-6154; www.lakepowell.com) offers boat cruises to Rainbow Bridge (April to October all day adult/child $124/84; mid-June to October half-day $81/50). Because of low water levels, seeing the arches is no longer possible from the boat but involves a 2-mile round-trip hike. Dinner cruises, sunset cruises and trips to Navajo Canyon (adult/child $59/35) and the waterside of Antelope Canyon ($38/23) are also offered.
###### Hiking & Mountain Biking
Ask at the Carl Hayden Visitor Center at Glen Canyon Dam for information and maps of the area's many hiking and mountain-biking trails. Lakeside Bikes ( 928-645-2266; 12 N Lake Powell Blvd) rents mountain bikes for $25 per day.
The most popular hike is the 1.5-mile round-trip trek to the overlook at Horseshoe Bend, where the river wraps around a dramatic stone outcropping to form a perfect U. Though it's short, the sandy, shadeless trail and moderate incline can be a slog. Toddlers should be secured safely in a backpack, as there are no guardrails at the viewpoint. The trailhead is south of Page off Hwy 89, across from mile marker 541.
The 15-mile Rimview Trail, a mix of sand, slickrock and other terrain, bypasses the town and offers views of the surrounding desert and Lake Powell. While there are several access points (pick up a brochure from the museum or chamber of commerce), a popular starting point is behind Lake View School at the end of N Navajo Dr.
#### Sleeping
You can camp anywhere along the Lake Powell shoreline for free, as long as you have a portable toilet or toilet facilities on your boat.
Courtyard by Marriott HOTEL $$
( 928-645-5000; 600 Clubhouse Dr; r $150-160, children under 18 free; ) Surroundedby a golf course away from the strip's noise and traffic, with attractive, spacious rooms and a quiet garden courtyard with a large pool, this hotel is a peaceful alternative to other chain hotels. It has a bar and a restaurant, but you'd be better off going elsewhere for a meal.
Lake Powell Resort RESORT $$
( 928-645-2433; www.lakepowell.com; 100 Lake Shore Dr; r $170-190, ste $250-280, childrenunder 18 free; ) This bustling resorton the shores of Lake Powell offers beautiful views and a lovely little pool perched in the rocks above the lake, but it is impersonal and frenetic. Rates for lake-view rooms with tiny patios are well worth the extra money. In the lobby you can book boat tours and arrange boat rental. Wi-fi is available in the lobby only.
Debbie's Hide a Way MOTEL $$
( 928-645-1224; www.debbieshideaway.com; 1178th Ave; ste $129-199; ) The owners encourage you to feel right at home – throw a steak on the grill, leaf through one of several hundred books that line bookshelves, or just hang out with other guests among the rose and fruit trees. All accommodation is in basic suites, rates include up to seven people, and there are free laundry facilities.
Lone Rock Beach CAMPGROUND $
(sites $18; ) Everyone here just pulls up next to the water and sets up house. It's a popular spot with college revelers, and can be busy and loud late into the night during the weekends. Escape to the dunes or the far edges of the lot if you're looking for quiet. There are bathrooms and outdoor cold showers.
#### Eating & Drinking
Unless otherwise noted, the following restaurants stretch along Dam Plaza, a back-to-back strip mall in the Safeway parking lot at the corner of Lake Powell Blvd and Navajo Dr. Starbucks is inside the Safeway.
Bean's Coffee CAFE $
(644f N Navajo Dr; mains $5-11; 6:30am-6pm Mon-Fri, 7am-6pm Sat, 8am-2pm Sun; ) While the coffee runs weak, this tiny cafe serves good breakfast burritos and sandwiches –try the tasty cashew chicken as a picnic lunch to go.
Slackers BURGERS $
(810 N Navajo Dr; mains $6-12; 11am-9pm Mon-Fri) A chalkboard menu includes excellent burgers (though no kick to the green chile) and hot or cold sub sandwiches. Count on long lunch lines, or call to order in advance. Picnic tables offer shaded outdoor strip-mall seating. Connects to Big Dipper Ice-Cream & Yogurt where, strangely, there's a DVD player with a selection of movies to pop in at your pleasure.
Blue Buddha Sushi Lounge SUSHI $$
(810 N Navajo; mains $14-26; 5-10pm Mon-Sat, to 9pm Sun, closed Mon & Sun Oct-May) With cold sake and a relaxing blue-hued modern decor, this ultra-cool hideaway hits the spot after a hotand dusty day in the Arizona desert. Beyond sushi, there's a limited menu including teriyaki chicken and blackened tuna.
Dam Bar & Grille AMERICAN $$
(644 N Navajo Dr; mains $8-18; 11am-10pm) Raft guides recommend the dependable pub fare, including steak, pasta and ribs. There's a microbrewery feel here, and the patio is pleasant on summer evenings, despite the strip-mall view.
Ranch House Grille DINER $
(819 N Navajo Dr; mains $6-13; 6am-3pm) There's not much ambiance but the food is good, the portions huge and the service fast. This is your best bet for breakfast. To get here from the dam, turn left off of N Lake Powell Blvd onto N Navajo Dr.
Jadi Tooh AMERICAN $$
(Antelope Point Marina; mains $12-23; 11am-10pm) A 'floating restaurant' with solid food at the Navajo-owned marina provides a peaceful respite from the bustling strip of Page, which is 8 miles southwest. Come for the relative quiet and the view.
Rainbow Room AMERICAN $$
( 928-645-2433; Lake Powell Resort, 100 Lake Shore Dr; 6-10am, 11am-2pm & 4-11pm) Perched above Lake Powell, picture windows frame dramatic red-rock formations against blue water. Your best bet is to eat elsewhere and come to the bar here for a beautiful sunset drink.
#### Information
The Glen Canyon National Recreation Area entrance fee, good for up to seven days, is $15 per vehicle or $7 per individual entering on foot or bicycle.
###### Emergency
National Park Service 24-hour Dispatch Center ( 928-608-6300)
Police station ( 928-645-2463; 808 Coppermine Rd)
###### Marinas
Marinas (except for Dangling Rope and Hite) rent boats, host rangers and small supply stores, and sell fuel. Aramark ( 800-528-6154; www.lakepowell.com) runs all the marinas except for Antelope Point, which is on Navajo land.
Antelope Point ( 928-645-5900) Peaceful Navajo-owned marina, 8 miles northeast of Page.
Bullfrog ( 435-684-3000) Connects to Halls Crossing marina by 30-minute ferry. On Lake Powell's west shore, 290 miles from Page.
###### Medical Services
Page Hospital ( 928-645-2424; Vista Ave at N Navajo Dr)
Pharmacy ( 928-645-8155; 650 Elm St; 9am-8pm Mon-Fri, 9am-6pm Sat, 10am-4pm Sun) Inside the Safeway Food & Drug.
###### Post
Post office ( 928-645-2571; 44 6th Ave; 8:30am-5pm Mon-Fri)
###### Tourist Information
In addition to Bullfrog Visitor Center and Carl Hayden Visitor Center, there is a third GCNRA Visitor Center 39 miles southwest of Page at Navajo Bridge in Marble Canyon.
Bullfrog Visitor Center ( 435-684-7423; 9am-5pm Wed-Sun, May-Oct) On the lake's north shore, this is a drive of more than 200 miles from Page.
Carl Hayden Visitor Center ( 928-608-6404; www.nps.gov/glca; 8am-7pm Memorial Day-Labor Day, to 4pm rest of the year) A well-stocked bookstore and the best source of regional information in Page. It's located at Glen Canyon Dam on Hwy 89, 2 miles north of Page.
#### Getting There & Away
Great Lakes Airline ( 928-645-1355, 800-554-5111; www.flygreatlakes.com) offers flights between Page Municipal Airport and Phoenix. Page sits 125 northwest of the North Rim.
Car rental is available through Avis ( 928-645-9347, 800-331-1212).
## NAVAJO RESERVATION
The mission statement on the Navajo Parks & Recreation website includes a famous Navajo poem that ends with the phrase 'May I walk in beauty.' This request is easily granted at many spots on the Navajo Reservation in northeastern Arizona. At 27,000 sq miles the reservation is the country's largest, spilling over into the neighboring states of Utah, Colorado and New Mexico. Most of this land is as flat as a calm sea and barren, until – all ofa sudden – Monument Valley's crimson red buttes rise before you or you come face-to-face with ancient history at the cliff dwellings at Canyon de Chelly and Navajo National Monuments. Elsewhere, you can walk in dinosaur tracks or be mesmerized by the shifting light of hauntingly beautiful Antelope Canyon.
While it's true that this remote northeastern corner of the state embraces some of Arizona's most photogenic and iconic landscapes, there's also plenty of evidence of the poverty, depression and alcoholism that affect Native American communities to this day. You'll see it in rusting, ramshackletrailers, or in crumbling social services buildings in small nowhere towns, or in the paucity of stores and businesses.
Many Navajo rely on the tourist economy for survival. You can help keep their heritage alive by staying on reservation land, purchasing their crafts or trying their foods, such as the ubiquitous Navajo taco.
For historic background on the Navajo, see Click here. Tips on reservation etiquette can be found on Click here.
#### Information
Unlike Arizona, the Navajo Reservation observes daylight saving time. The single best source of information for the entire reservation is the Navajo Tourism Office ( 928-871-6436; www.discovernavajo.com). Contact the Navajo Parks & Recreation Department ( 928-871-6647; www.navajonationparks.org) for general information about permits for hiking ($5 per day) and camping ($5-15), which are required. For a list of park offices selling permits, visit www.navajonationparks.org/permits.htm.
Pick up a copy of the _Navajo Times_ (www.navajotimes.com) for the latest Navajo news. Tune your radio to AM 660 KTNN for a mix of news and Native American music.
Keep in mind that due to historical and present-day problems, alcohol is illegal here.
#### Getting There & Around
You really need your own wheels to properly explore this sprawling land. Gas stations are scarce and fuel prices are higher than outside the reservation.
The only public transportation is provided by the Navajo Transit System ( 928-729-4002, 866-243-6260; www.navajotransit.com), but services are geared towards local, not tourist, needs. It operates daily buses on seven routes, including one that goes from Tuba City to Window Rock via the Hopi Reservation. There are also services between Kayenta, near Monument Valley, to Window Rock via Chinle and Tsaile near Canyon de Chelly; and from Window Rock to Gallup in New Mexico. Every route costs only $2.
### Tuba City & Moenkopi
Hwy 160 splits these contiguous towns in two: to the northwest, Tuba City is the largest single community in the Navajo Nation, with a handful more folks than Shiprock, New Mexico. To the southeast is the village of Moenkopi, a small Hopi island surrounded by Navajo land. Moenkopi has got a gas station, a new 24hr Denny's and one of the best hotels on either reservation – but doesn't have much else.
Tuba City is named for 19th-century Hopi chief Tuve (or Toova), who welcomed a group of Mormons down from Utah to build a village of their own next to Moenkopi. The best reason to stop on this side of Hwy 160 is the Navajo cultural museum.
Open since June 2007, the Explore Navajo Interactive Museum ( 928-640-0684; www.explorenavajo.com/go2/navajo_museum.cfm; cnr Main St & Moenave Rd; adult/child/senior $9/6/7; 10am-6pm Mon-Sat, noon-6pm Sun) is a perfect, if pricey, introductory stop for your reservation explorations and will deepen your understanding of the land, its people and their traditions. You'll learn why the Navajo call themselves the 'People of the Fourth World,' the difference between male and female hogans (traditional homes of the Navajo) and what the Long Walk was all about. Aspects of contemporary life, such as education, the role of the elders, the significance of clans and the popularity of rodeo, are also addressed.
Next door, and included in your entry fee, is a small museum about the Navajo Code Talkers, with a display explaining how the famously uncrackable code was designed.
Visits wrap up in the historic Tuba Trading Post, which dates back to the 1880s and sells authentic Native American arts and crafts.
#### Sleeping & Eating
Tuba City/Moenkopi is a convenient place to stay before or after a trip through the Hopi Reservation to the east.
Moenkopi Legacy Inn & Suites HOTEL $$
( 928-283-4500; www.experiencehopi.com; junction Hwys 160 & 264; r $139, ste $159-199, incl breakfast; ) Open since April 2010, this place brings a new level of luxury to town. The exterior is a stylized version of traditional Hopi village architecture, and the lobby, with a soaring ceiling supported by pine pillars, is stunning. Rooms have marble and granite baths and, best of all, reproductions of historic photographs from the Hopi archives at Northern Arizona University. Ask for a room with a balcony facing the inner courtyard. The continental breakfast is hearty, with eggs, potatoes and sausage as well as oatmeal and cereal.
Quality Inn HOTEL $$
( 928-283-4545; www.explorenavajo.com; cnr Main St & Moenave Rd; r $108-112, ste $153, incl breakfast; ) Comfortable, modern and well maintained, the Quality Inn has been a long time stand-by, and it still holds up. Room rates include breakfast at the popular Hogan Restaurant (cnr Main St & Moenave Rd; mains $6-14; breakfast, lunch & dinner) next door, which has an extensive menu of Southwestern, Navajo and American dishes. Smoking rooms available. Pets $10 per night.
Kate's Café DINER $
(cnr Main St & Edgewater Dr; mains $7-13; breakfast, lunch & dinner) Don't be put off by the booth with the posterior-eating hole in the seat, just sit on the other side. This ain't haute cuisine, but it serves up decent, locally popular diner grub.
For a latte and web-surfing, swing by Hogan Espresso & More (cnr Main St & Moenave Rd; 7am-7pm Mon-Fri, 9am-7pm Sat & Sun).
### Navajo National Monument
The sublimely well-preserved Ancestral Puebloan cliff dwellings of Betatkin and Keet Seel are protected as the Navajo National Monument ( 928-672-2700; www.nps.gov/nava; Hwy 564; admission free; 8am-6pm Jun–mid-Sep, 9am-5pm mid-Sep–May) and can only be reached on foot. It's no walk in the park, but there's truly something magical about approaching these ancient stone villages in relative solitude. The site is administered by the National Park Service, which controls access and maintains a visitor center 9 miles north of Hwy 160 at the end of paved Hwy 564. For a distant glimpse of Betatkin, follow the easy Sandal Trail about half a mile from the center. There's a free campground, Sunset View, with 31 first-come, first-served sites, and water nearby.
Betatkin, which translates as 'ledge house,' is reached on a ranger-led 2.5-mile hike (one-way) departing from the visitor center daily at 8:15am and 10am between June and September. Groups are limited to 25 people. Ranger availability and weather permitting, there's also a tour at 10am on weekends during the other months; be sure to phone ahead. Carry plenty of water; it's a tough slog back up to the canyon rim.
The 8.5-mile trail (one-way) to the astonishingly beautiful Keet Seel is steep, strenuous and involves crossing sand gullies and shallow streams, but it's well worth the effort. The trail is open from late May to early September and requires a backcountry permit reservable up to five months in advance. Call early since daily access is limited to 20 people; alternatively show up early on the day and hope for cancelations. You hike on your own but are met at the pueblo by a ranger who will take you on a tour. Because the hike is strenuous, most visitors stay at the primitive campground down in the canyon, which has composting toilets but no drinking water.
### Kayenta
A top contender for stray-dog capital of Arizona, Kayenta is a cluster of businesses and mobile homes around the junction of Hwys 160 and 163. It's only draw is being the closest town to Monument Valley, some 20 miles away. It has gas stations, motels, restaurants, a supermarket and an ATM.
The Burger King near the junction has a well-meaning but minimal exhibit on the Navajo Code Talkers. Roland's Navajoland Tours ( 928-697-3524) and Sacred Monument Tours ( 435-727-3218; www.monumentvalley.net) offer vehicle, hiking and horseback-riding tours through Monument Valley.
#### Sleeping & Eating
A dearth of options sends prices sky-high in summer when demand at the three main motels exceeds capacity. Rates drop by nearly half in the slower seasons.
Kayenta Monument Valley Inn MOTEL $$
( 928-697-3221; www.kayentamonumentvalleyinn.com; junction Hwys 160 & 163; r $229-249; ) Formerly the Holiday Inn, this two-story motel doesn't look like much from the outside, but the rooms flash a little modern style with big-screen TVs and cool chocolate-and-black accents. The front desk is helpful, and there's a restaurant on-site.
Wetherill Inn MOTEL $$
( 928-697-3231; www.wetherill-inn.com; 1000 Main St/Hwy 63; r incl breakfast $132; ) This motel has 54 standard-issue rooms huedin appealing earth tones. All have refrigerators and flat-screen TVs. Other amenities include an indoor pool and a laundry.
Hampton Inn HOTEL $$
( 928-697-3170; www.hamptoninn.com; junctionHwys 160 & 163; r incl breakfast from $189; ). The decor is Native American, and there's an outdoor pool perfect for chilling out in after a day on the dusty roads. For weekends in summer book well in advance. Kids under 18 stay free and pets are OK.
Golden Sands Cafe CAFE $$
( 928-697-3684; Hwy 163; mains $7-19; breakfast, lunch, dinner) Behind the Wetherill Inn is this friendly roadhouse with authentic Old West touches and a casual menu of American and Navajo dishes, including sandwiches with frybread and Navajo tacos.
### Monument Valley Navajo Tribal Park
Like a classic movie star, Monument Valleyhas a face known around the world. Her fiery red spindles, sheer-walled mesas and grand buttes have starred in films and commercials, and have been featured in magazine ads and picture books. Monument Valley's epic beauty is heightened by the drab landscape surrounding it. One minute you're in the middle of sand, rocks and infinite sky, then suddenly you're transported to a fantasyland of crimson sandstone towers soaring up to 1200ft skyward.
Long before the land became part of the Navajo Reservation, the valley was home to Ancestral Puebloans, who abruptly abandoned the site some 700 years ago. When the Navajo arrived a few centuries ago, they called it Valley Between the Rocks. Today, Monument Valley straddles the Arizona-Utah border and is traversed by Hwy 163.
The most famous formations are conveniently visible from the rough 17-mile dirt road looping through Monument Valley Navajo Tribal Park ( 435-727-5874; www.navajonationparks.org/htm/monumentvalley.htm; adult/child $5/free; visitor center 6am-8pm May-Sep, 8am-5pm Oct-Apr, scenic drive 6am-8:30pm May-Sep, 8am-4:30pm Oct-Apr). It's usually possible to drive it in your own vehicle, even standard passenger cars, but expect a dusty, bumpy ride. There are multiple overlooks where you can get out and snap away or browse for trinkets and jewelry offered by Navajo vendors. Most of the formations were named for what they look like: the Mittens, Eagle Rock, Bear and Rabbit, and Elephant Butte. Budget at least 1½ hours for the drive, which starts from the visitor center at the end of a 4-mile paved road off Hwy 163 near Goulding's Lodge. There's also a restaurant, gift shop, tour desk and the new View Hotel. National Park passes are not accepted for admission into the park.
The only way to get off the road and into the backcountry is by taking a Navajo-led tour on foot, on horseback or by vehicle. You'll see rock art, natural arches, and coves such as the otherworldly Ear of the Wind, a bowl-shaped wall with a nearly circular opening at the top. Guides shower you with details about life on the reservation, movie trivia and whatever else comes to mind. Guides have booths set up in the parking lot at the visitor center; they're pretty easygoing, so don't worry about high-pressure sales. Tours leave frequently in summer, less so in winter, with rates starting at $60 for a 90-minute motorized trip. Outfitters in Kayenta and at Goulding's Lodge also offer tours. If you want to have things set up in advance, check out the list of guides on the tribal park's website.
The only hiking trail you are allowed to take without a guide is the Wildcat Trail, a 3.2-mile loop trail around the West Mitten formation. The trailhead is at the picnic area, about a half-mile north of the visitor center
#### Sleeping & Eating
They built the View Hotel on the site of the old Mitten Campground, but you can still camp on a dusty patch of ground about a quarter mile north of the hotel. The only facilities are port-o-potties, but hey, you've got the view. It's $10 for up to five people, then an extra $10 for every five additional people.
View Hotel HOTEL $$
( 435-727-5555; www.monumentvalleyview.com; Hwy 163; r $219-229, ste $299-319; ) Probably the most aptly named hotel in Arizona, with Southwestern-themed rooms that are nice but nothing compared to their balconies. You'll never turn the TV on, at least while it's light outside. Rooms that end in numbers higher than 15 (like, say, 216) have unobstructed panoramas of the valley below; the best are on the third floor (and cost $20 more). The restaurant (mains $13 to $23) serves three OK meals a day in a dining room with floor-to-ceiling windows and an outdoor patio. Wi-fi available in the lobby only.
Goulding's Lodge MOTEL $$
( 435-727-3231; www.gouldings.com; r $185-205; ) This historic hotel a few miles west of Monument Valley has 62 modern rooms, most with views of the megaliths in the distance. The style is standard Southwestern, and each has a DVD player so you can watch one of the many movies shot here, available for rent ($5) in the lobby. The hotel's Stagecoach Dining Room (mains $8-27; 6:30am–9:30pm Utah time, shorter hours in winter) is a replica of a film set built for John Ford's 1949 Western _She Wore a Yellow Ribbon._ Get some roughage from the salad bar before cutting into the steaks or popular Navajo tacos. At lunchtime it often swarms with coach tourists. Pets cost $20 per pet per night.
Goulding's Camp Park CAMPGROUND $
( 435-727-3235; www.gouldings.com; tent sites $25, RV sites $25-44, cabins $79; ) Tucked snugly between red sandstone walls with a shot of the Mittens out of the mouth of the canyon, this is a particularly scenic full-service campground that includes a store, pool and laundry. The three pre-fab cabins can sleep up to six people (if some of them are small).
### Canyon De Chelly National Monument
It's a near soundless world, this remote and beautiful multipronged Canyon de Chelly (pronounced d- _shay_ ), far removed from time and space. Inhabited for 5000 years, it shelters prehistoric rock art and 1000-year-old Ancestral Puebloan dwellings built into alcoves.
Today, Canyon de Chelly ( 928-674-5500; www.nps.gov/cach; Chinle; admission free) is private Navajo land administered by the NPS. The name itself is a corruption of the Navajo word _tsegi,_ which means 'rock canyon.' The Navajo arrived in the canyon in the 1700s, using it for farming and as a stronghold and retreat for their raids on other tribes and Spanish settlers. But if these cliffs could talk, they'd also tell stories of great violence and tragedy. In 1805, Spanish soldiers killed scores of Navajo hiding deep in the canyon in what is now called Massacre Cave. In 1864, the US Army – led by Kit Carson – drove thousands of Navajos into the canyon and starved them into surrendering, then forced the survivors to march 300 miles – the Long Walk – to Fort Sumner in New Mexico. Four years later, the Navajos were allowed to return.
Today, about 80 Navajo families still raise animals and grow corn, squash and beans onthe land, allowing a glimpse of traditional life. Only enter hogans with a guide and don't take photographs without permission.
The mouth of the canyon is about 3 miles east of Chinle, where services include a gas station, supermarket, bank with ATM, motels and fast-food outlets.
#### Sights & Activities
If you only have time for one trip, make it the South Rim Drive, which runs along the main canyon and has the most dramatic vistas. The 16-mile road passes six viewpoints before dead-ending at the spectacular Spider Rock Overlook, with views of the 800ft freestanding tower atop of which lives Spider Woman, an important Navajo god. Start early so that you have Spider Woman all to yourself; the silence here is strangely invigorating as you watch birds soaring between you and the majestic spire. It's easy to see why this is a sacred spot for the Navajo. Budget about two hours for the round-trip, including stops.
For the most part, North Rim Drive follows a side canyon called Canyon del Muerto,which has four overlooks. At the first one, Antelope House Overlook, you'll have stunning cliff-top views of a natural rock fortress and cliff dwellings. To see the latter, walk to your right from the walled Navajo fortress viewpoint to a second walled overlook. With few walls and no railings, this overlook may not be suited for small children or pets. The North Rim Drive ends at the Massacre Cave Overlook, 15 miles from the visitor center. The road continues 13 miles to the town of Tsaile (say- _lee_ ), where Diné College has an excellent museum, as well as a library and bookstore with a vast selection of books about the Navajo.
Bring binoculars and water, lock your car and don't leave valuables in sight when taking the short walks at each scenic point. The lighting for photography on the north rim is best in early morning and on the south rim in late afternoon.
#### Tours
Entering the canyon maze is an amazing experience, as walls start at just a few feet but rise dramatically, topping out at about 1000ft. At many stops, Navajo vendors sell jewelry and crafts, usually at prices much lower than at the trading posts. Summer tours can get stifling hot and mosquitoes are plentiful, so bring a hat, sunscreen, water and insect repellent. For a list of approved tour guides, stop by the visitor center or check the park's website: www.nps.gov/cach/planyourvisit/things2do.htm.
###### Hiking
With one exception, you need a guide in order to hike anywhere in the canyon. Authorized guides are listed on the park website in the 'Plan Your Visit' section. You can also pick up the list at the park visitor center. A backcountry permit is required (but it's free). Expect to pay a guide about $25 per hour with a three-hour minimum. Rangers sometimes lead free half-day hikes in summer.
Otherwise, the steep and stunning White House Trail is your only option. Narrow switchbacks drop 550ft down from the White House Overlook on the South Rim Drive, about 6 miles east of the visitor center. It's only 1.25 miles to the stupendous White House Ruin, but coming back up is strenuous, so carry plenty of water and allow at least two hours. In summer, start out early or late in the day to avoid the worst of the heat.
###### Horseback Riding
Justin's Horse Tours HORSEBACK RIDING
( 928-674-5678) Located at the mouth of the canyon, Justin's has horses available year-round for $15 per person per hour, plus $15 an hour for the guide (two-hour minimum).
Totsonii RanchHORSEBACK RIDING
( 928-755-6209; www.totsoniiranch.com) Located about 1¼ miles beyond the end of the pavement on South Rim Drive, this place charges the same as Justin's Horse Tours. The most popular ride is the four-hour round-trip to Spider Rock ($100 per person; two-person minimum). Also offers an overnight trip starting at $350.
###### Four-Wheel Driving
Numerous companies offer 4WD trips into the canyon. Consider a tour with Thunderbird Lodge Tours ( 928-674-5841; www.tbirdlodge.com), based at the Thunderbird Lodge. They use Suburbans for small groups or, in summer, open-top heavy-duty 6WD propane-fuelled troop carriers. Locals call these 'shake-n-bake' tours. Half-day trips leave at 9am, 1pm and 2pm and cost $52/40 for adults/children. All-day tours ($83, no discounts) operate from March to November and include a picnic lunch.
Check with the visitor center for additionaltour operators. Expect to pay $150 for a three-hour tour for between one and three people.
#### Sleeping & Eating
Lodging near the canyon is limited and often booked solid in summer, so plan ahead. All three motels listed here are decidedly – and similarly – average.
###### Hotels & Motels
Best Western Canyon
de Chelly Inn MOTEL $$
( 928-674-5875; www.bestwestern.com; 100 Main St, Chinle; r $109; ) In Chinle but still close to the canyon, this two-story property has an indoor pool and sauna. Rooms are slightly larger than average, if a bit uninspired and dark. The on-site Junction Restaurant serves mediocre Native American and American dishes. The restaurant also shares its menu and dining room with a Pizza Hut, which was churning out the pies during our visit.
Thunderbird Lodge MOTEL $$
( 928-674-5841; www.tbirdlodge.com; d $115-171 $66-95; ) The closest lodging to the canyon entrance, this all-Navajo-staffed member of the Green Hotels Association has 73 rooms with TV and phone, most of them in a pink adobe lodge. Wi-fi is best in the rooms near the lobby. The cafeteria (mains $5-21; breakfast, lunch & dinner) serves mediocre American and Navajo food. Pets $30 per visit.
Holiday Inn HOTEL $$
( 928-674-5000; www.holidayinnchinle.com; BIA Route 7; r $117-129; ) Half a mile west of the visitor center, this adobe-style hotel offers modern rooms, a restaurant and a heated outdoor pool. Their front desk seems to be the friendliest of the bunch.
###### Campgrounds
Cottonwood Campground CAMPGROUND $
(campsites free) Near the visitor center, this NPS-run campground has 96 primitive sites on a first-come, first-served basis. Water is available from April to October, and there are restrooms but no hookups or showers. Fewer sites and bathrooms available in winter. At press time, the park service and the Navajo Nation were discussing the implementation of fees at the campground, so be prepared to pay to camp during your visit.
Spider Rock Campground CAMPGROUND $
( 928-674-8261; www.spiderrockcampground.com;tent/RV sites $10/15, hogans $29-39; ) This Navajo-run campground 12 miles from the visitor center on South Rim Dr is surrounded by piñon and juniper trees. Wi-fi is $2. No credit cards.
#### Information
En route to the canyon you'll pass the visitor center ( 928-674-5500; www.nps.gov/cach; 8am-5pm), which has information about guides and tours. Scenic drives skirting the canyon's northern and southern rim start nearby. Both are open year-round and, aside from one hiking trail, they are the only way to see the canyon without joining a guided tour.
### WINDOW ROCK
The tribal capital of Window Rock sits at the intersection of Hwys 264 and 12, near the New Mexico border. The namesake rock is a nearly circular arch high up on a red sandstone cliff in the northern part of town. At its base is the new Navajo Veterans Memorial Park ( 928-871-6647; www.navajonationparks.org/htm/veterans.htm; admission free; 8am-5pm), whose layout is patterned after a medicine wheel.
The sleek and modern Navajo Nation Museum ( 928-871-7941; cnr Hwy 264 & Loop Rd; admission by donation; 8am-5pm Mon, 8am-6pm Tue-Fri, 9am-5pm Sat) looks more imposing and interesting than it really is, with temporary shows that are hit or miss. For a superb selection of Navajo jewelry and crafts, swing by Navajo Arts & Crafts Enterprise (NACE; 928-871-4090; Hwy 264 at Rte 12; 9am-8pm Mon-Sat, noon-6pm Sun) next to the Quality Inn. Established in 1941, NACE is wholly Navajo operated and guarantees the authenticity and quality of its products.
The Navajo Nation Fair (www.navajonationfair.com) held in early September is a weeklong blowout with rodeos, the Miss Navajo Nation pageant, song and dance, livestock shows, horse races, a chile cook-off and lots of other events.
Rooms at the Quality Inn Navajo Nation Capital ( 928-871-4108; www.qualityinn.com; 48 W Hwy 264; r incl breakfast $78-93; ) are nothing fancy, but we liked the Southwestern motif. The hotel's biggest asset, though, is the falling-over-backwards staff. Rates include a filling breakfast in the reasonably priced restaurant serving Navajo, American and Mexican fare all day long.
### Ganado & Hubbell Trading Post
Widely respected merchant John Lorenzo Hubbell established this trading post ( 928-755-3475; www.nps.gov/hutr; admission free; 8am-6pm May-early Sep, 8am-5pm mid-Sep–Apr) in 1878 to supply Navajos returning from Fort Sumner with dry goods and groceries. Now run by the NPS, it still sells food, souvenirs and local crafts. Navajo women often give weaving demonstrations inside the visitor center. Hubbell himself was an avid collector of these woolen artworks as you'll discover on a tour of his house (adult/child $2/free), given at 10am, 11am, 1pm, 2pm and 3pm. Enjoy a free sample of Arbuckle's Ariosa Coffee (www.arbucklecoffee.com) in the visitor center. This smooth and tasty cowboy coffee, which began selling in the 1860s, was easy to transport and prepare on the trail.
The post is in the village of Ganado, about 30 miles south of Chinle/Canyon de Chelly and 40 miles north of the I-40.
## HOPI RESERVATION
Scattered across the tops of three rocky, buff-colored mesas and along the valleysbelow are the villages of the PeacefulOnes, which is what the Hopi call themselves. Their reservation – at the heart of their ancestral territory, though only containing a scant fraction of it – is like a 2410-sq-mile island floating in the Navajo Reservation. To the Hopi, Arizona's oldest and most traditional tribe, this remote terrain is not merely their homeland but also the hub of their spiritual world.
Deeply ingrained in the Hopi way is an ethic of welcoming strangers – they were even nice (for a long time, anyway) to Spanish conquistadors and missionaries. But decades of cultural abuses by visitors, even well-intentioned ones, have led Hopi villages to issue strict guidelines to protect their world. This is not just a matter of cultural survival, it's also about defending what is most deeply sacred to them.
Because of their isolated location, the Hopi have received less outside influence than other tribes and have limited tourist facilities. Aside from ancient Walpi on First Mesa, villages don't hold much intrinsic appeal for visitors. But a tour of the mesas with a knowledgeable guide can open the door to what's truly fascinating about this place: the people, their history and their traditions, which still thrive today. The Hopi are also extremely accomplished artists and craftspeople and it's well worth stopping at several shops along the main highway to peruse handmade baskets, kachina dolls, overlay silver jewelry and pottery.
Eleven of the 12 Hopi villages lie at the base or on the top of three mesas named by early European explorers, rather prosaically, First Mesa, Second Mesa and Third Mesa. They are linked by Hwy 264 along with the non-Hopi village of Keams Canyon. Narrow and often steep roads lead off the highway to the mesa tops. The twelfth village is Moenkopi, about 45 miles to the west, near Tuba City.
For an eclectically refreshing mix of background music, from Native American music to Cajun to blues to honky-tonk, turn your radio dial to KUYI 88.1, Hopi's radio station.
#### Sights
##### FIRST MESA
Three villages squat atop this mesa and another village, nontraditional Polacca, hugs its base. The road up is steep; if you're here by RV, leave it in Polacca and walk. The first village is Hano, which blends imperceptibly into Sichomovi, where you'll find the community center at Ponsi Hall ( 928-737-2262; 8:30am-4pm Apr-Oct, hours fluctuate in winter). From here, local guides lead tours (adult/youth/child $13/10/5) of the tiny village of Walpi, preceded by an introduction to Hopi culture and belief systems. The most dramatic of the Hopi enclaves, Walpi dates back to AD 900 and clings like an aerie onto the mesa's narrow end. Sandstone-colored stone houses seem to sprout organically from the cliffs. These days, their only inhabitants are a few older ladies who live without plumbing or electricity, just like in the old days.
Outside Ponsi Hall, local artisans sell pots, kachinas and _piki_ (a wafer-thin, dry rolled bread made from blue-corn meal) at fair prices.
It's best to call before visiting to confirm availability of tours, which may not run if there are private rituals scheduled on a particular day.
##### SECOND MESA
On Second Mesa, some 10 miles west of First Mesa, the Hopi Cultural Center Restaurant & Inn ( 928-734-2401; www.hopiculturalcenter.com) is as visitor-oriented as things get. It provides food and lodging, and there's also the small Hopi Museum ( 928-734-6650; adult/child $3/1; 8am-5pm Mon-Fri, 9am-3pm Sat), with walls full of historic photographs and simple exhibits that share just enough about the Hopi world to allow you to understand that it's something altogether different from the one you likely inhabit.
Second Mesa has three villages of which the oldest, Shungopavi, is famous for its Snake dances, where dancers carry live rattlesnakes in their mouths. Mishongnovi and Sipaulovi sometimes have Social or Butterfly dances open to the public.
##### THIRD MESA
The tribal capital of Kykotsmovi sits below Third Mesa with Batavi, Hotevila and Old Oraibi up on top. The latter was established around AD 1200 and vies with Acoma Pueblo in New Mexico for the title of the USA's oldest continuously inhabited village. Park next to Hamana So-O's Arts and Crafts ( 928-734-9375) and stick your head inside to say hi and let someone know you're going to walk around. The shop itself has some great locally carved kachinas.
#### Tours
When visiting Hopi country, the tour is the thing. So little about the place or the culture is obvious, even to the most astute outside eye, that visiting the villages with a knowledgeable local guide is really the only way to get a glimpse inside. Some guides include a trip to nearby Dawa Park, where thousands of ancient petroglyphs are etched into the rocks. Hopi Tours ( 928-206-7433; www.hopitours.com) are led by Micah Loma'omvaya, a member of the Bear Clan from Shungopavi and an experienced anthropologist and former tribal archaeologist. His engaging tours blend a trove of historical fact with the personal understanding of the Hopi world that comes from living in it. Bertram Tsavadawa of Ancient Pathways ( 928-797-8145; www.experiencehopi.com) and Gary Tso of Left-Handed Hunter Tour Company ( 928-734-2567; www.experiencehopi.com; lhhunter68@hopitelecom.net) are also recommended. Prices depend on tour length and group size.
#### Festivals & Events
Each village decides whether to allow non-Hopis at ceremonial dances. Some of the Kachina dances, held between January and July, are closed affairs, as are the famous Snake or Flute dances in August. It's much easier to attend Social dances and Butterfly dances, held late August through November. For upcoming festivities, check with the community development offices at each village. Not all public ceremonies are scheduled on a long-term calendar, and you may only hear about one by word of mouth. Be sure to ask while visiting if you're interested.
Kykotsmovi ( 928-734-2474)
Mews Consolidated Villages ( 928-737-2670)
Sichomovi ( 928-734-1258)
Sipaulovi ( 928-737-5426)
Some Hopi events are listed on www.sipaulovihopiinformationcenter.org/events.html. When attending these ceremonies, be respectful. For details on etiquette, see Click here.
#### Sleeping & Eating
The reservation's only hotel ( 928-734-2401; www.hopiculturalcenter.com/reservations; d mid-Mar–mid-Oct $105, mid-Oct–mid-Mar $85) is part of the Hopi Cultural Center. Reservations are essential, especially in summer when its 30 modern, if bland, rooms usually book out. The restaurant (breakfast & lunch $8-12, dinner $8-20; breakfast, lunch & dinner) is your chance to taste Hopi treats like _noqkwivi_ (lamb and hominy stew) served with blue-corn fry bread. Less adventurous palates will find the usual American fare – burgers and grilled chicken.
#### Information
Make your first stop the Hopi Cultural Center ( 928-734-2401; www.hopiculturalcenter.com) on Second Mesa to pick up information and get oriented. Information may be also be obtained from the Hopi Tribe Cultural Preservation Office ( 928-734-3612; www.nau.edu/~hcpo-p; 8am-5pm Mon-Fri) in Kykotsmovi (Third Mesa). Each village has its own rules for visitors, which are usually posted along the highways, but generally speaking any form of recording, be it camera, video or audiotape, or even sketching, is strictly forbidden. This is partly for religious reasons but also to prevent commercial exploitation by non-Hopis. Alcohol and other drug use is also prohibited.
As with the rest of Arizona (and different from the surrounding Navajo Reservation), the Hopi Reservation does not observe daylight saving time in summer. The climate is harsh – ungodly hot in summer and freezing cold in winter – so come prepared either way.
Hopi prefer cash for most transactions. There's an ATM outside the one store in Polacca. There's a hospital ( 928-737-6000) with 24hr emergency care in Polacca. For other emergencies, call the BIA police ( 928-738-2233).
Gas is cheaper outside the reservation, but there are filling stations in Keams Canyon and Kykotsmovi.
#### Getting There & Away
The Hopi mesas are about 50 miles east of Tuba City and 85 miles west of Window Rock via flat and largely uneventful Hwy 264. Three roads enter the reservation from I-40 in the south. Coming from Flagstaff, the closest approach is by heading east on I-10 to Winslow, then cutting north on Hwy 87 (130 miles). From Winslow it's 70 miles via Hwy 87, and from Holbrook 80 miles on Hwy 77. Buses operated by Navajo Transit System ( 928-729-4002, 866-243-6260; www.navajotransit.com) pass through on their daily route between Tuba City and Window Rock.
## WESTERN ARIZONA
Arizona may not be on the ocean but it does have a 'West Coast.' At least that's what wily marketers have dubbed the 1000-mile stretch of Colorado River that forms the state's boundary with California. After emerging from the Grand Canyon, the river gets tamed by a series of megadams, most famously Hoover Dam (Click here). In winter migratory flocks of birds arrive from frigid northern climes. The winged variety seeks out riverside wildlife refuges, while the two-legged 'snowbird' species packs dozens of dusty RV parks, especially in Yuma. Although summers are hellishly hot, the cool Colorado brings in scores of water rats and boaters seeking relief from the heat in such places as Lake Havasu and Laughlin.
### Bullhead City & Laughlin
Named for a rock that resembled the head of a snoozing bull, Bullhead City began as a construction camp for Davis Dam, built in the 1940s. The rock was eventually submerged by Lake Mojave, but the town stuck around and survives today, primarily because of the casinos across the Colorado River in Laughlin.
Its sister (but not twin) city, Laughlin, has a little more sizzle and is known by a number of nicknames: 'Vegas on the cheap', the 'un-Vegas,' the 'anti-Sin City.' It's all just fine by this gambling town, founded in 1964 by gaming impresario Don Laughlin, a high-school dropout from Minnesota. Theimage of good, clean fun (no leggy showgirls,no sleazy types touting escort services) is a winner with the blue-haired set and, increasingly, budget-strapped families looking for an inexpensive getaway.
Skip either town in summer when temperatures often soar to a merciless 120°F (almost 50°C).
#### Sleeping
Laughlin's big hotel-casinos are fantastic value, with spacious doubles starting at $30 during midweek and $60 on weekends. Most charge for wi-fi but some don't offer it at all, since they'd rather have you downstairs pulling slots. All are on Casino Dr, which parallels the river.
Aquarius Casino Resort HOTEL $
( 702-298-5111; www.aquariuscasinoresort.com; 1900 S Casino Dr, Laughlin; r $70-100, ste $209-329; ) The Aquarius hits the jackpot: chic, welcoming and budget friendly. The new lobby has art deco touches, while rooms are modern with big windows and flat-screen TVs. The Splash Cabaret has free entertainment on Friday and Saturday nights, and the pool and tennis court area is up on a rooftop mezzanine. Wi-fi is $12 per day or free on the casino level at Starbucks.
Golden Nugget HOTEL $
( 702-298-7111; www.goldennugget.com/laughlin; 2300 S Casino Dr; r $80-90; ) This cool and inviting place is the casino on which Vegas mogul Steve Wynn cut his teeth back in 1989. The latest owners of this 300-room 'boutique casino' have sunk big bucks into creating an intimate but classy experience with tropical-themed rooms, a palm-tree-flanked riverfront pool and above-average eateries. Rooms can drop as low as $23 during the week. Wi-fi is $10 per day.
Tropicana Express HOTEL $
( 702-298-4200; www.tropicanax.com; 2121 S Casino Dr, Laughlin; r $59-80; ) The 1500-room former Ramada Express has rolled into the 21st century without ditching its family-friendly train theme. The new rooms could give Vegas a run for its money with chocolate-brown contemporary furniture, leather headboards and pillow-top mattresses.
#### Eating & Drinking
All casinos feature multiple restaurants, usually including a buffet, a 24-hour cafe and an upscale steak house, along with bars and lounges. Even employees at other hotels say that Harrah's has the best buffet in town.
Saltgrass Steakhouse STEAKHOUSE $$
( 702-298-7153; 2300 S Casino Dr, Laughlin; mains $10-33; dinner Mon-Sat, 7am-10pm Sun) Surrender helplessly to your inner carnivore at this river-view Wild West-themed restaurant at the Golden Nugget. The yummy cuts of Angus beef are the way to go, but chargrilled chicken and fish also put in menu appearances.
Earl's Home Cookin' at the Castle AMERICAN $
( 928-754-1118; 491 Long Ave, Bullhead City; $5-21; 7am-8pm) Folks are friendly inside this turreted mock-castle in Old Bullhead, where the food sure tastes good and the $5.49 breakfast specials are a deal.
Pints Brewery & Sports Bar BREWERY $$
( 702-298-4000; 2010 S Casino Dr, Laughlin; mains $9-22; lunch Fri-Sun, dinner daily) This buzzy spot inside the Colorado Belle is home to Laughlin's only brewery. The open kitchen prepares wraps, burgers and wood-fired pizzas. Lots of TVs for sports fans.
Loser's Lounge BAR
( 702-298-2535; 1650 S Casino Dr, Laughlin; 7pm to late) Pictures of General Custer, Robert E. Lee and other famous 'losers' decorate the walls at this at this bar and dance-club fixture at the Riverside Resort. Live bands play chart music.
#### Information
Remember, Nevada time is one hour behind Arizona in winter, but in the same time zone in summer (Arizona doesn't observe daylight saving time).
Bullhead Area Chamber of Commerce ( 928-754-4121; 1251 Hwy 95; 8am-5pm Mon-Fri)
Laughlin Visitor Center ( 702-298-3321; www.visitlaughlin.com; 1555 S Casino Dr; 8am-4:30pm Mon-Fri) The visitor center and the chamber of commerce both have area info, including copies of the _Entertainer,_ a weekly guide to the Laughlin casino scene.
Post office (990 Hwy 95, cnr 7th St, Bullhead City; 10am-2pm Mon-Fri)
#### Getting There & Away
There are no longer any commercial flights into Bullhead City/Laughlin Airport. Las Vegas' McCarran International Airport is about 100 miles north of town and linked to Laughlin hotels by River City Shuttle ( 928-854-5253; www.rivercityshuttle.com) two times daily ($40 one way, 1¾ hours). Ferries go back and forth across the river between Bullhead and Laughlin.
### Route 66: Topock To Kingman
Coming from California, Route 66 enters Arizona at Topock, near the 20-mile Topock Gorge, a dramatic walled canyon that's one of the prettiest sections of the Colorado River. It's part of the Havasu National Wildlife Refuge ( 760-326-3853; www.fws.gov/southwest/refuges/arizona/havasu), a major habitat for migratory and water birds. Look for herons, ducks, geese, blackbirds and other winged creatures as you raft or canoe through the gorge. There are plenty of coves and sandy beaches for picnics and sunning. Companies renting boats include Jerkwater Canoe & Kayak ( 928-768-7753; www.jerkwatercanoe.com) in Topock, which launches day trips ($46) from Topock Marina. Rates include boat rental for the 17-mile float from Topock to Castle Rock and the return shuttle.
North of here, in Golden Shores, you can refuel on gas and grub before embarking on a rugged 20-mile trip to the terrifically crusty former gold-mining town of Oatman, cupped by pinnacles and craggy hills. Since the veins of ore ran dry in 1942, the little settlement has reinvented itself as a movie set and unapologetic Wild West tourist trap, complete with staged gunfights (daily at noon, 1:30pm, 2:15pm and 3:15pm) and gift stores named Fast Fanny's Place and the Classy Ass. And speaking of asses, there are plenty of them (the four-legged kind, that is) roaming the streets and shamelessly begging for food. You can buy hay squares in town. Stupid and endearing, they're descendents from pack animals left behind by the early miners.
Squeezed among the shops is the 1902 Oatman Hotel, a surprisingly modest shack (no longer renting rooms) where Clark Gable and Carole Lombard first shagged, presumably, on their wedding night in 1939. Clark apparently returned quite frequently to play cards with the miners in the downstairs saloon, which is awash in one-dollar bills (some $40,000 worth by the barmaid's estimate). At the time of research, the upstairs, where visitors used to be able to peek into the old guest rooms, was closed for renovations. Beyond Oatman, keep your wits about you as the road twists and turns past tumbleweeds, saguaro cacti and falling rocks as it travels over Sitgreaves Pass (3523ft) and corkscrews into the rugged Black Mountains before arriving in Kingman.
##### KINGMAN
Among Route 66 aficionados, Kingman is known as the main hub of the longest uninterrupted stretch of the historic highway, running from Topock to Seligman. Among its early 20th-century buildings you'll find the former Methodist church at 5th and Spring St where Clark Gable and Carole Lombard tied the knot in 1939. Hometown hero Andy Devine had his Hollywood breakthrough as the perpetually befuddled driver of the eponymous _Stagecoach_ in John Ford's Oscar-winning 1939 movie.
These days, Kingman feels like a place teetering between decline and revival. The historic Hotel Brunswick closed in 2010 due to hard times but on Beale St, the axis of historic downtown, some new eateries and galleries are sparking optimism.
Route 66 barrels through town as Andy Devine Ave. Parallel to it is up-and-coming Beale St. Supermarkets, gas stations and other businesses line up along northbound Stockton Hill Rd, which is also the road to take for Grand Canyon West.
#### Sights & Activities
Route 66 Museum MUSEUM
( 928-753-9889; www.kingmantourism.org; 120W Andy Devine Ave; adult/child/senior $4/free/3; 9am-5pm) On the second floor of the 1907 powerhouse, which also holds the visitor center, this small but engaging museum has the best historical overview of the Mother Road anywhere along it. Check out that crazy air conditioner on the 1950 Studebaker Champion!
Mohave Museum of History & Arts MUSEUM
( 928-753-3195; www.mohavemuseum.org; 400 W Beale St; adult/child/senior $4/free/3; 9am-5pm Mon-Fri, 1-5pm Sat) Admission to the Route 66 Museum also gets you into the Mohave Museum, a warren of rooms filled with extraordinarily eclectic stuff. All sorts of regional topics are dealt with, from frontier life to Andy Devine. There's also an entire wall of portraits of American first ladies.
Hualapai Mountain Park PARK
( 928-681-5700; www.mcparks.com; day use $5) In summer locals climb this nearby mountain for picnics, hiking and wildlife-watching amid cool ponderosa pine and aspen.
#### Festivals & Events
Historic Route 66 Fun Run CAR SHOW
( 928-753-5001; www.azrt66.com) Vintage car rally from Seligman to Topock on the first weekend in May.
Andy Devine Days Parade PARADE
( 928-753-4003; www.kingmantourism.org) Floatsand a rodeo in late September.
#### Sleeping
Kingman has plenty of motels along Andy Devine Ave north and south of the I-40. Rates start at about $32 per double, but the cheapest places are dingy and popular with down-on-their-luck long-term residents. Inspect before committing.
Hampton Inn & Suites HOTEL $$
( 928-692-0200; 1791 Sycamore Ave; www.hamptoninn.com; r incl breakfast $110-139; ) The best of the chains, the Hampton has clean and spacious rooms and is a good choice for families. There's a small outdoor pool for cooling off after a day on the road. Very welcoming.
Hualapai Mountain Park CAMPGROUND $
( 928-681-5700, 877-757-0915; www.mcparks.com; Hualapai Mountain Rd; tent/RV sites $15/25, cabins $70-125) Camp among granite rock formations and ponderosa pine at this pretty county park, some 15 miles south of town.
Hualapai Mountain Resort LODGE $
( 928-757-3545; www.hmresort.net; 4525 Hualapai Mountain Rd; r $79-99, ste $159; ) Think mountain-man chic: chunky wood furniture, bold paintings of wild game, a front porch that's made for elk- and wildlife-watching among the towering pines. The on-site restaurant serves lunch and dinner Wednesday through Sunday and breakfast on weekends.
Travelodge MOTEL $
( 928-757-1188; www.travelodge.com; 3275 E Andy Devine Ave; r incl breakfast $51-64; ) For budget travelers it's got everything you need: a Route 66-adjacent location, helpful staff, continental breakfast, a laundry, free wi-fi and a few rooms under $55.
Hilltop Motel MOTEL $
( 928-753-2198; www.hilltopmotelaz.com; 1901 E Andy Devine Ave; s/d $42/46; ) Rooms here are a bit of a throwback, but well kept. On Route 66, with nice views and a cool neon sign.
#### Eating & Drinking
Cellar Door WINE BAR $
( 928-753-3885; www.the-cellar-door.com; 414 E Beale St; appetizers under $8; 4-10pm Wed & Thu, 4pm-midnight Fri & Sat) This new wine bar offers about 140 wines by the bottle, 30 by the glass, an international selection of beers and tasty appetizer plates. It's a hot little spot that embodies the spirit of revival in Kingman.
Dambar Steakhouse STEAKHOUSE $$
( 928-753-3523; 1960 E Andy Devine Ave; lunch $6-11, dinner $10-22; lunch & dinner; ) This local landmark serves giant steaks in Old West bad-boy environs while keeping the kiddies happy with coloring placemats and crayons. Local characters hang out at the spit-and-sawdust saloon with cow-hide tablecloths.
Mr D'z Route 66 Diner DINER $
( 928-718-0066; 105 E Andy Devine Ave; mains $6-18; 7am-9pm) Get your _American Graffiti_ fix at this modern-vintage diner with its hot-pink and turquoise color scheme and cool memorabilia. Oprah herself gave the thumbs up to its cheeseburgers, onion rings and signature root-beer float when stopping by in 2006. Breakfast is served all day.
Beale Street Brews COFFEE SHOP $
(418 E Beale St; 7am-5pm Mon-Fri, 7am-4pm Sat & Sun; ) This cute indie coffee shop draws local java cognoscenti with its lattes, live music and poetry nights.
#### Information
Kingman Regional Medical Center ( 928-757-2101; www.azkrmc.com; 3269 Stockton Hill Rd)
Police ( 928-753-2191; 2730 E Andy Devine Ave)
Powerhouse Visitor Center ( 928-753-6106, 866-427-7866; www.kingmantourism.org; 120 W Andy Devine Ave; 8am-5pm). Lots of information about Route 66 attractions.
#### Getting There & Away
Great Lakes Airlines ( 800-554-511; www.flygreatlakes.com) provides the only commercial flights in and out of Kingman Airport, linking it daily to Phoenix.
Greyhound ( 928-757-8400; www.greyhound.com; 3264 E Andy Devine Ave; ticket office8am-1pm & 5:30-6pm) runs daily buses to Phoenix ($61, 5½ hours), Las Vegas ($46, three hours), Flagstaff ($56, 2½ hours), Los Angeles ($103, 11 hours) and elsewhere. Amtrak's ( 800-872-7245; www.amtrak.com) westbound _Southwest Chief_ stops at 11:46pm, the eastbound at 2:33am. There's a train waiting room at the corner of Andy Devine Ave (Route 66) and 4th St. It's not a full station and you cannot buy a ticket here, so book ahead.
### Around Kingman
##### CHLORIDE
The hills surrounding Chloride, some 20 miles northwest of Kingman, once spewed forth tons of silver, gold, copper and turquoise from as many as 75 mines. These days, this peaceful semi-ghost town is inhabited by quirky locals who create bizarre junk sculptures and proudly display them outside their ramshackle homes. You can post a letter in Arizona's oldest continuously operating post office (since 1862) or snap a picture of yourself behind bars at the crumbling jail. Up in the hills, reached via a super-rough 1.5-mile dirt road, are Roy Purcell's psychedelic rock murals. If you don't have a 4WD, hike up or risk a busted axle. Two gunfighting troupes stage rip-roarin' shoot-'em-ups at high noon on Saturday between September and June (and on the first and third Saturday in July and August). One of them is the ultimate 'guns and roses' – the world's only all-girl gun-fighting troupe, the Wild Roses of Chloride.
For maps and information, stop by the Mine Shaft Market ( 928-565-4888; 4940 Tennessee Ave; 8am-5pm Mon-Sat, 9am-5pm Sun).
When the sun goes down and the stars come out, you'll feel the true Wild West spirit. Bonnie and John operate a few simple but cozy adobe-walled rooms with squeaking mattresses at the Sheps Miners Inn ( 928-565-4251; 9827 2nd St; r $35-65). It's right behind Yesterdays ( 928-565-4251; 9827 2nd St; mains $7-20; lunch, dinner daily, breakfast Sat & Sun), their restaurant and Western saloon, with creaky wooden floors, vintage gas pumps and hand-painted murals. It serves hearty American grub, international beers and toe-tapping live music nightly. The only sad part? There's a dish on the menu called 'yesterday's salmon.'
### Route 66: Kingman To Williams
Past Kingman, Route 66 arcs north away from the I-40 for 115 dusty miles of original Mother Road through scrubby, lonely landscape. It merges with the I-40 near Seligman, then reappears briefly as Main St in Williams. Gas stations are rare, so make sure you've got enough fuel. The total distance to Williams is 130 miles.
##### KINGMAN TO PEACH SPRINGS
It's tempting to try to race the train on this lonely stretch of Mother Road where your only other friend is the pavement unfurling for miles ahead. The first opportunity for socializing arises in tiny Hackberry, where highway memorialist Robert Waldmire lures passers-by with his much loved Old Route 66 Visitor Center ( 928-769-2605; www.hackberrygeneralstore.com; 11255 E Rte 66; admission free; generally 9am-5pm) inside an eccentrically decorated gas station. It's a refreshing spot for a cold drink and souvenirs. Keep going and you'll pass through the blink-and-you'll-miss-them towns of Valentine and Truxton.
For information about Peach Springs, see Click here.
##### GRAND CANYON CAVERNS
Nine miles past Peach Springs, a plaster dinosaur welcomes you to the Grand Canyon Caverns & Inn ( 928-422-3223; www.gccaverns.com; Rte 66, Mile 115; 1hr tour adult/child $15/10; 9am-5pm Mar-Oct, 10am-4pm Nov-Feb; ), a cool subterranean retreat from the summer heat. An elevator drops 210ft underground to artificially lit limestone caverns and the skeletal remains of a prehistoric ground sloth. If you've seen other caverns these might not be as impressive, but kids get a kick out of a visit. The 30 to 45-minute short tour is wheelchair accessible. Since 2010, about 100 people have spent the night in the new Cavern Suite ($700), an underground 'room' with two double beds, a sitting area and multicolored lamps. If you ever wanted to live in one of those postapocalyptic sci-fi movies, here's your chance! One of the DVDs on offer is underground horror flick _The Cave_ – watch it here only if you're especially twisted.
Up on the surface, horseback tours (per 30min/hr $20/35) from the riding stable trot off on trail rides hourly and at sunset. The restaurant (mains $10-16; 7am-7pm) is nice if you already happen to be here; it has a small playground and serves burgers, sandwiches and fried food. The bar opens at 4pm and closes based on crowd-size. The campground (tent/RV sites $15/30) here has over 50 sites carved out of the juniper forest, plus new open-air, roof-free rooms (from $60) on raised platforms for star-gazers. The Caverns Inn (r $85-107; ) has rooms that are basic but well kept. There's wi-fi in the lobby. Pets are $5 per day with a refundable $50 deposit.
##### SELIGMAN
Some 23 miles of road slicing through rolling hills gets you to Seligman – a town that embraces its Route 66 heritage, thanks to the Delgadillo brothers, who for decades have been the Mother Road's biggest boosters. Juan sadly passed away in 2004, but octogenarian Angel and his wife Vilma still run Angel's Barbershop ( 928-422-3352; www.route66giftshop.com; 217 E Rte 66). OK, so he doesn't cut hair anymore, but the barber's chair is still there and you can poke around for souvenirs and admire license plates sent inby fans from all over the world. If Angel is around, he's usually happy to regale you with stories about the Dust Bowl era. He's seen it all.
Angel's madcap brother Juan used to rule prankishly supreme over the Snow Cap Drive-In ( 928-422-3291; 301 E Rte 66; dishes $3-6; 10am-6pm mid-Mar–Nov), a Route 66 institution now kept going by his sons Bob and John. The crazy decor is only the beginning. Wait until you see the menu featuring cheeseburgers with cheese and 'dead chicken!' Beware the fake mustard bottle... They sometimes open at 9am in mid-summer.
Two good restaurants stare each other down from opposite sides of Route 66. For friendly service and good American grub, try Westside Lilo's Cafe (415 W Rte 66; mains $5-16; 6am-9pm), which also has an outdoor patio. For beer and a few tongue-in-cheek menu items, try the Roadkill Café & OK Saloon (502 W Rte 66; breakfast $5-13, lunch $6-17, dinner $15-25; 7am-9pm) across the street, which has an all-you-can-eat salad bar, juicy steaks and burgers and, of course, the 'splatter platter.'
The most appealing hotel is Canyon Lodge ( 928-422-3255; 114 E Chino Ave; s/d incl breakfast $50/55; ) where each immaculately clean room is decked out in a '50s-inspired theme. We're partial to the Elvis Room, which dukes it out with the John Wayne Room for most popular among guests. For the best neon sign, look no further than the welcoming Supai Motel ( 928-422-4153; www.supaimotel.com; 134 W Chino Ave; s/d $48/54; ), a classic courtyard motel offering simple but perfectly fine rooms with refrigerators and microwaves. The Havasu Falls mural is an inspiring way to start the morning.
### Lake Havasu City
Lake Havasu City has all the unreal charm of a manufactured community. It also has London Bridge. Yes, that would be the original gracefully arched bridge that spanned the Thames from 1831 until 1967, when it was quite literally falling down (as predicted in the old nursery rhyme) and put up for sale. Robert McCulloch was busy developing a master-planned community on Lake Havasu and badly in need of some gimmick to drum up attention for his project. Bingo! McCulloch snapped up London Bridge for a cool $2.46 million, dismantled it into 10,276 slabs and reassembled it in the Arizona desert. The first car rolled across in 1971.
Listed in the _Guinness World Records_ as the world's largest antique, London Bridge may be one of Arizona's most incongruous tourist sites, but it's also among its most popular. Day-trippers come by the busload to walk across it and soak up faux British heritage in the kitschy-quaint English Village. The lake itself is the other major draw. Formed in 1938 by the construction of Parker Dam, it's much beloved by water rats, especially students on spring break (roughly March to May) and summer-heat refugees from Phoenix and beyond.
#### Sights & Activities
Once you've snapped pics of London Bridge, you'll find that most of your options are water related. Several companies offer boat tours (from around $20) from English Village. Options include one-hour narrated jaunts, day trips and sunset tours, which can usually be booked on the spot. Several companies along the waterfront in English Village rent jet skis and other watercraft.
London Bridge Beach BEACH
(1340 McCulloch Blvd) This sandy strip has palm trees, a sandy beach, playgrounds and a fenced dog park with faux fire hydrant in the middle, all with bridge views. It's off W McCulloch Blvd, behind Island Inn hotel. Nearby is the Lake Havasu Marina ( 928-855-2159; www.lakehavasumarina.com; 1100 McCulloch Blvd), which has boat ramps but no rentals.
Lake Havasu City
Top Sights
London Bridge B2
London Bridge Beach B3
Sleeping
1Heat B2
2London Bridge Resort C2
3Motel 6 B1
Eating
4Barley Brothers B2
5Javelina Cantina B2
6Red Onion D1
Drinking
7BJ's Tavern D2
8Wired D2
#### Sleeping
Rates fluctuate tremendously from summer weekends to winter weekdays. Local budgetand national chain hotels line London Bridge Rd.
Heat BOUTIQUE HOTEL $$
( 928-854-2833; www.heathotel.com; 1420 McCulloch Blvd; r $139-159; ste $191-256; ) The front desk doubles as a bar at Heat, the slickest hotel on Arizona's west coast. Rooms are hip and contemporary, and most have private patios with views of London Bridge. In the 'inferno' rooms, bathtubs fill from the ceiling! An outdoor cocktail lounge overlooking the bridge and the lake feels almost like the deck of a cruise ship.
Windsor Beach Campground CAMPGROUND $
( 928-855-2784; www.azstateparks.com; 699 London Bridge Rd; campsite $18) Sleep just steps from the water at this scenic beach and camping area at Lake Havasu State Park. Amenities include showers, boat-launch facilities and new hookups. The 1.5-mile Mohave Sunset Trail runs almost the full-length of the park. Day use is $15 per vehicle.
London Bridge Resort HOTEL $$
( 928-855-0888; www.londonbridgeresort.com; 1477 Queens Bay Rd; ste $139-269; ) Enjoy flat-screen TVs, new mattresses and rooms with views of London Bridge (of course) at this popular all-suite property, where a replica of a 1762 royal coach greets guest in the lobby. It's a good choice if you want pools, nightclubs, bars and restaurants all under one roof.
Motel 6 MOTEL $
( 928-855-3200; www.motel6.com; 111 London Bridge Rd; r $54-60; ) You know the drill: no-frills rooms, scratchy towels, cheap rates. This lakeside location is well-managed and close to London Bridge.
#### Eating & Drinking
There's no shortage of places to eat and drink in Havasu.
Angelina's Italian Kitchen ITALIAN $$
( 928-680-3868; 2137 W Acoma Blvd; mains $8-27; dinner Tue-Sat) If you like your Italian food cooked as if mama was behind the stove, you'll like this very busy hole in the wall on an industrial stretch east of downtown. It's cluttered and some of the patrons may be eccentric, but the home-cooked Italian weaves together pungent flavors like fine tapestry.
Red Onion AMERICAN $
( 928-505-0302; 2013 N McCulloch Blvd; mains $7-11; 8am-2pm daily, 4-8pm Thu & Fri) A step above a diner, a step below a bistro, the dining room here opens up onto Havasu's 'uptown district.' Try the omelets for a hearty start to your day. Service is friendly, if a bit disorganized.
Javelina Cantina MEXICAN $$
(www.javelinacantina.com; 1420 McCulloch Blvd; mains $11-18; 11am-9pm) The outdoor patio at this busy Mexican restaurant – owned by the folks behind Barley Brothers – has great views of London Bridge.
Wired COFFEE SHOP $
(www.wiredcoffeelhc.com; 2131 N McCulloch Blvd; mains under $6; 5:30am-5:30pm Mon-Fri, 6am-noon Sat & Sun; ) If every coffee shop could be this awesome, the world would be a better place. Welcoming staff, scrumptious pastries, free wi-fi, an inviting interior and fresh coffee – Wired is a great coffee shop. Wraps and sandwiches on sale for lunch. The Death Valley date cookie is tasty.
Barley Brothers PUB $$
( 928-505-7837; www.barleybrothers.com; 1425 McCulloch Blvd; mains $10-26; 11am-10pm) It's brews and the views at this busy microbrewery overlooking London Bridge. Steaks, burgers and salads are on the menu, but the place is known for its wood-fired pizzas. Lots of flat-screen TVs for sports fans, and beer drinkers can choose from one of six different microbrews. Biggest drawback? No outdoor patio.
BJ's Tavern BAR
(2122 N McCulloch Blvd; 6am-2am Mon-Sat) Inside there's a jukebox, pool tables and karaoke, while outdoors is a misted smoking patio.
#### Information
Lake Havasu Post Office ( 928-855-2361; 1750 N McCulloch Blvd; 8:30am-5pm Mon-Fri, 9am-1pm Sat)
Visitor center ( 928-855-5655; www.golakehavasu.com; 420 English Village; 9am-5pm; ) Has all the need-to-know info.
#### Getting There & Away
Lake Havasu is on Hwy 95, about 20 miles south of the I-40. There's no public transportation, but River City Shuttle ( 928-854-5253; www.rivercityshuttle.com) runs buses to Las Vegas' McCarran International Airport twice daily ($65 one way, 3¼ hours).
### Parker
Hugging a 16-mile stretch of the Colorado River known as the Parker Strip, this tiny town south of Lake Havasu is a convenient pit stop for those wanting to explore some of the region's unique riparian parks and preserves. All hell breaks loose in late January/early February when the engines are revved up for the Best in the Desert Parker 425 (www.bitd.com), an off-road race that lures up to 100,000 speed freaks. Contact the chamber of commerce ( 928-669-2174; www.parkertourism.com; 1217 California Ave; 8am-5pm Mon-Fri) for the lowdown.
Parker is 35 miles south of Lake Havasu via Hwy 95.
#### Sights & Activities
Water-skiing and jet-skiing, fishing, boating and tubing are popular here, and there are plenty of concessionaires along the Parker Strip.
Parker Dam DAM
Finished in 1938, this mighty dam formed Lake Havasu 15 miles north of town. It may not look it, but it is in fact the world's deepest dam, with 73% of its structural height of 320ft buried beneath the original riverbed. Although the interior of the dam has been off limits to tourists since September 11, 2001, you can drive over it between 5am and 11pm (although the road is too narrow for large RVs).
Buckskin Mountain State Park PARK
( 928-667-3231; www.azstateparks.com; 5476 N Hwy 95; admission per vehicle $10) Tucked along a mountain-flanked bend in the Colorado River about 11 miles north of Parker, this park has great family-friendly infrastructure with a playground, swimming beach, basketball court, cafe and grocery store (summer only). Campsites (tent & RV sites $30) are now available by reservation online or by phone. Tent campers who want to be close to the water should opt for a covered waterside cabana; those looking for quieter, more scenic desert camping can drive another mile north to the park's River Island Unit ( 928-667-3386; sites $25).
Bill Williams National Wildlife Refuge PRESERVE
( 928-667-4144; www.fws.gov/southwest/REFUGES/arizona/billwill.html; 60911 Hwy 95; 8am-4pm Mon-Fri, 10am-2pm Sat & Sun) Abutting Cattail Cove, where the Bill Williams River meets Lake Havasu, is this calm wildlife refuge, which helps protect the unique transition zone between Mohave and Sonoran desert ecosystems. On a finger of land pointing into the lake, there's a 1.4-mile interpretive trail through a botanic garden of native flora, with shaded benches and access to fishing platforms. Endangered birds like to roost in the largest cottonwood/willow grove along the entire length of the Colorado River. Entrance is between Mile 161 and 162.
Colorado River Indian Tribes Museum MUSEUM
( 928-669-8970; cnr Mohave Rd & 2nd Ave; admission by donation; 8am-noon, 1-5pm Mon-Fri) Surrounding Parker, the Colorado River Indian Reservation is inhabited by members of the Mohave, Chemehuevi, Navajo and Hopi tribes. Their stories, along with amazing handicrafts (the basket collection is famous), come to life at this recently expanded museum. Helpful staff will explain the meaning of various designs on the baskets, including the ancient, spirit-focused 'whirlwind' symbol that, unfortunately, became an international symbol of intolerance and hate as the Nazi swastika.
#### Sleeping & Eating
There aren't really any great properties in town, but if you must spend the night, the all-purpose, tribal-owned Blue Water Resort & Casino ( 928-669-7000; www.bluewaterfun.com; 13000 Resort Dr; r $140-150; ) is probably your best bet. The nicest rooms overlook the river marina. Also OK is the Budget Inn Motel ( 928-669-2566; 912 Agency Ave; r $55-65; ) which has spacious doubles, some with kitchenettes. Campsites are also available at Buckskin Mountain State Park (Click here).
For breakfast, try Coffee Ern's (1720 S California Ave; meals under $12; breakfast, lunch & dinner), which stuffs hungry stomachs with home-cooked goodness. They're not going to win any awards for service at Badenoch's on the Beach ( 928-669-2681; off Hwy 95; breakfast, lunch), but who's complaining when the Bloody Marys are $3? This is a booze-and-bikinis kinda place, where people pull in and hop off their watercraft. Order your burger or your patty-melt at the outside counter, grab a seat on the patio (all seating is outside) and consider whether you really need that $2 jello shot. Look for the big Badenoch's sign north of the casino.
### Yuma
The territorial prison here was nicknamed the Hellhole of the West based in part on the city's blazing-hot temperatures. Today, the 2007 remake of the 1957 classic _3.10 to Yuma_ has again brought recognition to this sprawling city at the confluence of the Gila and Colorado Rivers. It's also the birthplace of farmworker organizer César Chávez and the winter camp of some 70,000 snowbirds craving Yuma's sunny skies, mild temperatures and cheap RV park living. There ain't too much here for the rest of us to ease off the gas pedal, although recent efforts to revitalize the snug historic downtown have met with some success.
#### Sights
Yuma Territorial Prison
State Historic Park HISTORIC SITE
( 928-783-4771; www.azstateparks.com; 1 Prison Hill Rd; adult/child/under 7 $5/$2/free; 9am-5pm) Hunkered on a bluff overlooking the Colorado River, this infamous prison is Yuma's star atttraction, and its colorful past is engagingly illuminated in exhibits across the grounds. Between 1876 and 1909, 3069 convicts were incarcerated here for crimes ranging from murder to 'seduction under the promise of marriage.' The small museum is fascinating, with photos and descriptions of individual inmates and their offenses, including a display devoted to the 29 women jailed here. Walking around the yard, behind iron-grille doors and into cells crowded with stacked bunks, you might get retroactively scared straight. Don't miss the Dark Cell, a cave-like room where troublesome prisoners were locked together in a 5ft-high metal cage.
Yuma Quartermaster
Depot State Park HISTORIC SITE
( 928-329-0471; www.azstateparks.com; 201 N 4th Ave; 9am-5pm) Decades before the jail was built, Yuma became a crucial junction in the military supply lines through the West. Its role in getting gear and victuals to the troops is commemorated at the low-key quartermaster depot, set around a manicured green lawn.
Yuma Art Center GALLERY
( 928-329-6607; www.yumafinearts.org; 254 SMain St; 10am-6pm Tue-Thu, 10am-7pm Fri, 10am-5pm Sat) This welcoming downtown spot sells contemporary art in four galleries. It's next to the beautifully restored 1911 Historic Yuma Theater, which hosts concerts and theater from November to March.
#### Sleeping & Eating
Yuma has plenty of chain hotels, mostly around exit 2 off the I-8.
Best Western Coronado
Motor Hotel MOTEL $$
( 928-783-4453; www.bestwestern.com; 233 4th Ave; r incl breakfast $90-110; ) Red-tile roof, bright turquoise doors and newly upgraded rooms with flat-screen TVs – the oldest Best Western in the world doesn't feel old at all. You also get two swimming pools and a sit-down breakfast. Some rooms have kitchenettes, there are several laundry rooms and kids under 13 stay free.
Yuma Cabaña MOTEL $
( 928-783-8311; www.yumacabana.com; 2151 4th Ave; r $40-54, ste $70; ) The hallways are Soviet-bloc institutional, but rooms are cozy, clean and quiet, and the front desk is welcoming and helpful. Some rooms have plush sitting areas and kitchenettes. It's definitely one of the best-value places in town. Pets $6 per day. No wi-fi, but rooms are wired if your laptop is cable-ready.
Lutes Casino AMERICAN $
( 928-782-2192; www.lutescasino.com; 221 S Main St; mains under $10; 10am-8pm Mon-Thu, 10am-9pm Fri & Sat, 10am-6pm Sun) Lutes is awesome! If you're in town to see the prison, stop here for lunch afterwards. And note that the word casino is misleading – you won't find slots or poker at this 1940s-era hang-out, just a warehouse-big gathering spot filled with attic-like treasures hanging from the ceiling, old-school domino players, movie and advertising memorabilia, a dude playing the piano and a true cross-section of the town. To show you're in the know, order the 'especial' – a burger topped with a sliced hot dog. Antacid not included.
River City Grill FUSION $$
( 928-782-7988; www.rivercitygrillyuma.com; 600 W 3rd St; lunch $7-11, dinner $14-26; lunch Mon-Fri, dinner daily; ) Chic, funky and gourmet, with a shaded outdoor patio in back, the River has scrumptious crab cakes and brie-stuffed chicken, as well as mouthwatering vegetarian mains. Come here for a snappy weekday lunch or romantic dinner for two.
Da Boyz Italian Cuisine ITALIAN $$
( 928-783-8383; 284 S Main St; dishes $8-18; lunch & dinner; ) We're not crazy about da name, but this stylish downtown Italian eatery with big burgundy booths works well for a variety of travelers: solos, couples and girlfriends on getaways. It's also good family value. Look for filling gourmet pizzas and platters of pasta, plus a decent wine list.
#### Information
For maps and information, stop by the visitor center ( 928-783-0071; www.visityuma.com; 201 N 4th Ave; 9am-5pm) at its new location beside Yuma Quartermaster Depot State Park.
#### Getting There & Away
Yuma Airport ( 928-726-5882; www.yumainternationalairport.com; 2191 32nd St) has flights to Phoenix and Los Angeles. Greyhound ( 928-783-4403; 170 E 17 Pl) runs two buses daily to Phoenix ($42-54, 3¾ hours), while Amtrak's _Sunset Limited_ stops briefly at Yuma station (281 S Gila St) thrice weekly on its run between Los Angeles ($77, six hours) and New Orleans ($138, 41 hours).
## SOUTHERN ARIZONA
This is a land of Stetsons and spurs, where cowboy ballads are sung around the campfire and thick steaks sizzle on the grill. It's big country out here, beyond the confines of bustling college-town Tucson, where long, dusty highways slide past rolling vistasand steep, pointy mountain ranges. A place where majestic saguaro cacti, the symbolof the region, stretch out as far as the eye can see. Some of the Wild West's most classic tales were begot in small towns like Tombstone and Bisbee, which still attract tourists by the thousands for their Old West vibe. The desert air is hot, sweet and dry by day, cool and crisp at night. This is a land of stupendous sunsets; a place where coyotes still howl under starry, black-velvet skies.
### Tucson
An energetic college town, Tucson ( _too_ -sawn) is attractive, fun-loving and one of the most culturally invigorating places in the Southwest. Set in a flat valley hemmed in by craggy, odd-shaped mountains, Arizona's second-largest city smoothly blends Native American, Spanish, Mexican and Anglo traditions. Distinct neighborhoods and 19th-century buildings give a rich sense of community and history not found in the more modern and sprawling Phoenix. This is a town rich in Hispanic heritage (more than 40% of the population is Hispanic), so Spanish slides easily off most tongues and high-quality Mexican restaurants abound. The eclectic shops toting vintage garb, scores of funky restaurants and dive bars don't let you forget Tucson is a college town at heart, home turf to the 38,000-strong University of Arizona (UA).
Although it's fun to wander around the colorful historic buildings and peruse the shops, Tucson's best perks are found outside town. Whether you yearn to hike past giant cacti in the beautiful Saguaro National Park, watch the sun set over the rugged Santa Catalina Mountains or check out the world-class Arizona-Sonora Desert Museum, straying beyond the city limits is worth it.
Tucson lies mainly to the north and east of I-10 at its intersection with I-19, which goes to the Mexican border at Nogales. Downtown Tucson and the main historic districts are east of I-10 exit 258 at Congress St/Broadway Blvd, a major west–east thoroughfare. Most west–east thoroughfares are called streets, while most north–south thoroughfares are called avenues (although there is a sprinkling of roads and boulevards). Stone Ave, at its intersection with Congress, forms the zero point for Tucson addresses. Streets are designated west and east, and avenues north and south, from this point.
#### Sights & Activities
Most of Tucson's blockbuster sights, including the Saguaro National Park and the Arizona-Sonora Desert Museum, are on the city outskirts. The downtown area and 4th Ave near the university are compact enough for walking. Opening hours for outdoor attractions may change seasonally, typically opening at an earlier hour during the hot summer.
For avid explorers, the Tucson Attractions Passport ($15) may be a ticket to savings. It's available through www.visittucson.org/visitor/attractions/passport or at the visitor center and entitles you to two-for-one tickets and other discounts at dozens of major museums, attractions, tours and parks throughout southern Arizona.
Metropolitan Tucson
Sights
1 Aerospace Maintenance & Regeneration Center C3
2 Arizona-Sonora Desert Museum A3
3 Gates Pass Scenic Overlook B3
4 Mission San Xavier del Bac B4
5 Old Tucson Studios A3
6 Pima Air & Space Museum C4
7 Sabino Canyon C2
Activities, Courses & Tours
8 Mt Lemmon Ski Area D1
Sleeping
9 Desert Trails B&B D3
10 Gilbert Ray Campground A3
11 Hacienda del Sol C2
Eating
Grill at Hacienda del Sol (see 11)
12 Janos C2
13 Tiny's Saloon & Steakhouse B3
##### DOWNTOWN TUCSON
Downtown Tucson has a valid claim to being the oldest urban space in Arizona. Although spates of construction have marred the historical facade, this is still a reasonably walkable city center.
Tucson Museum of Art
& Historic Block MUSEUM
( 520-624-2333; www.tucsonmuseumofart.org; 140 Main Ave; adult/child/student/senior $8/free/3/6; 10am-4pm Tue-Sat, noon-4pm Sun) For a small city, Tucson boasts an impressive art museum. There's a respectable collection of Western and contemporary art, and the permanent exhibition of pre-Columbian artifacts will awaken your inner Indiana Jones. A superb gift shop rounds out the works. First Sunday of the month is free.
Presidio Historic District NEIGHBORHOOD
(www.nps.gov/nr/travel/amsw/sw7.htm) The Tucson Museum of Art is part of this low-key neighborhood, which embraces the site of the original Spanish fort and a ritzy residential area once nicknamed 'Snob Hollow.' This is (per current historical knowledge) one of the oldest inhabited places in North America. The Spanish Presidio de San Augustín del Tucson dates back to 1775, but the fort itself was built over a Hohokam site that has been dated to AD 700–900. The original fort is completely gone, although there's a short reconstructed section at the corner of Church Ave and Washington St.
The historical district teems with adobe townhouses and restored 19th-century mansions. Shoppers should steer towards Old Town Artisans (www.oldtownartisans.com; 201 N Court Ave), a block-long warren of adobe apartments filled with galleries and crafts stores set around a lush and lovely courtyard cafe (this use of an enclosed courtyard comes from Andalucia in southern Spain by way of North Africa). The area is bounded by W 6th St, W Alameda St, N Stone Ave and Granada Ave.
Fox Theatre HISTORIC BUILDING
( 520-624-1515; www.foxtucsontheatre.org; 17 W Congress St) This renovated art-deco theater on Congress St downtown is a 1930s beauty with fluted golden columns, water fountains and a giant sunburst mural radiating from the ceiling.
Barrio Histórico District/
Barrio Viejo NEIGHBORHOOD
This compact neighborhood was an important business district in the late 19th century. Today it's home to funky shops and galleries in brightly painted adobe houses. The Barrio centers on 100 S Stone Ave and is bordered by I-10, Stone Ave and Cushing and 17th St.
4th Avenue NEIGHBORHOOD
(www.fourthavenue.org) Linking historic downtown and the university, lively 4th Ave is a rare breed: a hip yet alt-flavored strip with a neighborhood feel and not a single chain store or restaurant, oops, except for Dairy Queen. The stretch between 9th St and University Blvd is lined with buzzy restaurants, coffee houses, bars, galleries, tattoo parlors, indie boutiques and vintage stores of all stripes.
Under the overpass that crosses 4th Ave and Broadway is the Tucson Portrait Project (www.tucsonportraitproject.com), one of our favorite public art projects anywhere. This wall-to-wall mosaic of about 7000 Tucsonian faces is a simple yet powerful testament to the diversity of the city's population.
The best time to visit 4th Ave is during the two annual street fairs held for three days in mid-December and late March or early April. See the 4th Ave website for details.
##### UNIVERSITY OF ARIZONA
Good university campuses manage to integrate the landscape into the learning space, and the UA campus is no exception. Rather than being a collection of public greens, it seamlessly integrates the desert – although there are some soft lawns for the students to lounge around on. There are several excellent museums on campus.
Arizona State Museum MUSEUM
( 520-621-6302; www.statemuseum.arizona.edu; 1013 E University Blvd; adult/child $5/free; 10am-5pm Mon-Sat) The oldest and largest anthropology museum in the Southwest provides a fantastic introduction to the history and culture of 10 regional NativeAmerican tribes. The main permanent exhibit about the tribes' cultural history is extensive, but easy to navigate and good for newbies and history buffs alike. These galleries are complemented by much-envied collections of minerals and Navajo textiles. Don't miss the impressive Wall of Pots and take a peek into the climate-controlled Pottery Vault (the museum has more than 20,000 whole vessels).
Tucson
Top Sights
Arizona State Museum B3
Center for Creative Photography B3
Sights
1Reid Park Zoo C4
2University of Arizona Museum of Art B3
Sleeping
3Arizona Inn B3
4Catalina Park Inn A3
5Flamingo Hotel A3
6Lodge on the Desert C3
Windmill Inn at St Philips Plaza (see 15)
Eating
7Lovin' Spoonfuls B2
8Mi Nidito A4
9Pasco Kitchen & Lounge A3
10Yoshimatsu B2
Drinking
11Nimbus Brewing Company C5
Entertainment
12Loft Cinema C3
Shopping
13Bookmans B2
14Native Seeds/SEARCH B1
15St Philips Plaza B1
Center for Creative Photography MUSEUM
(CCP; 520-621-7968; www.creativephotography.org; 1030 N Olive Rd; donations appreciated; 9am-5pm Mon-Fri, 1-4pm Sat & Sun) The CCP is known for its ever-changing, high-caliber exhibits and for administering the archives of Ansel Adams, perhaps the best-regarded landscape photographer in American history. The museum closes down between exhibits for an extended period, so check the website before visiting.
University of Arizona Museum of Art MUSEUM
( 520-621-7567; www.artmuseum.arizona.edu; 1031 Olive Rd; adult/child $5/free; 9am-5pm Tue-Fri, noon-4pm Sat & Sun) Across the road from the CCP, peruse 500 years of European and American paintings and sculpture. The permanent collection features such heavy hitters as Rodin, Matisse, Picasso and Pollock.
##### AROUND TUCSON
Several of Tucson's best attractions are about 15 miles west of the University. For a scenic, saguaro-dotted drive, follow Speedway Blvd west until it turns into W Gate Pass Rd. As you approach the top of Gates Pass, turn right into the Gates Pass Scenic Overlook where you'll have a sweeping view of the west that is especially nice at sunset.
Arizona-Sonora Desert Museum MUSEUM
( 520-883-1380; www.desertmuseum.org; 2021 N Kinney Rd; adult/child $14.50/4.50 Sep-May, $12/3 Jun-Aug; 8:30am-5pm Oct-Feb, 7:30am–5pm Mar–May, 7am–4:30pm Jun–Sep, to 10pm Sat Jun–Aug) Home to cacti, coyotes and super-tiny hummingbirds, this ode to the Sonoran desert is one part zoo, one part botanical garden and one part museum –a trifecta that'll keep young and old entertained for easily half a day. All sorts of desert denizens, from precocious coatis to playful prairie dogs, make their home in natural enclosures hemmed in by invisible fences. The grounds are thick with desert plants, and docents are on hand to answer questions and give demonstrations. There are two walk-through aviaries, a mineral exhibit inside a cave (kids love that one), a half-mile desert trail and an underground exhibit with windows into ponds where beavers, otters and ducks frolic. Strollers and wheelchairs are available, and there's a gift shop, art gallery, restaurant and cafe. A tip: wear a hat and walking shoes, and remember that the big cats are most active in the morning.
The museum is off Hwy 86, about 12 miles west of Tucson, near the western section of Saguaro National Park.
### WHEN YOU WISH UPON A LOVE TRIANGLE
In Barrio Histórico look for El Tiradito (356 S Main Ave), a 'wishing shrine' with a tale of passion and murder behind it. Locals say that in the 19th century a young man fell for his wife's mother. Her husband – his father-in-law – killed the young man. The dead lover was never absolved of his sins, and was thus turned away from the consecrated ground at the nearby Roman Catholic church, so he was buried under the front porch of the house that marks the spot of El Tiradito. Local folks took pity on the young man and began offering prayers and burning candles at the site; over time, El Tiradito became a shrine anyone would pray at to commemorate a lost loved one. The _Phoenix New Times_ ran a story that claimed El Tiradito was the only Catholic shrine in the country dedicated to a sinner buried in unconsecrated ground.
Saguaro National Park PARK
( 520-733-5100; www.nps.gov/sagu; 7-day pass per vehicle/bicycle $10/5; 7am-sunset) If you'restanding beside a docent at this cacti-filled park, don't refer to the limbs of the saguaro (sah- _wah_ -ro) as branches. As the docent will quickly tell you, the mighty saguaro grows _arms_ , not lowly branches – a distinction that makes sense when you consider their human-like features. They shake your hand, wave at you or draw a gun on you. They are also the most iconic symbol of the American Southwest, and an entire army of these majestic ribbed sentinels is protected in this national park. Their foot soldiers are the spidery ocotillo, the fluffy teddy bear cactus, the green-bean-like pencil cholla and hundreds of other plant species.
Central Tucson
Top Sights
El Tiradito A4
Tucson Museum of Art & Historic Block 0 A2
Sights
1Tucson Children's Museum C3
Sleeping
2El Presidio Bed & Breakfast Inn A2
3Hotel Congress C2
4Roadrunner Hostel & Inn D3
Eating
5Bison Witches D2
6Cafe Poca Cosa C2
7El Charro Café A1
8Hub Restaurant & Creamery C3
Drinking
9Che's Lounge D1
10Chocolate Iguana D1
11Surly Wench D1
Entertainment
Club Congress (see 3)
12Fox Theatre B3
13Plush D1
14Rialto Theatre C3
15Temple of Music & Art C4
16Tucson Music Hall A3
Shopping
17Antigone Books D1
18Food Conspiracy Cooperative D1
19Old Town Artisans A2
Saguaros grow slowly, taking about 15 yearsto reach a foot in height, 50 years to reach 7ft and almost a century before they begin to take on their typical many-armed appearance. The best time to visit is April, when the saguaros begin blossoming with lovely white blooms – Arizona's state flower. By June and July, the flowers give way to ripe red fruit that local Native Americans use for food.
Saguaro National Park is divided into two units separated by 30 miles and the city of Tucson. Both are equally rewarding and it's not necessary to visit them both. Note that trailers longer than 35ft and vehicles wider than 8ft are not permitted on the park'snarrow scenic loop roads.
The larger section is the Rincon Mountain District, about 15 miles east of downtown. The visitor center ( 520-733-5153; 3693 S Old Spanish Trail; 9am-5pm) has information on day hikes, horseback riding and backcountry camping. The latter requires a permit ($6 per site per day) and must be obtained by noon on the day of your hike. The meandering 8-mile Cactus Forest Scenic Loop Drive, a paved road open to cars and bicycles, provides access to picnic areas, trailheads and viewpoints.
Hikers pressed for time should follow the 1-mile round-trip Freeman Homestead Trail to a grove of massive saguaro. For a full-fledged desert adventure, head out on the steep and rocky Tanque Verde Ridge Trail, which climbs to the summit of Mica Mountain at 8666ft and back in 18 miles (backcountry camping permit required).
West of town, the Tucson Mountain District has its own visitor center ( 520-733-5158; 2700 N Kinney Rd; 9am-5pm). The Scenic Bajada Loop Drive is a 6-mile graded dirt road through cactus forest that begins 1.5 miles north of the visitor center. Two quick, easy and rewarding hikes are the 0.8-mile Valley View Overlook (awesome at sunset) and the half-mile Signal Hill Trail to scores of ancient petroglyphs. For a more strenuous trek we recommend the 7-mile King Canyon Trail, which starts 2 miles south of the visitor center near the Arizona-Sonora Desert Museum. Distances for all three hikes are round-trip.
Old Tucson Studios FILM LOCATION
( 520-883-0100; www.oldtucson.com; 201 S Kinney Rd; adult/child $17/11; 10am-6pm Oct-May, 10am-6pm Fri-Sun Jun-Sep) Nicknamed 'Hollywood in the Desert,' this old movie set of Tucson in the 1860s was built in 1939 for the filming of _Arizona_. Hundreds of flicks followed, bringing in an entire galaxy of stars, including Clint Eastwood, Harrison Ford and Leonardo DiCaprio. Now a Wild West theme park, it's mostly mom, pop, buddy and sis who are shuffling down its dusty streets. Shootouts, stagecoach rides, saloons, sheriffs and stunts are all part of the hoopla. The studios are a few miles southeast of the Arizona-Sonora Desert Museum off Hwy 86.
Pima Air & Space Museum MUSEUM
( 520-574-0462; www.pimaair.org; 6000 E Valencia Rd; adult/child/senior & military $13.75/8/11.75 Jun-Oct, $15.50/9/12.75 Nov-May; 9am-5pm, last admission 4pm) An SR-71 Blackbird spy plane, JFK's Air Force One and a massive B-52 bomber are among the stars of this extraordinary private aircraft museum. Allow at least two hours to wander through hangars and around the airfield where more than 300 'birds' trace the evolution of civilian and military aviation. If that's too overwhelming, consider joining the free 50-minute walking tour offered at 10:30am or 11:30am daily (1:30pm & 2:30pm December to April) or shell out an extra $6 for the one-hour tram tour departing at 10am, 11:30am, 1:30pm and 3pm.
Hardcore plane-spotters should call ahead to book space on the 90-minute bus tour of the nearby 309th Aerospace Maintenance & Regeneration Center (adult/child $7/4; Mon-Fri, departure times vary seasonally) – aka the boneyard – where almost 4000 aircraft are mothballed in the dry desert air. You don't need to pay museum admission to join this tour.
##### SANTA CATALINA MOUNTAINS
The Santa Catalinas northeast of Tucson are the best-loved and most visited among the region's mountain ranges. You need a Coronado Forest Recreation Pass ($5 per vehicle per day) to park anywhere in the mountain area. It's available at the USFS Santa Catalina Ranger Station ( 520-749-8700; www.fs.fed.us/r3/coronado; 5700N Sabino Canyon Rd; 8am-4:30pm) at the mouth of Sabino Canyon, which also has maps, hiking guides and camping information.
Sabino Canyon (www.sabinocanyon.com; 5900 N Sabino Canyon Rd), a lush, pretty and shaded mini-gorge, is a favorite year-round destination for both locals and visitors. Narrated hop-on, hop-off tram tours along the Sabino Canyon Trail ( 520-749-2861; www.sabinocanyon.com; adult/child $8/4) depart every half hour for a 45-minute, nine-stop loop with access to trailheads and riverside picnic areas. It's nicest in the afternoon, when the sun plays hide and seek against the canyon walls. The last stop is only 3.8 miles from the visitor center, so hikers can listen to the tram driver's narration on the way up then hike back to the visitor center, either on the road or on the lofty but exposed Telephone Line Trail. A non-narrated shuttle (adult/child $3/1) provides access to Bear Canyon and the trailhead to Seven Falls, which has picnic sites and swimming but no facilities. From the falls, the trail continues up as high as you want to go.
A great way to escape the summer heat is by following the super-scenic Sky Island Parkway (officially called Catalina Hwy), which meanders 27 miles from saguaro-dappled desert to pine-covered forest near the top of Mt Lemmon (9157ft), passing through ecosystems equivalent to a journey from Mexico to Canada. Budget at least three hours round-trip. Of the vista points, Babad Do'ag and Aspen are the most rewarding. There is no cost for the drive, but if you plan to explore the forest you must pay for the aforementioned $5 day-use permit, which can be purchased at the Forest Service fee station on the ascent.
In winter, Mt Lemmon has the southernmost ski area ( 520-576-1321; 10300 Ski Run Rd, Mt Lemmon; adult/child $37/20; late Dec-Mar) in the USA. With snow levels rather unpredictable, it's more about the novelty of schussing down the slopes with views of Mexico than having a world-class alpine experience. Rentals, lessons and food are available on the mountain.
#### Festivals & Events
Tucson knows how to party and keeps a year-round schedule of events. For details check out www.visittucson.org/visitor/events/majorevents.
Fiesta de los Vaqueros RODEO
(Rodeo Week; 520-741-2233; www.tucsonrodeo.com) Held the last week of February for over 85 years, the Fiesta brings world-famous cowboys to town and features a spectacular parade with Western-themed floats and buggies, historic horse-drawn coaches, folk dancers and marching bands.
Tucson Folk Festival MUSIC
(www.tkma.org) Held in early May, this music festival with more than 100 local, regional and national performers is put on by the Tucson Kitchen Musicians Association.
Tucson Gem and Mineral Show MINERAL SHOW
( 520-332-5773; www.tgms.org) This is the most famous event on the city's calendar, held on the second full weekend in February. It's the largest of its kind in the world, and an estimated 250 retail dealers who trade in minerals, crafts and fossils take over the Tucson Convention Center.
### TUCSON FOR CHILDREN
A global menagerie including giant anteaters and a Malayan Tiger delights young and old at the small and compact Reid Park Zoo ( 520-791-4022; www.tucsonzoo.org; 1100 S Randolph Way; adult/child/senior $7/3/5; 9am-4pm Sep-May, 8am-3pm Jun-Aug; ). Cap a visit with a picnic in the surrounding park, which also has playgrounds and a pond with paddleboat rentals.
Parents also sing the praises of the Tucson Children's Museum ( 520-792-9985; www.childrensmuseumtucson.org; 200 S 6th Ave; adult/child $8/6; 9am-8pm Mon, 9am-5pm Tue-Fri, 10am-5pm Sat & Sun Jun-Aug, closed Mon Sep-May; ), which has plenty of engaging, hands-on exhibits – from Dinosaur World to an aquarium.
#### Sleeping
Tucson's gamut of lodging options rivals Phoenix for beauty, comfort and location. Rates plummet as much as 50% between June and September, making what would otherwise be a five-star megasplurge an affordable getaway. If it's quaintness you're after, you'll love the old-time mansions resuscitated as B&Bs in the historic downtown district. Chains are abundant along the I-10 and around the airport.
Catalina Park Inn B&B $$
( 520-792-4541; www.catalinaparkinn.com; 309 E 1st St; r $140-170; ; closed Jul & Aug) Style, hospitality and comfort merge seamlessly at this inviting B&B just west of the University of Arizona and 4th Ave. Hosts Mark Hall and Paul Richard have poured their hearts into restoring this 1927 Mediterranean-style villa, and their efforts are on display in each of the six rooms, from the oversized and over-the-top peacock-blue-and-gold Catalina Room to the white and uncluttered East Room with iron canopy bed. The cacti-and-desert garden has lots of little corners for lazy afternoon cat naps.
Arizona Inn RESORT $$$
( 520-325-1541, 800-933-1093; www.arizonainn.com; 2200 E Elm St; r $259-333, ste $379-449; ) The historic feel of this resort provides a definite sense of being one of the aristocracy. The mature gardens and old Arizona grace provide a respite not only from city life but also from the 21st century. Sip coffee on the porch, take high tea in the library, lounge by the small pool or join in a game of croquet, then retire to rooms furnished with antiques. The on-site spa is our favorite in town.
Hacienda del Sol HISTORIC INN $$$
( 520-299-1501; www.haciendadelsol.com; 5501 N Hacienda del Sol Rd; r $195-300, ste $355-515; ) An elite, hilltop girls' school built in the 1920s, this relaxing refuge has artist-designed Southwest-style rooms and teems with unique touches like carved ceiling beams and louvered exterior doors to catch the courtyard breeze. Having been on the radar of Spencer Tracy, Katharine Hepburn and other legends, you'll know you're sleeping with history. Fabulous restaurant, too.
Hotel Congress HISTORIC HOTEL $$
( 520-622-8848; www.hotelcongress.com; 311 E Congress St; r $90-120; ) This beautifully restored 1919 hotel is a bohemianvintage beauty and a beehive of activity, mostly because of its popular cafe, bar and club. Infamous bank robber John Dillinger and his gang were captured here during their 1934 stay when a fire broke out at the hotel. Many rooms have period furnishings, rotary phones and wooden radios – but no TVs. Ask for a room at the far end of the hotel if you're noise-sensitive. Pets are $10 per night.
Flamingo Hotel MOTEL $
( 520-770-1910; www.flamingohoteltucson.com; 1300 N Stone Ave; r incl breakfast $60-105; ) The Flamingo is a top budget option, offering snazzy style, a convenient location near the University and a pretty darn good breakfast. Though recently purchased by the Quality Inn chain, it retains a lot of its great 1950s Rat Pack vibe, and the fact that Elvis slept here doesn't hurt. Rooms come with chic striped bedding, flat-screen plasma TVs, a good-sized desk and comfy beds. Pets are $20 per day. One drawback? Wi-fi can be a bit unreliable in the rooms.
Windmill Inn at St Philips Plaza HOTEL $$
( 520-577-0007; www.windmillinns.com; 4250 N Campbell Ave; r incl breakfast $120-134; ) Popular with University of Arizona fans during football season, this modern, efficient and friendly place wins kudos for spacious two-room suites (no charge for kids under 18), free continental breakfast, lending library, heated pool and free bike rentals. We couldn't shake the smell of baby powder, but really, who cares when cookies are served at 4pm?
El Presidio Bed & Breakfast Inn B&B $$
( 520-623-6151; www.bbonline.com/az/elpresidio; 297 N Main Ave; ste incl breakfast $125-155; ) The southern hospitality at this inviting hideaway sets it apart from its peers, and that's without mentioning the stunning, flower-infused central courtyard. Rooms in this 1886 Victorian adobe mansion in the Presidio Historic District reflect the regional history and style – look for fresh flowers, quilted beds and fine china. Each of the four units has a separate sitting room and two have kitchenettes. Days start with a full breakfast and end with complimentary drinks and snacks.
Desert Trails B&B B&B $$
( 520-885-7295; www.deserttrails.com; 12851 E Speedway Blvd; r incl breakfast $130-160, guesthouse $165; ) Outdoorsy types who want a personable B&B close to Saguaro National Park (Rincon Mountain District) have their answer at Desert Trails on the far eastern fringe of Speedway Blvd. Rooms may not be as chic as those in some of the historic B&Bs in town, but they're welcoming just the same. Even better? Host John Higgins, an avid backpacker, was a fireman for Saguaro National Park for six years and is glad to share his knowledge about the park's trails.
Roadrunner Hostel & Inn HOSTEL $
( 520-940-7280; www.roadrunnerhostelinn.com; 346 E 12th St; dm/r incl breakfast $20/40; ) Cultural and language barriers melt faster than snow in the desert at this small and friendly hostel within walking distance of 4th Ave. The guest kitchen and TV lounge are convivial spaces and freebies include coffee, tea and a waffle breakfast. The 1900 adobe building once belonged to the sheriff involved in capturing the Dillinger gang at the Hotel Congress in 1934. Closed between noon and 3pm. No credit cards.
Lodge on the Desert BOUTIQUE HOTEL $$
( 520-320-2000, www.lodgeonthedesert.com; 306 N Alvernon Way; r $159-249, ste $199-329; ) Rooms in this gracefullyaging 1930s resort are in hacienda-style casitas flanked by cacti and palm trees, and decorated in charmingly modern Southwest style. Many units have beamed ceilings or fireplaces. Dogs are $25 per night per pet.
Gilbert Ray Campground CAMPGROUND $
( 520-877-6000; Kinney Rd; tent/RV sites $10/20) Camp among the saguaros at this Pima County campground 13 miles west of downtown. It has 130 first-come, first-served sites along with water, but no showers. There are five tent-only sites. No credit cards.
#### Eating
Tucson's cuisine scene delivers a flavor-packed punch in everything from family-run 'nosherias' to five-star dining rooms. Intricately spiced and authentic Mexican and Southwestern fare is king here, and much of it is prepared fresh with regional ingredients.
Cafe Poca Cosa SOUTH AMERICAN $$
( 520-622-6400; www.cafepocacosatucson.com; 110 E Pennington St; lunch $13-15, dinner $19-26; lunch & dinner Tue-Sat) At this award-winning nuevo-Mexican bistro a Spanish-English blackboard menu circulates between tables because dishes change twice daily. It's all freshly prepared, innovative and beautifully presented. The undecided can't go wrong by ordering the Plato Poca Cosa and letting chef Suzana D'avila decide. Great margaritas, too.
Pasco Kitchen & Lounge AMERICAN $$
( 520-882-8013; www.pascokitchen.com; 820 E University Blvd; mains $9-14 11am-10pm Mon-Wed, 11am-11pm Thu, 11am-1am Fri & Sat, 11am-4pm Sun) The farmers market salad with yard bird is superb at this breezy new eatery near the University. The menu offers fresh, locally sourced comfort food that's prepared with panache and a few tasty twists – think grass-fed all natural burgers topped by braised pork belly and a fried egg, or grits with catfish and fried okra. The owners call it urban farm fare; we call it delicious. Service can be a bit too easygoing, but that may be a first-year kink.
Janos SOUTHWESTERN $$$
( 520-615-6100; 3770 E Sunrise Dr; mains $20-50, tasting menu with wine $80; dinnerMon-Sat) French-trained James Beard Award-winner Janos Wilder is a veritable wizard in creating Southwestern compositions with that certain _je ne sais quoi_. His dining room at the Westin La Paloma overlooks the entire valley and is perfect for big, long, romanticmeals like grilled beef tenderloin with lobster tail and truffled Bordelaise.
Grill at Hacienda del Sol SOUTHWESTERN $$$
( 520-529-3500; www.haciendadelsol.com/dining; 5501 N Hacienda del Sol Rd; mains $24-40, Sunday brunch adult/child $35/18; dinner daily, brunch Sun) The sunset views compete with the smart, grown-up ambience, the Spanish Colonial decor and, of course, the exquisitely composed nouvelle Southwesterncuisine featuring herbs, veggies and fruit grown on site. Oenophiles have an extensive wine list to ponder. Reservations are required.
Mi Nidito MEXICAN $
( 520-622-5081; www.minidito.net; 1813 S 4th Ave; mains $6-13; lunch & dinner Wed-Sun) When it comes to Tucson's two most popular Mexican restaurants, El Charro may have more customers, but Mi Nidito can claim celebrities like Bill Clinton and Enrique Iglesias, plus a somewhat cozier location. Ol' Bill's order at 'My Little Nest' has become the signature president's plate, aheaping mound of Mexican favorites – tacos,tostadas, burritos, enchiladas and more – groaning under melted cheese. Give the prickly pear cactus chili or the _birria_ (spicy, shredded beef) a whirl. Solo diners beware –the loudspeaker will boldly announce your name followed by 'party of one' when they're ready for you.
Lovin' Spoonfuls VEGETARIAN $$
( 520-325-7766; 2990 N Campbell Ave; lunch $6-8, dinner $9-11; 9:30am-9pm Mon-Sat, 10am-3pm Sun; ) Burgers, country-fried chicken, meatloaf, salads – the menu reads like those at your typical cafe but there's one big difference: no animal products will ever find their way into this vegan haven. Outstandingly creative choices include the cashew-mushroom pâté and the adzuki-bean burger.
Tiny's Saloon & Steakhouse AMERICAN $
( 520-578-7700; 4900 W Ajo Hwy; mains $6-18; 10am-10pm, bar open to midnight Fri; ) See that cluster of motorcycles and pick-up trucks in the parking lot? That's your true-blue sign of approval right there. Inside, once your eyes adjust, slide into a booth, nod at the regulars at the bar then order a steerburger with a cold beer. And toast your good fortune. A docent at the Pima Air & Space Museum told us that Tiny's has the best burgers in town, and we think he might be right. Truth be told? For a saloon, Tiny's is actually family friendly – at least during the day – and makes a nice stop after a day at the Arizona-Sonora Desert Museum or Saguaro National Park. Cash only but ATM on-site.
Hub Restaurant & Creamery AMERICAN $$
( 520-207-8201; www.hubdowntown.com; 266 E Congress Ave; lunch $9-17, dinner $9-17 11am-2am) The Hub has injected Congress Ave with industrial-chic style: red brick walls, lofty ceiling, wooden floors and, coolest of all, a walk-up ice-cream stand beside the hostess desk. Upscale comfort food is the name of the game here, from ahi tuna casserole to chicken pot pie, plus a few sandwiches and salads. Even if you don't want a meal, pop in for a kickin' scoop of gourmet ice cream. Choices include salted caramel and bacon scotch.
Yoshimatsu JAPANESE $
( 520-320-1574; 2660 N Campbell Ave; mains $8-17; lunch & dinner; ) Billing itself as a healthy Japanese eatery, Yoshimatsu uses mostly organic foods, eschews MSG and offers lots of vegetarian and vegan options. Order a bento box, steamy soup or rice bowl at the counter and eat in the woodsy front tavern, or get table service at the separate and more intimate sushi cafe in back.
Bison Witches SANDWICHES $
( 520-740-1541; www.bisonwitches.com; 326 4th Ave; sandwiches $6-8; food 11am-midnight: bar to 2am) At this funky deli to and bar, everything's made fresh and with healthy ingredients like grilled meats, avocado and sprouts. In addition to sandwiches, there are a few salads on the menu. The back patio is more for the smoking and drinking crowd.
El Charro Café MEXICAN $$
( 520-622-1922; 311 N Court Ave; mains $7-18; lunch & dinner) In this rambling, buzzing hacienda the Flin family has been making innovative Mexican food since 1922. They're particularly famous for the _carne seca_ , sundried lean beef that's been reconstituted, shredded and grilled with green chile and onions. The fabulous margaritas pack a Pancho Villa punch.
Gus Balon's DINER $
( 520-747-7788; 6027 E 22nd St; mains $4-9; 7am-3pm Mon-Sat) Tucson's premier breakfast destination is a great place to fuel up if you're heading off to hike in Saguaro National Park's eastern district. Twenty-four types of pie and the cinnamon rolls are huge.
### HOT DIGGETY DOG
Tucson's signature dish is the Sonoran hotdog, a tasty example of what happens when Mexican ingredients meet American processed meat and penchant for excess. So what is it? A bacon-wrapped hotdog layered with tomatillo salsa, pinto beans, shredded cheese, mayo, ketchup, mustard, chopped tomatoes and onions. We like 'em at El Guero Canelo (www.elguerocanelo.com; 100 E Congress St).
#### Drinking & Entertainment
###### Bars & Coffee Shops
Nimbus Brewing Company BREWERY
( 520-745-9175; www.nimbusbeer.com; 3850 E 44th St; 11am-11pm Mon-Thu, 11am-1am Fri & Sat, 11am-9pm Sun) A cavernous purple warehouse space, here at Nimbus the brewmeisters make ale of every color in the spectrum. No matter what type you prefer, it's likely to be a smooth guzzle. The taproom is at the end of E 44th St, past all the industrial buildings.
Che's Lounge BAR
( 520-623-2088; 350 N 4th Ave) Drinkers unite! If everyone's favorite revolutionary heartthrob was still in our midst, he wouldn't have charged a cover either. A slightly skanky but hugely popular watering hole with $1 drafts, a huge wraparound bar and local art gracing the walls, this college hangout rocks with live music Saturday nights.
Surly Wench BAR
( 520-882-0009; www.surlywenchpub.com; 424 4th Ave) This bat cave of a watering hole is generally packed with pierced pals soaking up $1.50 beer, giving the pinball machine a workout or head-banging to deafening punk, thrash and alt-rock bands. Shows start at 10pm.
Chocolate Iguana COFFEE SHOP
(www.chocolateiguanaon4th.com; 500 N 4th Ave; 8am-10pm Mon-Thu, 7am-10pm Fri, 8am-10pm Sat, 9am-6pm Sun) Chocoholics have their pick of sweets and pastries inside this green-and-purple cottage, while coffee loverscan choose from eight different coffee brews and a long list of specialty drinks. Also sells sandwiches and gifts.
###### Nightclubs & Live Music
The free _Tucson Weekly_ has comprehensive party listings, but for downtown-specific info pick up the _Downtown Tucsonian_ , also gratis. Another good source is www.aznightbuzz.com. Congress St in downtown and 4th Ave near the University are both busy party strips.
Club Congress LIVE MUSIC
( 520-622-8848; www.hotelcongress.com; 311 E Congress St; cover $7-13) Skinny jeansters, tousled hipsters, aging folkies, dressed-up hotties – the crowd at Tucson's most-happening club inside the grandly aging Hotel Congress defines the word eclectic. And so does the musical line-up, which usually features the finest local and regional talent. Wanna drink at a bar? Step inside the adjacent Tap Room, open since 1919.
Rialto Theatre LIVE MUSIC
( 520-740-1000; 318 E Congress St; cover $16-46) This gorgeous 1920 vaudeville andmovie theater has been reborn as a top venue for live touring acts. Featuring everything from rock to hip-hop, flamenco to swing, plus the odd comedian; basically anyone too big to play at Club Congress across the street.
Plush LIVE MUSIC
( 520-798-1298; www.plushtucson.com; 340 E 6th St; cover $5) Plush is another club to watch when it comes to catching cool bands from LA, Seattle, Chicago and beyond. There's usually a line-up of two or three holding forth in the main room where the light is mellow and the sound is not. Head to the pub-style lounge in front to rest eardrums between sets. At the corner of 4th Ave and 6th St.
IBT's GAY CLUB
( 520-882-3053; 616 N 4th Ave; no cover) At Tucson's most sizzling gay fun house, the theme changes nightly – from drag shows to techno dance mixes to karaoke. Chill on the patio, check out the bods, or sweat it out on the dance floor.
###### Cinemas & Performing Arts
It's always worth checking out what's on at the deco Fox Theatre ( 520-547-3040; www.foxtucsontheatre.org; 17 W Congress St), a gloriously glittery venue for classic and modern movies, music, theater and dance.
For indie, art-house and foreign movies head to Loft Cinema ( 520-795-0844; www.loftcinema.com; 3233 E Speedway Blvd).
Check the online calendar for outdoor summer concerts at St Philips Plaza (www.stphilipsplaza.com; 4280 N Campbell Ave), typically on Friday and Sunday nights.
The Arizona Opera ( 520-293-4336; www.azopera.org) and Tucson Symphony Orchestra ( 520-792-9155; www.tucsonsymphony.org)perform between October and April at the Tucson Music Hall (260 S Church Ave). The Arizona Theatre Company ( 520-622-2823; www.arizonatheatre.org), meanwhile, puts on shows from September to April at the Temple of Music & Art (330 S Scott Ave), a renovated 1920s building.
#### Shopping
Old Town Artisans (201 N Court Ave) in the Presidio Historic District is a good destination for quality arts and crafts produced in the Southwest and Mexico. Also recommended is St Philips Plaza (4280 N Campbell Ave), where standouts include the Obsidian Gallery (www.obsidian-gallery.com) for art and jewelry and Bahti Indian Arts (www.bahti.com) for Native American wares.
For fun, eclectic shopping you can't beat 4th Ave, where there's a great cluster of vintage stores between 8th and 7th Sts. Food Conspiracy Cooperative (412 4th Ave, sandwiches $8-10) is great for stocking up on organic produce and products, while the Chocolate Iguana has an impressive array of chocolate candy, as well as cute gifts.
The special Native Seeds/SEARCH (www.nativeseeds.org; 3061 N Campbell Ave; 526 4th Ave), which recently moved from 4th Ave, sells rare seeds of crops traditionally grown by Native Americans, along with quality books and crafts.
###### Bookstores
Antigone BooksBOOKS
(411 N 4th Ave; www.antigonebooks.com; 10am-7pm Mon-Thu, 10am-9pm Fri & Sat, noon-5pm Sun) Great indie bookstore with a fun, girl-power focus.
Bookmans BOOKS
(www.bookmans.com; 1930 E Grant Rd; 9am-10pm; ) Well-stocked Arizona indie chain and locals' hangout.
#### Information
###### Emergency
Police ( 520-791-4444; http://cms3.tucsonaz.gov; 270 S Stone Ave)
###### Media
The local mainstream newspapers are the morning _Arizona Daily Star_ (http://azstarnet.com) and the afternoon _Tucson Citizen_ (http://tucsoncitizen.com). The free _Tucson Weekly_ (www.tucsonweekly.com) is chock-full of great entertainment and restaurant listings. _Tucson Lifestyle_ (www.tucsonlifestyle.com) is a glossy monthly mag. Catch National Public Radio (NPR) on 89.1.
###### Medical Services
Tucson Medical Center ( 520-327-5461; www.tmcaz.com/TucsonMedicalCenter; 5301 E Grant Rd) 24-hour emergency services.
###### Post
Post office ( 520-629-9268; 825 E University Blvd, Suite 111; 8am-5pm Mon-Fri, 9am-12:30pm Sat)
###### Tourist Information
Coronado National Forest Supervisor's Office ( 520-388-8300; www.fs.fed.us/r3/coronado; Federal Bldg, 300 W Congress St; 8am-4:30pm Mon-Fri) Provides information on trekking and camping in Coronado National Forest.
Tucson Convention & Visitors Bureau ( 520-624-1817, 800-638-8350; www.visittucson.org; 100 S Church Ave; 9am-5pm Mon-Fri, to 4pm Sat & Sun) Ask for its free _Official Destination Guide_.
#### Getting There & Away
Tucson International Airport ( 520-573-8100; www.flytucsonairport.com) is 15 miles south of downtown and served by eight airlines, with nonstop flights to five destinations including Las Vegas, Los Angeles, San Francisco and Atlanta.
Greyhound ( 520-792-3475; www.greyhound.com; 471 W Congress St) and its partners run up to nine direct buses to Phoenix ($20-27.25, two hours), among other destinations.
The _Sunset Limited_ train, operated by Amtrak ( 800-872-7245; www.amtrak.com; 400 E Toole Ave), comes through on its way west to Los Angeles ($62, 10 hours, three weekly) and east to New Orleans ($173, 36 hours, three weekly).
#### Getting Around
All major car-rental agencies have offices at the airport. Arizona Stagecoach ( 520-889-1000; www.azstagecoach.com) runs shared-ride vans into town for about $29 per person. A taxi from the airport to downtown costs around $25 to $27. Taxi companies include Yellow Cab ( 520-624-6611; www.yellowcabtucson.com) and Allstate Cab ( 520-881-2227).
The Ronstadt Transit Center (215 E Congress St, cnr Congress St & 6th Ave) is the main hub for the public Sun Tran ( 520-792-9222; www.suntran.com) buses serving the entire metro area. Fares are $1.50, or $3.50 for a day pass.
### Tucson to Phoenix
If you just want to travel between Arizona's two biggest cities quickly, it's a straight 120-mile shot on a not terribly inspiring stretch of the I-10. However, a couple of rewarding side trips await those with curiosity and a little more time on their hands.
Picacho Peak State ParkSTATE PARK
( 520-466-3183; http://azstateparks.com; I-10,exit 219; per vehicle $7 mid-Sep–late May; 5am-9pm) Distinctive Picacho Peak (3374ft) sticks out from the flatlands like a desert Matterhorn, about 40 miles northwest of Tucson. The westernmost battle of the American Civil War was fought in this area, with Arizonan Confederate troops killing two or three Union soldiers before retreating to Tucson and dispersing, knowing full well that they would soon be greatly outnumbered. The battle is reenacted every March with much pomp, circumstance and period costumes.
The pretty state park has a visitor center ( 8am-5pm) that acts as a jump-off point for trails onto the mountain. If you're fit, you can walk to the peak of the mountain via a rugged trail that includes cables and catwalks. Camping (campsites $25) is available at 85 electric, first-come, first-served sites; suitable for tents or RVs.
Biosphere 2BIOSPHERE
( 520-838-6200; www.b2science.org; 32540 S Biosphere Rd, Oracle; adult/child/senior $20/13/18; 9am-4pm) Built to be completelysealed off from Biosphere 1 (that would be Earth), Biosphere 2 is a 3-acre campus of glass domes and pyramids containing five ecosystems: tropical ocean, mangrove wetlands, tropical rainforest, savannahand coastal fog desert. In 1991, eight biospherians were sealed inside for a two-year tour of duty from which they emerged thinner but in pretty fair shape. Although this experiment was ostensibly a prototype for self-sustaining space colonies, the privately funded endeavor was engulfed in controversy. Heavy criticism came after the dome leaked gases and was opened to allow a biospherian to emerge for medical treatment. After several changes in ownership, the sci-fi-esque site is now a University of Arizona-run earth science research institute. Public tours take in the biospherians' apartments, farm area and kitchen, the one-million gallon 'tropical ocean' and the 'technosphere' that holds the mechanics that made it all possible.
Biosphere 2 is near Oracle, about 30 miles north of Tucson via Hwy 77 (Oracle Rd) or 30 miles east of the I-10 (exit 240, east on Tangerine Rd, then north on Hwy 77). No pets.
Casa Grande Ruins
National MonumentNATIONAL MONUMENT
( 520-723-3172; www.nps.gov/cagr; 1100 W Ruins Dr, Coolidge; adult/child $5/free; 9am-5pm) Built around AD 1350, Casa Grande (Big House) is the country's largest Hohokam structures still standing, with 11 rooms spread across four floors and mud walls several feet thick. Preserved as a national monument it's in reasonably good shape, partly because of the metal awning that's been canopying it since 1932. Although you can't walk inside the crumbling structure, you can peer into its rooms. A few strategically placed windows and doors suggest that the structure may have served as an astronomical observatory. The ball court is one of more than 200 that have been found in major Hohokam villages throughout the region. Experts aren't 100% sure of the purpose of these oval pits, but they may be linked to similar courts used for ball games by the Aztecs.
The visitor center has exhibits about the Hohokam society and Casa Grande itself, including a model of what the place may have originally looked like. Ranger-led 30-minute tours are available between December and April. Call for times.
The ruins are about 70 miles northwest of Tucson. Leave the I-10 at exit 211 and head north on Hwy 87 towards Coolidge and follow the signs. Don't confuse the monument with the modern town of Casa Grande, west of the I-10.
### West of Tucson
West of Tucson, Hwy 86 cuts like a machete through the Tohono O'odham Indian Reservation, the second-largest in the country. Although this is one of the driest areas in the Sonora Desert, it's an appealing drive for anyone craving the lonely highway – however, you can expect to see a number of green-and-white border patrol SUVs cruising past. Listen for the sounds of the desert: the howl of a coyote, the rattle of a snake. The skies are big, the land vast and barren. Gas stations, grocery marts and motels are sparse, so plan ahead and carry plenty of water and other necessities.
For details about what to expect if you're stopped by a border patrol agent see Click here.
##### KITT PEAK NATIONAL OBSERVATORY
Dark and clear night skies make remote Kitt Peak ( 520-318-8726; www.noao.edu/kpno; Hwy 86; admission to visitor center by donation; 9am-3:45pm) a perfect site for one of the world's largest observatories. Just west of Sells, 56 miles southwest of Tucson, this 6875ft-high mountaintop is stacked with two radio and 23 optical telescopes, including one boasting a staggering diameter of 12ft.
There's a visitor center with exhibits and a gift shop, but no food. Guided one-hour tours (adult/child $7.75/4 Nov-May, $5.75/3 Jun-Oct; 10am, 11:30am & 1:30pm) take you inside the building housing the telescopes, but alas you don't get to peer through any of them. To catch a glimpse of the universe, sign up for the Nightly Observing Program (adult/student/senior $48/44/44; closed mid-Jul–Aug), a three-hour stargazing session starting at sunset and limited to 46 people. This program books up weeks in advance but you can always check for cancellations when visiting. And dress warmly! It gets cold up there. For this program, children must be at last eight years old.
There's no public transportation to the observatory, but Adobe Shuttle ( 520-609-0593) runs vans out here from Tucson for $280 for four people.
##### ORGAN PIPE CACTUS NATIONAL MONUMENT
If you truly want to get away from it all, you can't get much further off the grid than this huge and exotic park ( 520-387-6849; www.nps.gov/orpi; Hwy 85; per vehicle $8) along the Mexican border. It's a gorgeous, forbidding land that supports an astonishing number of animals and plants, including 28 species of cacti, first and foremost its namesake organ-pipe. A giant columnar cactus, it differs from the more prevalent saguaro in that its branches radiate from the base. Organ-pipes are common in Mexico but very rare north of the border. The monument is also the only place in the USA to see the senita cactus. Its branches are topped by hairy white tufts, which give it the nickname 'old man's beard.' Animals that have adapted to this arid climate include bighorn sheep, coyotes, kangaroo rats, mountain lions and the piglike javelina. Your best chance of encountering wildlife is in the early morning or evening. Walking around the desert by full moon or flashlight is another good way to catch things on the prowl, but wear boots and watch where you step.
Winter and early spring, when Mexican gold poppies and purple lupine blanket the barren ground, are the most pleasant seasons to visit. Summers are shimmering hot (above 100°F, or 38°C) and bring monsoon rains between July and September.
The only paved road to and within the monument is Hwy 85, which travels 26 miles south from the hamlet of Why to Lukeville, near the Mexican border. After 22 miles you reach the Kris Eggle Visitor Center ( 8am-5pm), which has information, drinking water, books and exhibits. Ranger-led programs run from January to March.
#### Sights & Activities
Two scenic drives are currently open to vehicles and bicycles, both starting near thevisitor center. The 21-mile Ajo Mountain Drive takes you through a spectacular landscape of steep-sided, jagged cliffs and rock tinged a faintly hellish red. It's a well-maintained but winding and steep gravel road navigable by regular passenger cars (not recommended for RVs over 24ft long). If you prefer to let someone else do the driving, ask at the visitor center about ranger-led van tours available from January to March. The other route is Puerto Blanco Drive, of which only the first 5 miles are open, leading to a picnic area and overviews.
Unless it's too hot, the best way to truly experience this martian scenery is on foot. There are several hiking trails, ranging froma 200yd paved nature trail to strenuous climbs of over 4 miles. Cross-country hiking is also possible, but bring a topographical map and a compass and know how to use them – a mistake out here can be deadly. Always carry plenty of water, wear a hat and slather yourself in sunscreen.
#### Sleeping & Eating
The 208 first-come, first-served sites at Twin Peaks Campground (tent/RV sites $12) by the visitor center are often full by noon from mid-January through March. There's drinking water and toilets, but no showers or hookups. Tenters might prefer the scenic, if primitive, Alamo Canyon Campground (campsites $8), which requires reservations at the visitor center. There's no backcountry camping because of illegal border crossings.
No food is available at the monument, but there's a restaurant and a small grocery in Lukeville. The closest lodging is in Ajo, about 11 miles north of Why, on Hwy 85.
###### Dangers & Annoyances
Rubbing up against the Mexican border, this remote monument is a popular crossing for undocumented immigrants and drug smugglers, and large sections are closed to the public. A steel fence intended to stop illegal off-road car crossings marks its southern boundary. In 2002, 28-year-old ranger Kris Eggle, for whom the visitor center is named, was killed by drug traffickers while on patrol in the park. Call ahead or check the website for current accessibility.
### CROSSING THE BORDER
For more information on crossing the Mexican border, check out Click here.
### South of Tucson
From Tucson, the I-19 is a straight 60-mile shot south through the Santa Cruz River Valley to Nogales on the Mexican border. A historical trading route since pre-Hispanic times, the highway is unique in the US because distances are posted in kilometers – when it was built there was a strong push to go metric. Speed limits, however, are posted in miles!
Though not terribly scenic, I-19 is a ribbon of superb cultural sights with a bit of shopping thrown in the mix. It makes an excellent day trip from Tucson. If you don't want to backtrack, follow the much prettier Hwys 82 and 83 to the I-10 for a 150-mile loop.
#### Sights & Activities
Mission San Xavier del BacMISSION
( 520-294-2624; www.sanxaviermission.org; 1950 W San Xavier Rd; donations appreciated; 7am-5pm) The dazzling white towers of this mission rise from the dusty desert floor 8 miles south of Tucson – a mesmerizing mirage just off I-19 that brings an otherworldly glow to the scrubby landscape surrounding it. Nicknamed 'White Dove of the Desert,' the original mission was founded by Jesuit missionary Father Eusebio Kino in 1700 but was mostly destroyed in the Pima uprising of 1751. Its successor was gracefully rebuilt in the late 1700s in a harmonious blend of Moorish, Byzantine and Mexican Renaissance styles. Carefully restored in the 1990s with the help of experts from the Vatican and still religiously active, it's one of the best-preserved and most beautiful Spanish missions in the country.
Nothing prepares you for the extraordinary splendor behind its thick walls. Your eyes are instantly drawn to the wall-sized carved, painted and gilded retable behind the altar, which tells the story of creation in dizzying detail. In the left transept the faithful line up to caress and pray to a reclining wooden figure of St Francis, the mission's patron saint. Metal votive pins shaped like body parts have been affixed to his blanket, offered in the hope of healing.
A small museum explains the history of the mission and its construction. Native Americans sell fry bread, jewelry and crafts in the parking lot.
From I-19, take exit 92.
Titan Missile MuseumMUSEUM
( 520-625-7736; www.titanmissilemuseum.org; 1580 W Duval Mine Rd, Suarita; adult/child/senior $9.50/6/8.50; 8:45am-5:30pm Nov-Apr, 8:45am-5pm May-Oct) Cold War history comes frighteningly alive at this original Titan II missile site, where a crew stood ready 24/7 to launch a nuclear warhead within seconds of receiving a presidential order. The Titan II was the first liquid-propelled Intercontinental Ballistic Missile (ICBM) that could be fired from below ground and could reach its target –halfway around the world or wherever – in 30 minutes or less. On alert from 1963 to 1986,this is the only one of 54 Titan II missile sitesnationwide that has been preserved as a museum. The one-hour tours (last tour is anhour before closing), which are usually led byretired military types, areboth creepy and fascinating. After descending 35 feet and walkingthrough several 3-ton blast doors, you enterthe Control Room where you experience a simulated launch before seeing the actual (deactivated, of course) 103ft-tall missile still sittingin its launch duct. The tour is wheelchair accessible. Exhibits in the small museum trace the history of the Cold War and related topics.
The museum is 24 miles south of Tucson, off I-19 exit 69.
TubacVILLAGE
Tubac, about 45 miles south of Tucson, started as a Spanish fort set up in 1752 to stave off Pima attacks. These days, the tiny village depends entirely on tourists dropping money for crafts, gifts, jewelry, souvenirs, pottery and paintings peddled in its 100 or so galleries, studios and shops. Compact and lined with prefab, adobe-style buildings, it's an attractive but somewhat sterile place.
Tumacácori National Historic ParkMUSEUM
( 520-398-2341; www.nps.gov/tuma; I-19 exit 29; adult/child $3/free; 9am-5pm) Three miles south of Tubac, this pink-and-cream edifice shimmers on the desert like a conquistador's dream. In 1691 Father Eusebio Kino and his cohort arrived at the Tumacácori settlement and quickly founded a mission to convert the local Native Americans. However, repeated Apache raids and the harsh winter of 1848 drove the priests out, leaving the complex to crumble for decades. For self-guided tours of the hauntingly beautiful ruins (ask for the free booklet) start at the visitor center, which also has a few exhibits. Skip the 15-minutevideo and plunge into the cool church alcoves and thorny gravesites. An impressive mass is held here on Christmas Eve.
Santa Cruz Chili & Spice LANDMARK
( 520-398-2591; www.santacruzchili.com; 1868 E Frontage Rd; 8am-5pm Mon-Fri, from 10am Sat, to 3pm summer) South of the mission, this spice factory has been in business for more than 60 years and sells just about every seasoning under the sun – the stuff to get is its homemade chile pastes. Free samples available too.
Tubac Presidio State Historic
Park & Museum MUSEUM
( 520-398-2252; http://azstateparks.com; 1 Burruel St; adult/child $4/2; 9am-5pm) The foundation of the fort is all that's left at this state park, which is within walking distance of Tubac's shops and galleries. The attached museum has some worthwhile exhibits, including Arizona's oldest newspaper-printing press from 1859 and lots of information on the de Anza expedition to California.
#### Festivals & Events
Festivals pop off in Tubac all year; check the town's websites for exact dates (wwwtubacaz.com, www.tubacarizona.com). The Tubac Arts & Crafts Festival is held in early February; Taste of Tubac showcases local culinary flair in early April; Anza Days, on the third weekend in October, are marked by historical reenactments, including some pretty cool parade ground maneuvers by faux-Spanish mounted lancers; and in early December the streets light up during Luminaria, a Mexican-influenced Christmas tradition.
#### Sleeping & Eating
Tubac Country Inn B&B $$
( 520-398-3178; www.tubaccountryinn.com; 13 Burruel St; r $90-175; ) The decor at this charming five-room inn is best described as Southwest-lite: Navajo prints, Native American baskets and chunky wood furniture. A breakfast basket is delivered to your door in the morning.
Old Tubac Inn AMERICAN $$
( 520-398-3161; 7 Plaza Rd; dishes $9-21; lunch & dinner) Our favorite place to eat – and drink – in town. It's a combination of cowboy stop and family restaurant, which makes for an interesting vibe. The food is the everywhere-in-Arizona mix of beef and Mexican; it cooks up a fine cheeseburger.
Wisdoms Café MEXICAN $$
( 520-398-2397; www.wisdomscafe.com; 1931 E Frontage Rd; dishes $6.25-16; lunch & dinner) This institution has been satisfying locals since 1944. The Mexican-themed menu heavily touts the signature 'fruit burros' (a fruit-filled crispy tortilla rolled in cinnamon and sugar). We think it executes an excellent take on the enchilada. Located 2 miles south of Tubac.
#### Information
There are approximately 100 galleries, art studios and crafts stores in town. As exhibitions and artists constantly rotate it's hard to recommend any one place over the next, but seeing as Tubac is a small village, you can wander all it has to offer very easily on foot.
For more information stop by the Tubac Welcome Center ( 520-398-2704; www.tubacaz.com; 2 Tubac Rd; 10am-1pm Jun-Sep, to4pm Oct-May), run by the chamber of commerce.
#### Getting There & Away
Tubac is 50 miles south of Tucson off I-19; the main exit into town is exit 34
### Patagonia & the Mountain Empire
Sandwiched between the border, the Santa Rita Mountains and the Patagonia Mountains is one of the shiniest hidden gems in the Arizona travel catalogue. In a valley by the small town of Patagonia are long vistas of lush, windswept upland grassland; dark, knobby forest mountains; and a crinkle of slow streams. The valleys that furrow across the landscape occupy a special microclimate that is amenable to wine grapes. It may not be the Napa Valley, but who needs 20 chardonnay varietals when you boast a juxtaposition of hard-bitten cowboys and artistic refugees?
Patagonia and smaller Sonoita (and tiny Elgin) sit almost 5000ft above sea level, so the land here is cool and breezy. The first two towns were once important railway stops, but since the line closed in 1962 tourism and the arts have been their bread and butter. The beauty of the montane grasslands was not lost on film scouts; the musical _Oklahoma_ and John Wayne's _Red_ _River_ were both filmed here.
#### Sights & Activities
Patagonia Lake State Park PARK
( 520-287-6965; http://azstateparks.com/Parks/PALA/index.html; 400 Patagonia Lake Rd; vehicle/bike $10/3; 4am-11pm) A brilliant blue blip dolloped into the mountains, 2.5-mile-long Patagonia Lake was formed by the damming of Sonoita Creek. About 7 miles southwest of Patagonia, the lake is open year-round. At 4050ft above sea level, buffeted by lake and mountain breezes, the air is cool – making this a perfect spot for camping, picnicking, walking, bird-watching, fishing, boating and swimming. The campsite (with/without hookups $25/17) makes a fine base for exploring the region.
Patagonia-Sonoita Creek Preserve PRESERVE
( 520-394-2400; www.nature.org/arizona; 150 Blue Heaven Rd; admission $5; 6:30am-4pm Wed-Sun Apr-Sep, from 7:30am Oct-Mar) A few gentle trails meander through this enchanting riparian willow forest. Managed by the Nature Conservancy, the preserve supports seven distinct vegetative ecosystems, four endangered species of native fish and more than 300 species of birds, including rarities from Mexico. For bird-watchers, the peak migratory season is April and May, and late August to September. There are guided nature walks offered on Saturday morning at 9am.
Reach the preserve by going northwest on N 4th Ave in Patagonia, then south on Pennsylvania Ave, driving across a small creek and continuing another mile.
###### Wineries
The Arizona wine industry is starting to attract some notice in the viticulture world. All of the following wineries offer tastingsfor $7, which is a pretty cheap way to get pleasantly sloshed in some beautiful, sun-kissed hill country.
Callaghan Vineyards WINERY
( 520-455-5322; www.callaghanvineyards.com; 336Elgin Rd; 11am-3pm Fri-Sun) About 20 miles east of Patagonia, Callaghan has traditionally been one of the most highly regarded wineries in the state. To get here, head south on Hwy 83 at the village of Sonoita, then east on Elgin Rd.
### BIRD BRAINS
As you drive down Pennsylvania Ave to the Patagonia-Sonoita Creek Preserve, you'll notice Paton House (Blue Heaven Rd), just across the first creek crossing, on your left. A chain-link fence surrounds the property, and you'll likely see several cars parked outside. The backyard of the house is decked out with binoculars, birding books and sugar feeders that attract rare hummingbirds, including (according to local birders) the most reliable violet-crowned hummingbird sightings in the USA. It's free and there are no official hours (if the gate to the backyard is closed, that means don't come in), but donations for the feeders are appreciated. William and Marion Paton, the couple who started the bird-watching program, have passed away. The house is currently rented by people who want to maintain their legacy, but there's a chance the status may have changed when you visit.
The famed Roadside Rest Area is in a scenic canyon 4.2 miles southwest of Patagonia. It's ostensibly a run-of-the-mill pullout that runs off Hwy 82, which also happens to be one of the most famous birding spots in the state. This is a relatively reliable place to catch the rare rose-throated bectard, as well as more common avian fauna such as the canyon wren. Be careful if you stop, as cars may pull over to park at any time.
Canelo Hills Vineyard & Winery WINERY
( 520-455-5499; www.canelohillswinery.com; 342Elgin Rd; 11am-4pm Fri-Sun Sep-May, 11am-4pm Sat only Jun-Aug) Almost next door to Callaghan – and sharing the same sweeping views – is Canelo Hills, which does a pretty nice Riesling.
Dos Cabezas Winery WINERY
( 520-841-1193; www.doscabezaswinerystore.com;3248 Hwy 82; 10:30am-4:30pm Thu-Sun) This cute, rustically pretty family-run operation is in Sonoita, near the crossroads of Hwys 82 and 83.
#### Sleeping
The only really cheap sleeping option is camping at Patagonia Lake State Park. Otherwise, there are some great B&Bs in and around town.
Duquesne House B&B $$
( 520-394-2732; www.theduquesnehouse.com; 357Duquesne Ave, Patagonia; r $125; ) This photogenic, ranch-style B&B was once a boarding house for miners. Today, there are three spacious, eclectically appointed suites with their own distinct garden areas where you can watch the sun set, listen to the birds chirp, smell the rosemary and generally bliss out. On Tuesday and Wednesday the B&B offers a 'Bed, No Bread' special – $110 per night with no breakfast.
Whisper's Ranch B&B $$
( 520-455-9246; www.whispersranch.com; 1490 Hwy 83; r $100-140; ) For a more traditional out-West experience get out to Canelo, about 30 miles east of Patagonia, and shack up with the cowboys. Amid rolling hills of oakforest inhabited by bobcats and javelinas, Whisper's is run with green sensibility (water is recycled, for example), and exudes a frontier attitude and energy. The rooms are decidedly rustic-chic; the homemade meals are to die for. Whisper's Animal Sanctuary (www.rrheartranch.com), which takes in abused horses, is next door and open for tours.
#### Eating & Drinking
Canela Bistro NEW AMERICAN $$
( 520-455-5873; www.canelabistro.com; 3252 Hwy82, Sonoita; mains $16-24; 5-9pm Thu, 3-9pm Fri & Sat, 10am-3pm Sun) This bistro offers some of the classiest fare in the Mountain Empire. This is Nouveau American French Laundry-style fare sourced from the Southwest; green chile is made with farm-raised pork while the quiche comes with local red peppers.
Velvet Elvis PIZZERIA $
( 520-394-2102; www.velvetelvispizza.com; 29 Naugle Ave, Patagonia; mains $8-26; 11:30am-8:30pm Thu-Sun) A velvet Elvis does indeed make an appearance at this gourmet pizza joint in Patagonia, but he keeps things low-key from his perch above the register. Motorcyclists, foreign visitors, date-night couples – everybody visiting the area – rolls in at some point for one of the 13 designer pies. These diet-spoilers will make you feel like Elvis in Vegas: fat and happy.
Grasslands, A Natural
Foods Cafe CAFE $$
( 520-455-4770; www.grasslandscafe.com; 3119Hwy 93, Sonoita; mains $9-16; 10am-3pm Thu-Sat, 8am-3pm Sun) Homemade chile-and-cheddar croissants, vegetable pies, organic egg salad, prickly-pear jam and a few German specialties – the hearty fare at this well-run bakery and cafe is locally sourced and organic. It's a great stop for a healthy lunch (lots of vegetarian and gluten-free selections). The chocolate-chip cookies are delicious. Cash only.
Gathering Grounds Cafe COFFEE SHOP $
( 520-394-2097; 319 McKeown Ave, Patagonia; mains under $5; breakfast & lunch; ) Sip a civilized cup o' Joe, nibble a scone and surf the net.
Wagon Wheel Saloon BAR $
(www.wagonwheelpatagonia.com; 400 Naugle Ave,Patagonia) Kick it cowboy-style at the WagonWheel, where the bar is big, the 'art' is taxidermied and the pool table is ready for action.
#### Information
The main road is Hwy 82, the Patagonia Hwy. Patagonia, with about 800 people, is the local center of activity (we use the term loosely). The folks in the visitor center ( 520-394-9186, 888-794-0060; www.patagoniaaz.com; 307 McKeown Ave; 10am-5pm Mon-Sat, 10am-4pm Sun), in Mariposa Books & More, are friendly and helpful. Sonoita isn't much more than an intersection, and Elgin is just the name for a swath of unincorporated land 20 minutes east of Sonoita. Keep your dial tuned to KPUP 100.5, the awesome local radio station.
#### Getting There & Away
Patagonia and the Mountain Empire are connected to the rest of the state by Hwys 82 and 83; the closest major town is Nogales, 20 miles to the southwest.
### Sierra Vista & Around
Sierra Vista isn't that exciting, but there are several sites within driving distance that warrant your attention. The chamber of commerce ( 520-458-6940; www.sierravistachamber.org, www.visitsierravista.com; 21 E Wilcox Dr; 8am-5pm Mon-Fri, 9am-4pm Sat) serves as a visitor center for the region.
#### Sights
Ramsey Canyon Preserve PRESERVE
( 520-378-2785; www.nature.org; Ramsey CanyonRd; adult/child $5/free, free 1st Sat of month; 8am-5pm daily, closed Tue & Wed Sep-Feb) A sycamore- and yucca-weaved dome some 5500ft in the sky marks where the HuachucaMountains meet the Rockies, the Sierra Madres and the Sonoran Desert. This beautiful Nature Conservancy-owned preserve is one of the best hummingbird bagging spots in the USA. Up to 14 species of the little birds flit over the igneous outcrops and a wiry carpeting of trees throughout the year, with especially heavy sightings from April to September. At lower altitudes an incredible diversity of wildlife stalks through the river canyon that geographically defines this area. You can spot coatis, cougars and javelinas, but perhaps the most famous resident is the critically endangered Ramsey Canyon leopardfrog, found nowhere else in the world.
Visitation is limited by the 23 parking spots in the visitor center, which is decked out with hummingbird feeders. A very easy 0.7-mile nature-loop trail leaves from here, as well as guided walks on Monday, Thursday and Saturday at 9am, March through October. The reserve is about 11 miles (25 minutes' drive) south of Sierra Vista off Hwy 92. Drive all the way to the very end of Ramsey Canyon Rd, bearing left onto the driveway at the final cul-de-sac.
San Pedro Riparian National
Conservation Area PRESERVE
( 520-439-6400; www.blm.gov/az/st/en.html; Fry Blvd) About 95% of Arizona's riparian habitat has become victim to overgrazing, logging and development, so what little riverfront ecosystem remains is incredibly important to the state's ecological health. Some 350 bird species (many endangered), 84 mammalspecies and nearly 41 species of reptiles and amphibians have been recorded along the 40-mile stretch of the San Pedro River within the conservation area. It's the healthiest riparian ecosystem in the Southwest. Unfortunately it's also become a corridor for drug smuggling from Mexico, so suspicious activity should be reported.
The visitor center ( 9:30am-4:30pm), in the 1930s San Pedro House, is 6 miles east of Sierra Vista on Fry Blvd. From here you can access several hiking trails.
#### Sleeping
Casa de San Pedro B&B B&B $$
( 520-366-1300; http://bedandbirds.com; 8033 S Yell Lane; r $169; ) This stylish but inviting place feels like the home of your favoritewealthy friend. Ten comfy rooms with Mexican hardwood furnishings are organizedaround a lovely courtyard and gardens. The common areas are so relaxing, guests might be found snoozing on a couch in the middle of the day! As with many properties in this area, it's maximized for bird-watching fun – it's also the closest accommodations to the San Pedro Riparian National Conservation Area.
Battiste's B&B B&B $$
( 520-803-6908; www.battistebedandbirds.com; 4700 E Robert Smith Lane, Hereford; r $150; ) This B&B is oriented toward bird-watching,and features cozy rooms arrayed in colorful, Southwestern decor. The owners have counted more than 50 bird species in their backyard alone and each spring host a nesting elf owl that has become a local attraction. Rate reduced to $135 per night if staying multiple nights. Air-conditioningavailable in one room, the other is fan-cooled.
Sierra Suites HOTEL $$
( 520-459-4221; www.sierravistasuites.com; 391 E Fry Blvd; r $99-115; ) The beige brick exterior doesn't inspire much confidence, but once inside, all is quickly forgiven. The airy lobby fronts a customer-oriented hotel that works well for birders and businesspeople alike. It's also popular with those headed to nearby Fort Huachuca. Enjoy a buffet breakfast, a remodeled weight room and an on-site laundry. Rooms have fridges and microwaves.
#### Eating
Angelika's German Imports GERMAN $
( 520-458-5150; 1630 E Fry Blvd; mains $5-13; 10am-5pm Tue-Thu, 10am-8pm Fri, 10am-7pm Sat) Right beside Hwy 92, this cozy place is a takeout sandwich shop, a simple eatery and a small grocery all tucked into one spot. All three sell German specialties. German is spoken here too, but you might just hear, in English, a simple farewell: 'Be careful out there and watch out for the others.' Indeed we will.
Café Sierra CAFE $
(www.sierravistaaz.gov; 2600 E Tacoma; mains under $10; 7am-4pm Mon, 7am-6pm Tue-Thu, 7am-5pm Fri, 10am-5pm Sat; ) Yes, we're recommending an eatery inside the Sierra Vista library. But you know what? This is a nice, low-key spot to surf the net while nibbling a scone and sipping coffee. The chocolate-chip cookies are fantastic. Sandwiches available too.
### Tombstone
The grave markers at Boothill Cemetery typically include the cause of death: Murdered. Shot. Killed by Indians. Suicide. One quick stroll around the place tells you everything you need to know about living – or dying – in Tombstone in the late 1800s. How did this godforsaken place come to be? In 1877, despite friends' warnings that all he would find was his own tombstone, prospector Ed Schieffelin braved the dangers of Apache attack and struck it rich. He named the strike Tombstone, and a legend was born. This is the town of the infamous 1881 shootout at the OK Corral, when Wyatt Earp, his brothers Virgil and Morgan and their friend Doc Holliday gunned down outlaws Ike Clanton and Tom and Frank McLaury. The fight so caught people's imaginations, it not only made it into the history books but also onto the silver screen – many times. Watch the 1993 _Tombstone_ , starring Kurt Russell and Val Kilmer, to get you in the mood.
Most boomtowns went bust but Tombstone declared itself 'Too Tough to Die.' Tourism was the new silver and as the Old West became en vogue, Tombstone didn't even have to reconstruct its past – by 1962 the entire town was a National Historic Landmark. Yes, it's a tourist trap; but a delightful one and a fun place to find out how the West was truly won.
#### Sights
Walking around town is free, but you'll pay to visit most attractions.
OK Corral HISTORIC SITE
( 520-457-3456; www.ok-corral.com; Allen St btwn 3rd & 4th Sts; admission $10, without gunfight $6; 9am-5pm) Site of the famous gunfight on October 26, 1881, the OK Corral is the heart of both historic and touristic Tombstone. It has models of the gunfighters and other exhibits, including CS Fly's early photography studio and a recreated 'crib,' the kind of room where local prostitutes would service up to 80 guys daily for as little as 25¢ a pop. Fights are reenacted at 2pm (with an additional show at 3:30pm on busy days).
Tickets are also good next door at the kitschy Tombstone Historama, a 25-minute presentation of the town's history using animated figures, movies and narration (by Vincent Price). Pick up your free copy of the Tombstone _Epitaph_ reporting on the infamous shootout at the historic newspaper office, now the Tombstone Epitaph Museum ( 520-457-2211; near cnr 5th & Fremont Sts; admission free; 9:30am-5pm).
The losers of the OK Corral – Ike Clantonand the McLaury brothers – are buried (in row 2), along with other desperados, at Boothill Graveyard off Hwy 80 about a quarter-mile north of town. The entrance is via a gift shop but admission, thankfully, is free ($2 for list of specific graves, with location). Some headstones are twistedly poetic. The oft-quoted epitaph for Lester Moore, a Wells Fargo agent, reads:
Here lies Lester Moore
Four slugs from a 44
No less, no more.
Tombstone Courthouse
State Historic Park MUSEUM
( 520-457-3311; http://azstateparks.com/Parks/TOCO/index.html; 223 Toughnut St; adult/child $5/2; 9am-5pm) Seven men were hanged in Tombstone's courthouse courtyard, and today a couple of nooses dangle ominouslyfrom the recreated gallows. The story behind their hangings is explained inside this rambling Victorian building, which also displays an eclectic bunch of items relating to the town's history. Check out the tax licenses for prostitutes and the doctor's bullet-removal kit. The exhibits are somewhat different from those at the OK Corral, making it worth a stop.
Bird Cage Theater HISTORIC SITE
( 520-457-3421; 517 E Allen St; adult/child/senior $10/7/9; 8am-6pm) Packed tight with antiques and history, the Bird Cage serves as Tombstone's attic. In the 1880s it was a one-stop sin-o-rama. Besides onstage shows, it was a saloon, dance hall, gambling parlor and a home for 'negotiable affections.' The very name derives from the 14 compartments lining the upper floor of the auditorium – like boxes at the opera – where the 'soiled doves' entertained their customers. The entire place is stuffed with dusty old artifacts that bring the period to life, including a faro gambling table used by Doc Holliday, a big black hearse, a fully furnished 'crib' and a creepy 'merman.' And, of course, the theater is haunted.
Rose Tree Museum MUSEUM
( 520-457-3326; cnr 4th & Toughnut Sts; adult/child $5/free; 9am-5pm) In April the world's largest rosebush – planted in 1886 – puts on an intoxicating show in the courtyard of this museum, a beautifully restored Victorian home still owned by the Maciafamily. The inside is brimming with family and town memorabilia, including a 1960 photograph showing the matriarch with Robert Geronimo, son of the Apache chief.
Staged Shootouts REENACTMENT
These days, lawlessness in Tombstone takes the form of rip roarin' shootouts. Apart from the 2pm show at the OK Corral, there are daily shows at Helldorado Town ( 520-457-9035; 339 S 4th St, at Toughnut St). Stop by the chamber of commerce for current times.
#### Festivals & Events
Tombstone events revolve around weekends of Western hoo-ha with shootouts (of course!), stagecoach rides, fiddling contests, 'vigilette' fashion shows, mock hangings and melodramas. The biggest event is Helldorado Days (www.helldoradodays.com; third weekend in October). See the chamber of commerce website for details about other events, which include Wyatt Earp Days (Memorial Day weekend), Vigilante Days (second weekend in August) and Rendezvous of the Gunfighters (Labor Day weekend).
#### Sleeping
Properties increase their rates during special events; reservations are recommended at these times.
Larian Motel MOTEL $
( 520-457-2272; www.tombstonemotels.com; 410 E Fremont St; r $70-90; ) This one's a rare breed: a motel with soul, thanks to the personalized attention from proprietor Gordon, cute retro rooms named for historical characters (Doc Holliday, Curly Bill, Wyatt Earp) and a high standard of cleanliness. It's also close to the downtown action. Children under 14 stay free.
Tombstone Bordello B&B B&B $
( 520-457-2394; www.tombstonebordello.com; 107W Allen St; r $89-99; ) This fascinating place used to be a house of ill-repute, and the names of the rooms – Shady Lady, Fallen Angel – embrace its colorful past. The 10-room B&B, built in 1881, was once owned by Big Nose Kate. The Victorian-style bedrooms (which held up to four working girls) feel very much of the era, so much so that some of the former residents are said to haunt the building.
Best Western Lookout Lodge MOTEL $$
( 520-457-2223; www.bestwesterntombstone.com;801 N Hwy 80; r incl breakfast $98-108; ) On a hill about five minutes from town; this property gets high marks for its spacious rooms overlooking the Dragoon Mountains, pretty gardens and outdoor firepit – and its Ranch 22 restaurant with cooked breakfast included. Pets are $20 per night, per pet.
Katie's Cozy Cabins CABIN $
( 520-457-3963; www.cabinsintombstone.com; 16 W Allen St; r $89 Sun-Thu, $99 Fri & Sat, 2-night minimum on weekend; ) Four new cabins sleep up to six people. Upstairs lofts have a double bed, while the rooms below have a couple of bunks.
#### Eating
It's a tourist town, so don't expect any culinary flights of fancy. In keeping with its Old West theme, the food is mostly standard American and Mexican.
Longhorn Restaurant AMERICAN $$
( 520-457-3405; www.thelonghornrestaurant.com;501 E Allen St; mains $7-19; 7:30am-9pm) The original 'Bucket of Blood Saloon,' this was where Virgil Earp was shot dead from a 2nd-floor window in 1881. Enjoy a cowboy breakfast or spike your cholesterol with a 14oz steak.
The Depot Steak House STEAKHOUSE $$
( 520-457-3404; 60 S 10th St; mains $8-26; 4pm-8:30pm Wed & Thu, 4pm-9:30pm Fri, noon-9:30pm Sat, noon-8:30pm Sun) Pelts, rifles and steer skulls dot the walls of this locals' favorite just north of downtown. The menu is mainly cowboy fare – steaks, ribs and burgers – but there are a few chicken dishes and salads. Service was a bit haphazard on our visit, but the food was fine. For pool and beer, wander through the doorway to Johnny Ringo's Bar, named for the legendary outlaw and Wyatt Earp antagonist.
Café Margarita MEXICAN $$
( 520-457-2277; 131 S 5th St; mains $7-15; 11am-8pm) Formerly Nellie Cashman's in the Russ House, this new eatery serves Mexican fare as well as a few Italian dishes. Eat inside or on the patio. Enjoy live music on Friday and Saturday nights. Biggest bummer? No free chips and salsa.
#### Drinking
There's little more to do in the evening than to go on a pub crawl – or make that a saloon stagger.
Crystal Palace Saloon BAR
(www.crystalpalacesaloon.com; 436 E Allen St, at 5th St; 11am-10pm Sun-Thu, to 1am Fri & Sat) This lively saloon was built in 1879 and has been completely restored. It's a favorite end-of-the-day watering hole with Tombstone's costumed actors or anyone wanting to play outlaw for a night.
Big Nose Kate's BAR
(www.bignosekates.info; 417 E Allen St; 10am-midnight) Full of Wild West character, Doc Holliday's girlfriend's bar features great painted glass, historical photographs and live music in the afternoons. Down in the basement is the room of the Swamper, a janitor who dug a tunnel into the silver mine shaft that ran below the building and helped himself to buckets of nuggets. Or at least so the story goes...
#### Information
Police ( 520-457-2244; 315 E Fremont St)
Post office ( 520-457-3479; 100 Haskell St; 8:30am-4:30pm)
Tombstone Chamber of Commerce ( 520-457-3929, 888-457-3929; www.tombstonechamber.com; 395 E Allen St, at cnr of 4th St; 9am-5pm)
#### Getting There & Away
Tombstone is 24 miles south of the I-10 via Hwy 80 (exit 303 towards Benson/Douglas). The Patagonia Hwy (Hwy 82) links up with Hwy 80 about 3 miles north of Tombstone. There is no public transport into town.
### Bisbee
At first glance, Bisbee isn't that attractive. Wedged between the steep walls of Tombstone Canyon, its roads are narrow and twisty, the buildings old and fragile, and there's a monstrous open-pit mine gaping toward the heavens at the east end of town. You drove all the way here for this? But then you take a closer look. Those 19th-century buildings are packed tight with classy galleries, splendid restaurants and charming hotels. As for the citizens, well, just settle onto a bar stool at a local watering hole and a chatty local will likely share all of the town's gossip before you order your second drink.
Bisbee built its fortune on ore found in the surrounding Mule Mountains. Between 1880 and 1975, underground and open-pit mines coughed up copper in sumptuous proportions, generating more than $6 billion worth of metals. Business really took off in 1892 when the Phelps Dodge Corporation, which would soon hold a local monopoly, brought in the railroad. By 1910 the population had climbed to 25,000, and with nearly 50 saloons and bordellos crammed along Brewery Gulch, Bisbee quickly gained a reputation as the liveliest city between El Paso and San Francisco.
As the local copper mines began to fizzle in the 1970s, Bisbee began converting itself into a tourist destination. At the same time hippies, artists and counterculture types migrated here and decided to stay. The interweaving of the new creative types and the old miners has produced a welcoming bunch of eccentrics clinging to the mountainside. It's one of the coolest places (weather and attitude) in southern Arizona – and definitely worth the drive.
Hwy 80 runs through the center of town. Most businesses are found in the Historic District (Old Bisbee), along Main St and near the intersection of Howell and Brewery Aves. Many businesses close from Monday to Wednesday.
#### Sights & Activities
Walking through Old Bisbee – up winding back alleys, steep staircases and cafe- and shop-lined Main St – is a delight in itself. For sweeping views, walk up OK St above the southern edge of town. A path at the top leads to a hill where locals have built colorful shrines filled with candles, plastic flowers and pictures of the Virgin Mary.
Bisbee
Sights
1Bisbee Mining & Historical Museum C2
2Bisbee Museum of the Bizarre B2
Sleeping
3Copper Queen Hotel C1
Eating
4Cafe Roka A2
5Poco B2
Drinking
6Bisbee Coffee Co B2
7Bisbee Grand Hotel B2
8Old Bisbee Brewing Company C1
9St Elmo's C1
Shopping
10Atalanta Music & Books B2
11Bisbee Bicycle Brothel C1
12Bisbee Stitches Teeny Tiny Toy Store A2
Bisbee Mining & Historical Museum MUSEUM
( 520-432-7071; www.bisbeemuseum.org; 5 Copper Queen Plaza; adult/child/senior $7.50/3/6.50; 10am-4pm) Located in the 1897 former headquarters of the Phelps Dodge Corporation, this museum is affiliated with the Smithsonian Institution, and it shows. It does an excellent job delineating the town's past, the changing face of mining and the use of copper in our daily lives. You even get to 'drive' a shovel with a dipper larger than most living rooms.
Queen Mine MINE
( 520-432-2071; www.queenminetour.com; 478 Dart Rd, off Hwy 80; adult/child $13/5.50; 9am-3:30pm; ) Don miners' garb, grab a lantern and ride a mine train 1500ft into one of Bisbee's famous copper mines. In the early 20th century this was the most productive mine in Arizona, famous for producing particularly deep-shaded turquoise rocks known as Bisbee Blue. The tour, which lasts about an hour, is good fun for the kids, but maybe not so much for the claustrophobic.
To see the aftermath of open-pit mining, drive a half-mile south on Hwy 80 to the not-so-truthful 'Scenic View' sign. It's pointing toward the Lavender Pit, an immense stair-stepped gash in the ground that produced about 600,000 tons of copper between 1950 and 1974. It's ugly, but it's impressive.
#### Tours
To get the scoop on the town's turbulent past, join a fun and engaging walking tour (http://londonswalkingtour.blogspot.com/p/history.html) with local historian Michael London, an eccentric bearded character who looks like he's just walked off a movie set. The one-hour tours cost $10 and leave from the visitor center.
Stop by the visitor center for information on jeep tours and ghost walks.
#### Sleeping
Bisbee is refreshingly devoid of chain hotels, with most lodging in historic hotels or B&Bs. Weekends often fill early, so come midweek if you don't have a reservation.
Shady Dell QUIRKY $
( 520-432-3567; www.theshadydell.com; 1 Douglas Rd; rates $50-145) This fun-loving trailer park has a deliciously retro twist: each 'unit' is an original 1950s travel trailer, meticulously restored and outfitted with period accoutrements such as vintage radios (playing '50s songs upon arrival) and record players. All have tiny kitchens, some have toilets, but showers are in the bathhouse. A 1947 Chris Craft yacht and a tiki-themed bus are also available. Units use swamp coolers for cold air.
Jonquil Motel MOTEL $
( 520-432-7371; www.thejonquil.com; 317 Tombstone Canyon Rd; r $90-115; ) The inviting Jonquil is as retro in its styling as anywhere else in Bisbee. In this case, however, the decor is artily done-up roadside motel, not frilly Victorian B&B. We immediately fell for the 60ft mural that wraps around the property, based on the 1928 poem 'Romance Sonámbulo' by Federico García Lorca. The rooms are a bit on the small side, but excellent value for money.
School House Inn B&B $$
( 520-432-2996; www.schoolhouseinnbb.com; 818Tombstone Canyon; r incl breakfast $89-149; ) Report to the Principal's Office or get creative in the Art Room. No matter which of the nine darling rooms in this converted 1918 school you choose, you'll be charmed by the detailed decor, the homey comforts, and John (the proprietor). Relax below the 160-year-old live oak in the patio. Rates include a delicious full breakfast.
Copper Queen Hotel HOTEL $$
( 520-432-2216; www.copperqueen.com; 11 Howell;r $122-197; ) Howdy pilgrim. Is John Wayne your man? Then reserve yourself Room 109 because the Duke did indeed sleep here. The Copper Queen is a grand old dame that's welcomed guests since 1902. It's a splendid find with a vibe that merges casual, late-19th-century elegance with modern amenities. Rooms vary in size and comfort.
### WHAT THE...?
The fantastical Bisbee Museum of the Bizarre ( 520-432-2000; 28 Main St; $3; 11am-5pm Thu-Mon) displays the death mask of John Dillinger, Bigfoot's footprint, a two-headed squirrel, and a shrunken head (named Fred) – the sort of kitschy crap that makes you proud to be an American, dammit. It's in the back of the Source Within.
#### Eating
Poco VEGETARIAN $
( 520-432-3733; 15 Main St (Peddlar's Alley); mains $7.50-10; 11am-8pm Wed-Sun; ) Wow! People were talking about this new courtyard cafe as far away as Patagonia, and it's easy to see why: upbeat and accommodating service, a Mexican-inspired menu (it all sounds good) and mostly organic ingredients that burst with savory goodness. Did we mention it's vegetarian? Trust us: grab a spot in line, order at the counter then settle in on the patio for one of southern Arizona's simplest but tastiest meals. And remember, you can never go wrong with the burritos. Or the cupcakes. Or the... Just go!
Cafe Roka NEW AMERICAN $$$
( 520-432-5153; 35 Main St; dinner $15-29; dinner Thu-Sat) Past the art-nouveau steel door awaits this sensuously lit grown-up spot with innovative American cuisine that is at once smart and satisfying. The four-course dinners include salad, soup, sorbet and a rotating choice of mains. The welcoming central bar is great for solo diners, and if you chat with your neighbors you might just hear some juicy town gossip. Reservations recommended.
Screaming Banshee PIZZERIA $$
( 520-432-6788; 2 Copper Queen Plaza; mains $8-18; lunch & dinner) Fancy a helping of electric mushrooms or a B Hill Burger?Drop by this cozy and casual eatery that welcomes you with warm words, historical photographs and imaginative takes on American standards. Get a side of beer-battered fries to share.
High Desert Market & Café CAFE $
( 520-432-6775; 203 Tombstone Canyon; mains $5-9; 7am-7pm) This cheerful nosh spot serves breakfast along with fresh and custom-made sandwiches and salads opposite the Iron Man, a 1935 socialist-aesthetic statue of a manly, bare-chested miner. Its shelves are stocked with local and imported produce and products.
Bisbee Breakfast Club BREAKFAST $
(www.bisbeebreakfastclub.com; 75a Erie St; mains under $10; 7am-3pm) The breakfasts at this longtime favorite seem to have have lost a touch of their wow factor. That being said, this bustling eatery is still the see-and-be-seen spot in town, and the food remains pretty darn yummy.
#### Drinking
Old Bisbee Brewing Company BREWERY
(www.oldbisbeebrewingcompany.com; 200 ReviewAlley) This new watering hole serves up eight lip-smacking brews, including root beer.
St Elmo's BAR
(36 Brewery Ave) This 100-year-old dive is Arizona's oldest bar. Today, a boisterous mix of thirsty locals and tourists keep things hoppin'. The signed beer mugs behind the cash register belong to regulars.
Bisbee Grand Hotel BAR
(www.bisbeegrandhotel.com; 61 Main St) The bar in the bottom of the Grand Hotel in downtown has a cool punk rock meets Old West vibe. In fact, we saw a young buck with a handlebar moustache more kick-ass than Wyatt Earp's. Hipster or cowboy? We weren't 100% sure, but no one seemed to mind either way.
Bisbee Coffee Co COFFEE SHOP
(www.bisbeecoffee.com; 2 Copper Queen Plaza; 6:30am-9pm; ) This easy-going coffee shop, which sits between the post office and the visitor center, serves java strong enough to get you through a double shift on the tourist track.
#### Shopping
You can't walk in Bisbee without tripping on an art gallery. There's a wide range of styles and quality; have a wander up Main St to get a feel for what's out there.
Atalanta Music & Books BOOKS
( 520-432-9976; 38 Main St) A chaotic whirlwind of used books.
Bisbee Bicycle Brothel BICYCLES
( 520-432-2922; www.bisbeebicyclebrothel.com; 43 Brewery Ave) The 'best little wheelhouse in Arizona' has vintage bicycles from as far back as the 1940s. You can't rent wheels here, but why rent when you'll be so tempted to own? Sells some pretty awesome T-shirts and assorted Bicycle Brothel gear as well.
Bisbee Stitches Teeny Tiny Toy Store TOYS
( 520-432-8028; www.bisbeestitches.com; 40Main St) This delightful little shop sells homemade and hip toys for kids and kids-at-heart.
#### Information
Bisbee Visitor Center ( 520-432-3554, 866-224-7233; www.discoverbisbee.com; 2 Copper Canyon Plaza; 9am-5pm)
Copper Queen Hospital ( 520-432-5383; www.cqch.org; 101 Cole Ave) 24-hour emergency services.
Police ( 520-432-2261; 1 Hwy 92)
Post office ( 520-432-2052; 6 Main St; 7:30am-noon Mon-Fri, 9am-noon Sat)
#### Getting There & Away
Bisbee is about 50 miles south of the I-10 (exit 303 towards Benson/Douglas), 25 miles south of Tombstone, and only about 10 miles north of the Mexican border.
### Chiricahua National Monument
Cutting an arrow-straight swath south from the I-10 past fields of swaying blond grass, fence-trapped tumbleweeds and the virtualghost-town of Dos Cabezas, Hwy 186 provides no clue as to the natural treasurehiding in the mountains beyond. Pronounced 'cheery-cow-wha,' Chiricahua National Monument ( 520-824-3560; www.nps.gov/chir; Hwy 181; adult/child $5/free) is one of Arizona's most unique and evocative landscapes; a wonderfully rugged yet whimsical wonderland. Rain, thunder and wind have chiseled volcanic rocks into fluted pinnacles, natural bridges, gravity-defying balancing boulders and soaring spires reaching skyward like totem poles carved in stone. The remoteness made Chiricahua a favorite hiding place of Apache warrior Cochise and his men. Today it's attractive to birds and wildlife: bobcats and bears are often sighted on the hiking trails. Also watch for deer, coatis and javelinas.
Past the entrance, the paved Bonita Canyon Scenic Drive climbs 8 miles to Massai Point at 6870ft, passing several scenic pullouts and trailheads along the way. RVs longer than 29ft are not allowed beyond the visitor center ( 8am-4:30pm), which is about 2 miles along the road.
To explore in greater depth, lace up your boots and hit the trails. Eighteen miles of hiking trails range from easy, flat 0.2-mile loops to strenuous 7-mile climbs. A hikers' shuttle bus leaves daily from the visitor center at 8:30am, going up to Massai Point for $2. Hikers return by hiking downhill.
If you're short on time, hike the Echo Canyon Trail at least half a mile to the Grottoes, an amazing 'cathedral' of giant boulders where you can lie still and enjoy the wind-caressed silence. The most stupendous views are from Massai Point, where you'll see thousands of spires positioned on the slopes like some petrified army.
Bonita Campground (campsites $12), near the visitor center, has 22 first-come, first-served sites that often fill by noon. There's water, but no hookups or showers. Wilderness camping is not permitted inside the monument, but there is a USFS campground (www.fs.fed.us/r3/coronado) about 5 miles up Pinery Rd, which is near the park entrance station.
The monument is about 37 miles off I-10 at Willcox.
### Benson & Around
A railway stop since the late 1800s, Benson is best known as the gateway to the famous Kartchner Caverns, among the largest and most spectacular caves in the USA. This wonderland of spires, shields, pipes, columns, soda straws and other ethereal formations has been five million years in the making, but miraculously wasn't discovered until 1974. In fact, its very location was kept secret for another 25 years in order to prepare for its opening as Kartchner Caverns State Park ( reservations 520-586-2283, information 520-586-4010; http://azstateparks.com/Parks/KACA/index.html; Hwy 90; park entrance per vehicle/bicycle $6/3, Rotunda Tour adult/child $23/13, Big Room Tour mid-Oct–mid-Apr $23/13; 10am-3pm Mon-Fri Jun-Sep, to 3:40pm Sat & Sun, vary other times of the year). Two 90-minute tours are available, both equally impressive. The Big Room Tour closes to the public around mid-April, when a colony of migrating female cave myotis bats starts arriving from Mexico to roost and give birth to pups in late June. Moms and baby bats hang out until mid-September before flying off to their wintering spot. While a bat nursery, the cave is closed to the public.
The focus here is on education, so there are a number of rules – no purses, no water, no cameras, no touching the walls –to protect the delicate ecosystem. Tours often sell-out far in advance, so make reservations – online or by phone – early. The entrance is 9 miles south of I-10, off Hwy 90, exit 302.
About 15 miles east of Benson, in Dragoon, the private, nonprofit Amerind Foundation( 520-586-3666; www.amerind.org; 2100 N Amerind Rd; adult/child/senior $8/5/7; 10am-4pm Tue-Sun) exhibits Native American artifacts, history and culture from tribes from Alaska to Argentina, from the Ice Age to today. The Western gallery has exceptional works by such renowned artists as Frederic Remington and William Leigh. It's right off I-10 exit 318.
The complex is near Texas Canyon in the Little Dragoon Mountains, which is known for its clumps of giant and photogenic granite boulders. For a closer look, swing by the historic Triangle T Guest Ranch ( 520-586-7533; www.azretreatcenter.com; 4190Dragoon Rd; casitas $149-189, cabins/bunkhouses $225/425; ), where you can arrange horseback rides ($45 per hour), enjoy refreshments in the saloon or spend the night in fairly basic casitas. Tenters ($20) and RVers ($20 to $30) can set up among the rocks.
Campers can also spend the night at the KOA Campground ( 520-586-3977; http://koa.com/campgrounds/benson; 180 W Four FeathersLn; tent sites $27, RV sites $37-40, cabins $49, lodges $85-135; ). Otherwise, lodging in Benson is mostly about chain motels, which cluster off I-10 exits 302 and 304. One budget option is Motel 6 ( 520-586-0066; www.motel6.com; 637 Whetstone Commerce Dr; r $40), which is just off I-10 and almost a straight shot north from Kartchner Caverns via Hwy 90.
Benson isn't exactly the spot to experience a culinary tour de force – with the exception of Magaly's ( 520-720-6530; 675 W 4th St; mains $7-10; lunch & dinner), a cute little hacienda that serves up very good Mexican food. The house red chile is rich and spicy and damn delicious. For quick-and-easy coffee before your next adventure, drive through Old Benson Ice Cream Stop, ( 520-586-2050; 102 W 4th St; 6:30am-9pm Sun-Thu, 9:30pm Fri & Sat) beside the railroad tracks. It also sells 44 flavors of soft serve.
Benson is about 50 miles southeast of Tucson and 65 miles northeast of Patagonia. If you're approaching from any direction but the south you'll get here via I-10; if coming from the south, use Hwy 90 or Hwy 80. The main exit into town is exit 303 off I-10. Amtrak's _Sunset Limited_ comes through thrice weekly on its run between Los Angeles and New Orleans.
### THE BOOKS, MY FRIEND, ARE SINGING IN THE WIND
While you're in Benson, make sure to stop by the Singing Wind Bookshop ( 520-586-2425; www.bensonvisitorcenter.com; 700 W Singing Wind Rd; 9am-5pm), which is surely one of the great indie bookstores in the Southwest. Winnifred 'Winn' Bundy keeps tens of thousands of titles arranged in lovely literary chaos on a ranch 4 miles north of Benson. There's an excellent selection of Southwestern-themed books, but with this volume of stock there's something for every taste on the shelves. Winn herself is often around; if you get a chance to chat with her, do so and enjoy the company of one of the true great characters of the American West. To get here, enter Benson (likely from I-10). Go north on Occtillo St for about 2.5 miles until you see the sign for Singing Wind Bookshop on your right. It's about half a mile down a dirt road from here. After you enter through the gate, close it behind you.
## EASTERN ARIZONA
From Flagstaff east to the New Mexico line, the most dominant scenic feature often seems to be the Burlington Northern-Santa Fe Railway freights that run alongside the interstate. But there are some iconic Route 66 sites along here, and a few spots that will surprise you just off the road.
### Meteor Crater
The wooly mammoths and ground sloths that slouched around northern Arizona 50,000 years ago must have got quite a nasty surprise when a fiery meteor crashed into their neighborhood, blasting a hole some 550ft deep and nearly 1 mile across. Today the privately owned crater ( 928-289-5898; www.meteorcrater.com; adult/child/senior $15/8/14; 7am-7pm summer, shorter hours rest of the year) is a major tourist attraction with exhibits about meteorites, crater geology and the Apollo astronauts who used its lunar-like surface to train for their moon missions. You're not allowed to go down into the crater, but there are guided one-hour rim walking tours departing from 9:15am to 2:15pm (free with admission). The crater is about 6 miles off I-40 exit 233, 35 miles east of Flagstaff and 20 miles west of Winslow.
### Winslow
'Standing on a corner in Winslow, Arizona...'Sound familiar? Thanks to the Eagles' catchy '70s tune 'Take It Easy', lonesome little Winslow is now a popular stop on the tourist track. In a small park (www.standinonthecorner.com; 2nd St & Kinsley Ave) on Route 66 you can pose with a life-size bronze statue of a hitchhiker backed by a charmingly hokey trompe l'oeil mural of that famous girl – oh Lord! – in a flatbed Ford. Up above, a painted eagle poignantly keeps an eye on the action, and sometimes a red antique Ford parks next to the scene. In 2005 a fire gutted the building behind the mural, which was miraculously saved.
#### Sights & Activities
Homolovi State Park PARK
( 928-289-4106; http://azstateparks.com; per vehicle $7; visitor center 8am-5pm) Closed in 2010 during the state budget crisis, this grasslands park beside the Little Colorado River re-opened in 2011 with a shorter name (it was formerly Homolovi Ruins State Park) and a renewed commitment to protect the artifacts and structures within this sacred Hopi ancestral homeland. Before the area was converted into a park in 1993, bold thieves used backhoes to remove artifacts. Today, short hikes lead to petroglyphs and partly excavated ancient Native Americansites. There's a first-come, first-served campground (tent & RV sites $25), with electric hookups, water and showers, near the Homolovi ruins. The park is 3 miles northeast of Winslow via Hwy 87 (exit 257).
Lorenzo Hubbell Trading Post MUSEUM
( 928-289-2434; 523 W 2nd St; 9am-5pm Mon-Fri, 9am-3pm Sat) Built in 1917, this trading post was tilting toward ruin until the chamber of commerce renovated it and took possession in 2009. Now it's a beautiful rustic space that's part visitor center, part museum.
#### Sleeping & Eating
Winslow is a handy base for the Hopi Reservation (Click here), some 60 miles northeast of here. There are plenty of chain hotels and restaurants off I-40 at exit 253.
La Posada HISTORIC HOTEL $$
( 928-289-4366; www.laposada.org; 303 E 2nd St; r $109-169; ) An impressively restored 1930 hacienda designed by star architect du jour Mary Jane Colter, this was the last great railroad hotel built for the Fred Harvey Company along the Santa Fe Railroad. Elaborate tilework, glass-and-tin chandeliers, Navajo rugs and other details accent its palatial Western-style elegance. They go surprisingly well with the splashy canvases of Tina Mion, one of the three preservation-minded artists who bought the rundown place in 1997. The period-styled rooms are named for illustrious former guests, including Albert Einstein, Gary Cooper and Diane Keaton.
Turquoise Room SOUTHWESTERN $$
(La Posada; breakfast $6-11, lunch $9-13, dinner $17-32; 7am-9pm) Even if you're not staying at La Posada, treat yourself to the best meal between Flagstaff and Albuquerque at its unique restaurant. Dishes have a neo-Southwestern flair, the placemats are handpainted works of art, and there's a children's menu as well. If the fried squash blossoms are on the appetizer menu, toast your good fortune and order up, for the gods have smiled on you today.
#### Information
The visitor center ( 928-289-2434; www.winslowarizona.org; 523 W 2nd St; 9am-5pm Mon-Fri, 9am-3pm Sat year-round, 9am-3pm Sun mid-Jun–mid-Aug) can be found inside the recently renovated Lorenzo Hubbell Trading Post.
#### Getting There & Away
Greyhound buses stop at McDonald's at 1616 N Park Dr, but tickets aren't sold here; you can buy them in advance online or from the driver (at their discretion). The _Southwest Chief_ stops daily (westbound at 7:50pm, eastbound at 5:39am) at the unstaffed Amtrak station (501 E 2nd St). Tickets can be purchased onboard, but are twice as pricey as they are with advance reservations.
### Holbrook
In the 1880s Holbrook may have been one of the wickedest towns in the Old West ('too tough for women and churches'), but today this collection of rock shops and gas stations is better known as the Route 66 town with the wacky wigwam motel. It's also a convenient base from which to explore Petrified Forest National Park and its fossilized wood.
For the best selection and quality of petrified wood and other rocks and minerals, stop by Jim Gray's Petrified Wood Co ( 928-524-1842; www.petrifiedwoodco.com; cnr Hwys 77 & 180; 7:30am-8pm), an expansive complex about a mile south of town. Polished and primed pieces of the ancient wood for sale here can cost up to $16,000. The smooth and unique coffee tables are hard to resist.
#### Sights & Activities
Navajo County Historical Museum MUSEUM
( 928-524-6558; 100 E Arizona St; donations appreciated; 8am-5pm Mon-Fri, 8am-4pm Sat & Sun) The 1898 county courthouse is home to an eclectic assortment of historic local exhibits as well as Holbrook's chamber of commerce and visitor center. Each room of the museum highlights a different aspect of Holbrook's history. A creepy highlight is the old county jail, where the windowless cells were still being used as recently as 1976.
#### Sleeping & Eating
A full array of chain hotels are spaced along the northern part of Navajo Blvd.
Travelodge MOTEL $
( 928-524-6815; www.travelodge.com; 2418 E Navajo Blvd; r incl breakfast $58-65; ) This well-run place is a budget find, and it feels more like a mom-and-pop than part of a national chain. Spotless standard rooms all come with refrigerators and microwaves. The continental breakfast includes scrambled eggs and sausage. Before you book online, give the manager a call and he might give you a lower rate.
Wigwam Motel MOTEL $
( 928-524-3048; www.galerie-kokopelli.com/wigwam; 811 W Hopi Dr; r $52-58; ) Embrace the schlock of Route 66 at this motel, where each room is its own concrete tipi. Each is outfitted with restored 1950s hickory log-pole furniture and retro TVs.
Joe & Aggie's Cafe MEXICAN, AMERICAN $$
(121 W Hopi Dr; mains $5-15; 6am-8pm Mon-Sat) This Route 66 favorite is a bit uninspired, but its tacos, enchiladas, burgers and chicken-fried steak are fine for anyone looking for dependable grub after a hard day of sightseeing. The salsa served with the free chips has a satisfying kick.
Mesa Italiana ITALIAN $$
( 928-524-6696; 2318 E Navajo Blvd; mains $11-21; lunch Mon-Fri, dinner daily) Locals vouch for this place.
#### Information
For online information, check out www.holbrookchamberofcommerce.com/holbrook.
Police ( 928-524-3991; 120 E Buffalo)
Post office ( 928-524-3311; 100 W Erie; 9am-5pm Mon-Fri, 10am-2pm Sat)
Visitor center ( 928-524-6558; 100 E ArizonaSt; 8am-5pm Mon-Fri, 8am-4pm Sat & Sun) In the county courthouse.
#### Getting There & Away
Greyhound ( 928-524-2255) stops at the Circle K at 101 Mission Lane, where you can buy tickets.
### Holbrook to New Mexico
East of Holbrook, Route 66 barrels on as I-40 for 70 miles before entering New Mexico just beyond Lupton. The only attraction to break the monotony of the road is the section cutting through the Painted Desert in Petrified Forest National Park.
##### PETRIFIED FOREST NATIONAL PARK
Forget about green. The 'trees' of the Petrified Forest are fragmented, fossilized logs scattered over a vast area of semidesert grassland. Sounds boring? Not so! First, many are huge – up to 6ft in diameter –and at least one spans a ravine to form a natural bridge. Second, they're beautiful. Take a closer look and you'll see extravagantly patterned cross-sections of wood shimmering in ethereal pinks, blues and greens. And finally, they're ancient: 225 million years old, making them contemporaries of the first dinosaurs that leapt onto the scene in the Late Triassic period.
The trees arrived via major floods, only to be buried beneath silica-rich volcanic ash before they could decompose. Groundwater dissolved the silica, carried it through the logs and crystallized into solid, sparkly quartz mashed up with iron, carbon, manganese and other minerals. Uplift and erosion eventually exposed the logs. Souvenir hunters filched thousands of tons of petrified wood before Teddy Roosevelt put a stop to the madness and made the forest a national monument in 1906 (it became a national park in 1962). Scavenge some today and you'll be looking at fines and even jail time.
Aside from the logs, the park also encompasses Native American ruins and petroglyphs, plus an especially spectacular section of the Painted Desert north of the I-40.
Petrified Forest National Park ( 928-524-6228; www.nps.gov/pefo; per vehicle $10; 7am-7pm May-Aug, 7am-6pm Mar, Apr & Sep, 8am-5pm Oct-Feb), which straddles the I-40, has an entrance at exit 311 off I-40 in the north and another off Hwy 180 in the south. A 28-mile paved scenic road links the two. To avoid backtracking, westbound travelers should start in the north, eastbound ones in the south.
A video describing how the logs were fossilized runs regularly at the Painted Desert Visitor Center, near the north entrance, and the Rainbow Forest Museum near the South Entrance. Both have bookstores, park exhibits and rangers that hand out free maps and information pamphlets.
The scenic drive has about 15 pullouts with interpretive signs and some short trails, but there's no need to stop at each and every one in order to appreciate the park. Two trails near the southern entrance provide the best access for close-ups of the petrified logs: the 0.6-mile Long Logs Trail, which has the largest concentration, and the 0.4-mile Giant Logs Trail, which is entered through the Rainbow Forest Museum and sports the park's largest log.
A highlight in the center section is the 3-mile loop drive out to Blue Mesa, where you'll be treated to 360-degree views of spectacular badlands, log falls and logs balancing atop hills with the leathery texture of elephant skin. Nearby, at the bottom of a ravine, hundreds of well-preserved petroglyphs are splashed across Newspaper Rock like some prehistoric bulletin board. Hiking down is verboten, but free spotting scopes are set up at the overlook.
There's more rock art at Puerco Pueblo, but the real attraction here is the partly excavated 100-room ruins that may have been home to as many as 1200 people in the 13th century.
North of the I-40 you'll have sweeping views of the Painted Desert, where naturepresents a hauntingly beautiful palette, especially at sunset. The most mesmerizing views are from Kachina Point behind the Painted Desert Inn (admission free; 9am-5pm year-round), an old adobe turned museum adorned with impressive Hopi murals.
Kachina Point is also the trailhead for wilderness hiking and camping. There are no developed trails, water sources or food, so come prepared. Overnight camping requires a free permit available at the visitor centers.
There are no accommodations within the park and food service is limited to snacks available at the visitor centers. The closest lodging is in Holbrook.
Top of section
# New Mexico
**Includes »**
Albuquerque
Santa Fe
Taos
Mora Valley & Northeastern New Mexico
Chaco Canyon & Northwestern New Mexico
Silver City & Southwestern New Mexico
Carlsbad Caverns & Southeastern New Mexico
Roswell
### Why Go?
It's called the 'Land Of Enchantment' for a reason. Maybe it's the drama of sunlight and cloud shadow playing out across endlessly rolling juniper-speckled hills; or the traditional mountain villages of horse pastures and adobe homes; or the gentle magnificence of the 13,000-foot Sangre de Cristo range; or the volcanoes, river canyons and vast desert plains spread beneath an even vaster sky. The beauty sneaks up on you, then casts a powerful spell. Mud-brick _santuarios_ filled with sacred folk art; ancient and contemporary Indian pueblos; real-life cowboys and legendary outlaws; chile-smothered enchiladas: all add to the distinct vibe of otherness that often makes New Mexico feel like a foreign country.
Maybe the state's indescribable charm is best expressed in the iconic paintings of Georgia O'Keeffe. She herself exclaimed, on her very first visit: 'Well! Well! Well!...This is wonderful! No one told me it was like this.'
But seriously, how could they?
### When to Go
Mid-Aug–mid-Oct New Mexico at its best: gorgeous weather, wild sunflowers, chile harvest, fiestas.
Christmas season Ski the Sangres, walk Canyon Rd on Christmas Eve, join in local holiday traditions.
June–mid-Aug Prime time for outdoor activities. But beware the monsoon storms!
### Best Places to Eat
»San Marcos Café (Click here)
»Trading Post Cafe (Click here)
»Ellis Store Country Inn (Click here)
»Pie-O-Neer Café (Click here)
»Coyote Café (Click here)
### Best Places to Stay
»Earthships (Click here)
»St James Hotel (Click here)
»Christ in the Desert Monastery (Click here)
»Los Poblanos (Click here)
»La Fonda (Click here)
### New Mexico Planning
Due to major differences in altitude, when it's comfy in the lower, southern part of the state, it might be freezing in the northern mountains. Likewise, when the weather's perfect in Santa Fe, it's scorching in Carlsbad. If traveling around the state, bring a versatile wardrobe. With rare exception, casual dress is the way to go in New Mexico.
If you're afraid of spicy foods, order your chile (green, red or 'Christmas') on the side – but do try it. If you enjoy hot foods, beware: New Mexican chile is said to have addictive properties!
### DON'T MISS
Steeped in traditional Native American and Hispanic cultures, soulful Santa Fe has world-class art, gourmet restaurants and great local food, old adobe architecture and famous festivals. An hour-and-a-half north is Taos, the famous artist community and hippy haven, known for the nearby historic Pueblo and world-class ski area. These two towns feel like nowhere else in the USA. Both sit beneath the Sangre de Cristo Mountains, which are laced with hiking/biking trails and wilderness backpacking routes.
Further south, tiny Lincoln, set in a scenic valley along the meandering Rio Bonito, oozes Wild West history as the former stomping grounds of Billy the Kid.
Among the state's most fantastic natural features are White Sands National Monument – where you can play among gleaming white dunes that ripple, swell and curl through the Tularosa Basin – and Carlsbad Caverns National Park, where you can walk through a massive underground fantasyland of stalagmites and stalactites. Most beautiful of all might be the Ghost Ranch area, where you'll find the landscape that so vividly influenced Georgia O'Keeffe.
### Tips for Drivers
»New Mexico's main arteries are I-40 – which cuts east–west from Texas to Arizona via Albuquerque – and I-25, running north–south from the Colorado border, through Santa Fe and Albuquerque to Las Cruces. I-40 is occasionally closed in spring due to windstorms; both interstates may close during heavy blizzards in winter.
»Along highways in the south, you'll hit Border Patrol checkpoints with dogs (hint: think twice before bringing your cannabis prescription down from Denver).
»Interstate speed limits are 75mph, while state highways may go to 70mph.
»For road conditions, call 800-432-4269 or visit www.nmroads.com.
### TIME ZONE
New Mexico is on Mountain Time (seven hours behind GMT) and observes daylight savings. During daylight savings, it's one hour ahead of Arizona – otherwise they're the same.
### Fast Facts
»Population: 2 million
»Area: 121,599 sq miles
»Sales tax: 5-8%
»Albuquerque to Las Cruces: 223 miles, 3½ hours
»Gallup to Tucumcari: 311 miles, 4½ hours
»Santa Fe to Taos: 70 miles, 1½ hours
### State Bird
The roadrunner can run nearly 20mph and kills and eats rattlesnakes.
### Resources
»All About New Mexico: www.psych.nmsu.edu/~linda/chilepg.htm
»New Mexico CultureNet: www.nmcn.org
»New Mexico Department of Tourism: www.newmexico.org
### New Mexico Highlights
Immerse yourself in art and culture in the iconic state capital, Santa Fe (Click here)
Visit the famous Pueblo, ski fluffy powder and get your mellow on in groovy Taos (Click here)
Hike high peaks and camp beside alpine lakes in the Pecos Wilderness (Click here)
Walk in the bootprints of Billy the Kid in historic Lincoln (Click here)
Explore the underground fantasyland of Carlsbad Caverns National Park (Click here)
Slide down the mesmerizing dunes at White Sands National Monument (Click here)
Get healed at the 'Lourdes of America' – the Santuario de Chimayo (Click here)
Wonder at the mystery of ancient civilization at Chaco Culture National Historical Park (Click here)
Trek through rugged wilderness and climb into cliff dwellings in Gila National Forest (Click here)
###### History
People roamed this land as far back as 10,500 BC, but by Francisco Vasquez de Coronado's arrival in the 16th century, Pueblo Indians made up the dominant communities. Santa Fe was established as the Spanish colonial capital around 1610, after which Spanish settlers and farmers fanned out across northern New Mexico and missionaries began their often violent efforts to convert the area's Puebloans to Catholicism. Following a successful revolt in 1680, Native Americans occupied Santa Fe, until 1692 when Don Diego de Vargas recaptured the city.
In 1851 New Mexico became US territory. Native American wars, settlement by cowboys and miners, and trade along the Santa Fe Trail further transformed the region, and the arrival of the railroad in the 1870s created an economic boom.
Painters and writers set up art colonies in Santa Fe and Taos in the early 20th century, and in 1912 New Mexico became the 47th state. A top-secret scientific community descended on Los Alamos in 1943 and developed the atomic bomb. Some say that four years later, aliens crashed outside of Roswell. Maybe that's why New Mexico is now poised to become a leader in space tourism and commercial space flights.
###### New Mexico Scenic Routes
One of the best ways to explore New Mexico is to travel its scenic highways. Eight have been selected as National Scenic Byways (www.byways.org) – though they are not necessarily the most striking stretches of pavement in the state. Just a few of the most rewarding roads you can drive:
Billy the Kid Scenic Byway (www.billybyway.com) This mountain-and-valley loop in southeastern New Mexico swoops past Billy the Kid's stomping grounds (Click here), Smokey Bear's gravesite and the orchard-lined Hondo Valley. From Roswell (Click here), take Hwy 380 west.
High Road to Taos The back road between Santa Fe (Click here) and Taos (Click here) passes through sculpted sandstone desert, fresh pine forests and rural villages with historic adobe churches and horse-filled pastures. The 13,000ft Truchas Peaks soar above. From Santa Fe, take Hwy 84/285 to Hwy 513, then follow the signs.
NM Hwy 96 From Abiquiú Lake to Cuba (Click here), this little road wends through the heart of Georgia O'Keeffe country, beneath the distinct profile of Cerro Pedernal, then past Martian-red buttes and sandstone cliffs striped purple, yellow and ivory.
NM Hwy 52 Head west from Truth or Consequences (Click here) into the dramatic foothills of the Black Range, past the old mining towns of Winston and Chloride (Click here). Continue north, emerging onto the sweeping Plains of San Augustin before reaching the bizarre Very Large Array (Click here).
### DID YOU KNOW?
New Mexico is the only state with an official state question: 'red or green? – referring to chile, of course! You'll hear it every time you order New Mexican food. Feeling ambivalent? Choose 'Christmas' and try both.
For more scenic drives and the lowdown on Route 66, check out Click here.
###### Dangers & Annoyances
Albuquerque sits over 5000ft above sea level, Santa Fe and Taos are at 7000ft and the mountains top 13,000ft – so if you're arriving from sea level, you may feel the altitude. Take it easy for the first day or two, and be sure to drink plenty of water to help get adjusted – a good idea, anyway, considering how arid the state is. Combined with altitude, the 300-plus days of sunshine also make this an easy place to get sunburned. And New Mexico leads the nation in lightning-strike deaths per capita, so be cautious if hiking in exposed areas during monsoon thunderstorms, which can be downright apocalyptic.
If you're into outdoor adventures, your New Mexico plans may hinge on how wet or dry the year has been. Ski areas may have some of the best or worst conditions in the West depending on snowfall; national forests sometimes close completely during severe summer drought.
Back around 1880, Territorial Governor Lew Wallace wrote, 'Every calculation based on experience elsewhere fails in New Mexico.' In many regards, that's still true today. Things here just don't work the way you might expect. That, paired with the entrenched _mañana_ mindset, might create some baffling moments. Our advice: just roll with it.
###### Getting There & Away
Most travelers fly into Albuquerque International Sunport (ABQ), but a few flights also land in Santa Fe (SAF).
Amtrak offers passenger train service on the Southwest Chief, which runs between Chicago and Los Angeles, stopping in Raton, Las Vegas, Lamy (for Santa Fe), Albuquerque and Gallup. A Native American guide hops aboard between Albuquerque and Gallup to provide insightful commentary. The Sunset Limited stops in Deming on its way from Florida to Los Angeles.
Greyhound buses travel to some New Mexico towns, but service has been cut back in recent years. Some areas in the state now have regional transport systems that connect small villages and larger towns and are either extremely cheap or free. But due to limited public transport options and the long distances, renting a car is the best choice for most visitors. For more information on driving, see Tips for Drivers (Click here), New Mexico Scenic Routes and Route 66 & Scenic Drives (Click here).
For more information on transportation throughout the Southwest, see Click here.
## ALBUQUERQUE
This bustling crossroads has an understated charm, one based more on its locals than on any kind of urban sparkle. In New Mexico's largest city, folks are more than happy to share history, highlights and must-try restaurants – making this much more than just the dot on the Route 66 map where Bugs Bunny should have turned left.
Centuries-old adobes line the lively Old Town area, and the shops, restaurants and bars in the hip Nob Hill zone are all within easy walking distance of each other. Good hiking is abundant just outside of town, through evergreen forests or among panels of ancient petroglyphs, while the city's modern museums explore space and nuclear energy. There's a vibrant mix of university students, Native Americans, Hispanics and gays and lesbians. You'll find square dances and yoga classes flyered with equal enthusiasm, and see ranch hands and real-estate brokers chowing down beside each other at hole-in-the-wall _taquerías_ (Mexican fast-food restaurants) and retro cafes.
#### Sights
Central Ave is Albuquerque's main street, passing through Old Town, downtown, the university, Nob Hill and the state fairground. Street addresses often conclude with a directional designation, such as Wyoming NE: the center point is where Central Ave crosses the railroad tracks, just east of downtown. For instance, locations north of Central Ave and east of the tracks would have a NE designation.
Most of Albuquerque's top sites are concentrated in Old Town, a straight shot down Central Ave from Nob Hill and the University of New Mexico (UNM). Some of the best attractions, however – including the Indian Pueblo Cultural Center, Petroglyph National Monument and Sandia Peak Tramway – are more far-flung and most easily accessible by car.
### ALBUQUERQUE IN...
#### One Day
Jump-start your belly with a plate of huevos rancheros from Frontier, before heading to the Indian Pueblo Cultural Center, where you'll get a head start on a primo Pueblo education.
Next up visit the BioPark, which has a zoo, aquarium, botanical gardens and nature trails along the bosk. Head back into town for lunch, grabbing a bite at Golden Crown Panaderia, then wander over to Old Town for the afternoon. Walk off lunch admiring the San Felipe de Neri Church, browsing galleries and catching up on your snake trivia at the American International Rattlesnake Museum. Dine outdoors in Nob Hill; Albuquerque's grooviest neighborhood is thick with eateries.
#### Two Days
Wander around the Petroglyph National Monument, then head over to Rudy's Bar-B-Q for lunch before blowing your mind at the National Museum of Nuclear Science and History. Reach the top of Sandia Crest before sunset, either by Tramway or by scenic road, for expansive views of the Rio Grande Valley. When you get back down, linger over delicious food and wine at the Slate Street Café & Wine Loft.
##### OLD TOWN
Some of the quaint adobe shops lining the alleyways of Old Town have been here since 1706, when the first 15 Spanish families called the newly named Albuquerque their home. From the town's founding until the arrival of the railroad in 1880, Old Town Plaza was the hub of daily life. With many museums, galleries and original buildings within walking distance, this is the city's most popular tourist area. As you walk around, try to keep your mind's eye trained partly on the past. Imagine this area as it began, with a handful of hopeful families grateful to have survived a trek across hundreds, in some cases thousands, of miles of desert wilderness. Free guided walking tours ( 11am Tue-Sun, mid-Apr–mid-Nov) are offered by the Albuquerque Museum of Art & History.
American International
Rattlesnake Museum MUSEUM
(www.rattlesnakes.com; 202 San Felipe St NW; adult/child $3.50/2.50; 10am-5pm Mon-Sat, 1-5pm Sun) If you've ever been curious about serpents, this is the museum for you. It's possibly the most interesting museum in town, and you won't find more species of rattlesnake in one place anywhere else in the world. Come here for the lowdown on one of the world's most misunderstood snakes.
Albuquerque Museum of Art & History MUSEUM
(www.cabq.gov/museum; 2000 Mountain Rd NW; adult/child $4/1; 9am-5pm Tue-Sun) Conquistador armor and weaponry are highlights at this museum, where visitors can study the city's tricultural Native American, Hispanic and Anglo past. There's also a great gallery featuring the work of New Mexican artists. Family art workshops are offered on Saturdays at 2:30pm, and gallery tours are given daily at 2pm. Admission is free on the first Wednesday of the month and on Sundays until 1pm.
San Felipe de Neri Church CHURCH
(www.sanfelipedeneri.org; Old Town Plaza; 7am-5:30pm daily, museum 9:30am-4:30pm Mon-Sat). The church dates from 1793 and is Old Town's most famous photo op. Mass is held daily at 7am; Sunday Mass is at 7am, 10:15am and noon.
Turquoise Museum MUSEUM
(www.turquoisemuseum.com; 2107 Central Ave NW; admission $4; 9:30am-3pm Mon-Sat) At this museum visitors get an enlightening crash course in determining the value of stones – from high quality to fakes. Joe Dan Lowry, the turquoise expert who owns the museum, is as opinionated as he is knowledgeable, so you're in for an interesting time!
Also in the Old Town are ¡Explora! (Click here) children's museum/science center and the New Mexico Museum of Natural History & Science (Click here).
##### DOWNTOWN
Albuquerque's small downtown isn't the epicenter for action that it was some decades ago, when Route 66 was a novelty and reason enough to set out from either coast in a big '55 Chevy. City planners and business owners have tried in recent years to restore some of that fab '50s neon while encouraging trendy restaurants, galleries and clubs, with mixed success. On Saturday nights, Central Ave is jammed with 20-somethings cruising in low riders to see and be seen. Note: the area around the Alvarado Transportation Center has a particularly sketchy vibe.
##### NOB HILL & UNM AREA
A fun and funky place to shop, eat, see art films or get a haircut at a cigar/wine bar, this stretch of Central Ave starts at UNM and runs east to about Carlisle Blvd. Fashion-lovers can browse colorful shops for that unique outfit or accessory; artists will find inspiration and supplies. Even those not looking for anything in particular should find something of interest to muse over. See Shopping, below, for recommended stores.
University of New Mexico MUSEUMS
( www.unm.edu; Central Ave NE). There are 8 museums and galleries, along with loads of public art, packed onto the grounds of UNM. This small but peaceful campus is also home to a performing arts center and the Tamarind Institute (www.tamarind.unm.edu; 9am-5pm Mon-Fri), which helped save the art of lithography from extinction in the 1960s and '70s. The Maxwell Museum of Anthropology (www.unm.edu/~maxwell; 10am-4pm Tue-Sat) is one of the best of its kind in the country. Visit the UNM Welcome Center ( 505-277-1989; 2401 Redondo Dr; 8am-5pm Mon-Fri) for information and maps.
### ALBUQUERQUE'S MOUNTAIN: SANDIA CREST
Albuquerqueans always know which way is east thanks to 10,378ft Sandia Crest, sacred to Sandia Pueblo and well named for both its wavelike silhouette and the glorious pink ( _sandia_ is Spanish for 'watermelon') its granite cliff s glow at sunset. There are three ways to the top.
Beautiful 8-mile (one-way) La Luz Trail (FR 444; parking $3) is the most rewarding, rising 3800ft from the desert, past a small waterfall to pine forests and spectacular views. It gets hot, so start early. Take Tramway Blvd east from I-25, then turn left on FR 333 to the trailhead.
Sandia Peak Tramway (Click here) is the most extravagant route to the top; ride round-trip or take the tram up then hike down La Luz, walking two more miles on Tramway Trail to your car.
Finally you can drive, via NM 14, making a left onto Sandia Crest Rd (NM 165). The road is lined with trailheads and picnic spots (a daily $3 parking fee covers all of them), and low-impact camping ($3) is allowed by permit throughout Cibola National Forest. The choices are endless, but don't skip the easy 1-mile round-trip to Sandia Man Cave, where the oldest human encampment in North America was discovered in 1936. Bring a flashlight. The trailhead is along Hwy 165, north of the spur road to Sandia Crest.
At the top, the Sandia Crest Visitor Center ( 505-248-0190; NM 165; 10amsunset in winter, to 7pm in summer) offers nature programs daily; Sandia Crest House (dishes $3-8), in the same building, serves burgers and snacks. This is the jumping-off point for the exquisite Sandia Crest Trail. With incredible views either way you go, paths lead north along the ridgeline for 11 miles and south along the ridge for 16.
Take the trail 2 miles south, past Kiwanis Cabin rock house, to the tram terminal and High Finance ( 505-243-9742; www.sandiapeakrestaurants.com; lunch mains $7-15, dinner mains $20-30; 11am-9pm), where the food is nothing special but the views are fabulous.
This is also the site of Sandia Peak Ski Park ( 505-242-9052; www.sandiapeak.com; lift tickets adult/child $50/40; 9am-4pm Dec-Mar & Jun-Sep), a smallish but scenic ski area. In summer, the park has a bike and lift combo for $58 (with $650 deposit) – you get a bike and lift pass to blaze those downhill runs all day long; note that bikes aren't allowed on the tram.
##### METROPOLITAN ALBUQUERQUE
Indian Pueblo Cultural Center MUSEUM
( 505-843-7270; www.indianpueblo.org; 2401 12th St NW; adult/child $6/3; 9am-5pm) Operated by the All Indian Pueblo Council, the cultural center is a must-see even on the shortest of Albuquerque itineraries. The history exhibits are fascinating, and the arts wing features the finest examples of each Pueblo's work. The IPCC also houses a large gift shop and retail gallery. Along with serving Pueblo-style cuisine, the on-site Pueblo Harvest Café (mains $5-8; 8am-3pm Mon-Fri, to 5pm Sat & Sun; ) has weekend art demonstrations, bread-baking demos and dances.
Petroglyph National Monument ARCHAEOLOGICAL SITE
(www.nps.gov/petr) More than 20,000 petrogyphs are etched on basalt along the edge of an ancient lava field. Stop by the visitor center, on Western Trail at Unser Blvd, to determine which of three viewing trails – in different sections of the park – best suits your interests. Rinconada Canyon has the longest trail (2.2 miles round-trip) and is best if you want some solitude; Boca Negra Canyon features three short trails; Piedras Marcadas has 300 petroglyphs along a 1.5-mile trail. To leave the city behind for great views but no rock art, hit the Volcanoes Trail. Note: smash-and-grab thefts have been reported at some trailhead parking lots, so don't leave valuables in your vehicle. The visitor center is 7.5 miles north of Old Town; head west on I-40 across the Rio Grande and take exit 154 north.
Old Town Albuquerque
Top Sights
Albuquerque Museum of Art & History B1
American International Rattlesnake Museum B2
San Felipe de Neri Church B2
Sights
1 !Explora! D2
3 New Mexico Museum of Natural History & Science C1
3 Turquoise Museum A2
Sleeping
4 Böttger Mansion B3
5 Casas de Sueños A3
Eating
6 Antiquity A2
7 Church Street Cafe B1
8 Garcia's Kitchen C4
9 Seasons Rotisserie & Grill B1
Shopping
10 Palms Trading Post D4
11 Silver Sun B3
Sandia Peak Tramway CABLE CAR
(www.sandiapeak.com; Tramway Blvd; vehicles $1, adult/child $20/12; 9am-8pm Wed-Mon, from5pm Tue Sep-May, 9am-9pm Jun-Aug) Albuquerque's most famous attraction is the world's longest aerial tram, rising 2.7 miles from the desert floor to the top of 10,378ft Sandia Peak. Views are spectacular any time (but sunsets are particularly brilliant). The tramway is in the northeast corner of Albuquerque; take the Tramway Rd exit off I-25.
National Museum of Nuclear Science & History MUSEUM
(www.nuclearmuseum.org; 601 Eubank Blvd SE;adult/child & senior $8/7; 9am-5pm; ) Exhibits here examine the Manhattan Project, the history of arms control and the use of nuclear energy as an alternative energy source. Docents here are retired military, and they're very knowledgeable. There are interactive activities for kids. To get there from Central Ave, turn south on Eubank.
National Hispanic Cultural Center CULTURAL BUILDING
(www.nhccnm.org; 1701 4th St SW; adult/child $3/free, admission free Sun; 10am-5pm Tue-Sun) In the historic Barelas neighborhood, this center for Hispanic visual, performing and literary arts has three galleries and the nation's premier Hispanic genealogy library. Each June it hosts the Festival Flamenco.
South Valley & North Valley NEIGHBORHOOD
These traditional agricultural areas near the Rio Grande are characterized by open spaces, small ranches, farms, and _acequias_ (traditional irrigation ditches that also mark walking paths). Chickens and horses roam fields between historical adobe and wood-frame houses and newer developments. The 39-sq-mile South Valley is bordered by I-25, I-40 and the West Mesa and volcanic cliffs.
North Valley is more mixed and upscale, with a reputation as affluent, pastoral, quiet and determined to keep it that way. Although it's just 7 miles from downtown Albuquerque, it feels like a world away. This 100-sq-mile area is roughly bordered by I-40, I-25, the Rio Grande and the Bernalillo–Sandoval County line.
Corrales NEIGHBORHOOD
This village, just north of North Valley, was established by Spanish settlers in 1710 but was home to Tewa Indians for centuries before that – they were practicing irrigated agriculture here 1300 years ago. Even more rural than North Valley, Corrales offers splendid strolling through the bosk (riparian woods) and along _acequias_. Take NM 448 north into the village and then drive or walk along any side roads – most are unpaved and will reward with earthy scents as scampering rabbits and quail crisscross your path among 200-year-old adobes and modern replicas. There's also a surprising amount of fine wine being made in these hills.
Gruet Winery WINERY
(www.gruetwinery.com; 8400 Pan American Fwy NE; 10am-5pm Mon-Fri, from noon Sat) Gives daily tours at 2pm and free tastings. Off I-40, north of city center.
Casa Rondeña WINERY
(www.casarodena.com; 733 Chavez Rd NW; 10am-6pm Mon-Sat, from noon Sun) Only gives tours during the area's summer Lavender Festival and charges $5 for tastings. In the Los Ranchos area of the North Valley; turn east off of Rio Grande Blvd to get here.
#### Activities
###### Hiking
Sandia Crest is Albuquerque's outdoor playground, popular for skiing and hiking (see Click here). Elena Gallegos Picnic Area (Simms Park Rd; weekday/weekend parking $1/2; 7am-7pm mid-Oct–mid-Apr, to 9pm mid-Apr–mid-Oct), in the foothills of the Sandias, is a popular jumping-off point for hiking, running and mountain-biking trails; some are wheelchair-accessible. Go early in the day before the sun gets too hot, or at dusk to take advantage of the panoramic views and watch the city lights begin twinkling below. You might be lucky enough to hear a chorus of howling coyotes at sunset. Follow Simms Park Rd from Tramway Blvd, south of the Sandia Peak Tramway.
###### Cycling
Cycling is big in Albuquerque, both for beginners and national-level competitors. Get outfitted at Northeast Cyclery ( 505-299-1210; 8305 Menaul NE; rentalsper day $25) and head out. Download a useful city map at www.cabq.gov/bike to find dedicated off-road tracks along arroyos. To ride along the Rio Grande, park at the Albuquerque BioPark and follow the riverside trail north or south. (The smell of green chiles roasting at local factories is best appreciated if you head south during autumn; the path is less urban if you head north.)
###### Walking
Walking the irrigation ditches is a downright local thing to do. Get a decent city map from the visitor center (many hotels also have them) and find the thin blue lines branching out in North Valley from the Rio Grande between Montaño Rd and Paseo del Norte and around Rio Grande Blvd. _Acequias_ are bordered by walking paths, a gift to early-morning risers who value cool temperatures in the summer.
###### Rock Climbing
Rock climbers itching to hit the wall will dig the Stone Age Climbing Gym ( 505-341-2016; www.climbstoneage.com; 4201 Yale Blvd NE; day pass $14; noon-11pm Mon-Fri, 10am-8pm Sat & Sun), offering 12,000 sq ft of professionally designed climbing terrain simulating a variety of real rock features. Classes are offered and you can rent gear. For real rock, there are lots of great routes in the Sandias. To get here, take Comanche Rd exit off I-25
#### Tours
Story of New Mexico Program GENERAL
( 505-277-2527; www.dcereg.com) The UNM Department of Continuing Education offers excellent lectures on all things New Mexico, as well as tours to Santa Fe and events like the Folk Art Market, Indian Market and opera, and gallery tours along the High Road to Taos by top-notch guides. Advance registration is required.
#### Festivals & Events
Friday's _Albuquerque Journal_ (www.abqjournal.com) includes a venue section with an exhaustive listing of festivals and activities. The following are most notable.
Gathering of Nations Powwow CULTURAL
(www.gatheringofnations.com) Features dance competitions, displays of Native American arts and crafts, and the 'Miss Indian World' contest. Held in late April.
Zia Regional Rodeo RODEO
(www.nmgra.com) Three days of riding and roping, sponsored by the NM Gay Rodeo Association. Mid-August.
Bernalillo Wine Festival WINE
(www.newmexicowinefestival.com; admission $12)Locally produced wine, and live music too, staged about 15 minutes north of Albuquerque – a real treat if you're in town in early September.
New Mexico State Fair RODEO
(www.exponm.com) A biggie rodeo, live music, games and rides; runs for 16 days in September.
International Balloon Fiesta BALLOON
(www.balloonfiesta.org) The largest balloon festival in the world. You just haven't lived until you've seen a three-story-tall Tony the Tiger land in your hotel courtyard, which is exactly the sort of thing that happens during the nine-day festival, held between the first and second weekends in October.
### ALBUQUERQUE FOR CHILDREN
Albuquerque has lots on offer for kids – from hands-on museums to cool hikes.
To give your little one a lesson in astronomy or a chance to check out the latest educational IMAX flick on a five-story-tall screen, visit the New Mexico Museum of Natural History & Science (www.nmnaturalhistory.org; 1801 Mountain Rd NW; adult/child $7/4; 9am-5pm; ). It also has a number of kid-friendly activities and exhibits – children dig the Hall of Jurassic Supergiants and Dynatheater.
Hands-on science is the focus at ¡Explora! (www.explora.us; 1701 Mountain Rd NW; adult/child $8/4; 10am-6pm Mon-Sat, from noon Sun; ), where kids of all ages learn through playing with bubbles and balls and water and blocks. Most could stay here happily all day.
Adults will get as much out of the Albuquerque BioPark (www.cabq.gov/biopark; adult/child three parks $12/5, per park $7/3; 9am-5pm; ) as children. When the weather is nice, and you're traveling with family, the place is especially appealing for the combo ticket to three kid-friendly attractions: a zoo, an aquarium and a botanic gardens. It's a good-value way to stay entertained all day. Set on 60 shady acres along the Rio Grande, the park's Rio Grande Zoo (903 10th St NW) is home to more than 250 species. There's a lot going on here: sea-lion feedings take place daily at 10:30am and 3:30pm, camel rides are offered in the spring and summer, and an entertaining summertime live animal show happens at 11am and 2pm Wednesday through Sunday. Meanwhile the Albuquerque Aquarium (2601 Central Ave NW), 2.5 miles northwest of the zoo, has a 285,000-gallon shark tank.
On the flora side, visit the Rio Grande Botanic Gardens , next to the aquarium, and let the kids marvel at the 10,000-sq-ft glass conservatory filled to the brim with Mediterranean and desert fauna. Special garden events include a Butterfly Pavilion from May to September.
Tingley Beach (1800 Tingley Ave SW; admission free; sunrise-sunset; ) is connected to the aquarium and botanic gardens. This beloved open space includes fishing ponds stocked with rainbow trout, a children's pond and trails. You'll need a fishing license (day pass $12), but fortunately they are sold on-site at the gift shop ( 9am-5pm). A little train connects the Zoo, Aquarium/Botanic Gardens and Tingley Beach; it runs approximately every half-hour.
When the kids have had enough learning (or they're hot), Cliff's Amusement Park (www.cliffsamusementpark.com; 4800 Osuna NE; admission $25; Apr-Sep; ) is a great reward. The park has about 25 rides, including a roller coaster, water rides, a play area and other traditional favorites. Hours vary.
#### Sleeping
Although Albuquerque has about 150 hotels (all full during the International Balloon Fiesta and the Gathering of Nations), it's not exactly swimming in interesting nonmotel lodging.
If you're looking for budget lodgings, inexpensive motels line Central Ave in metropolitan Albuquerque, concentrated around the I-25 on-ramp and east of Nob Hill. You can score a room in the $35 to $45 range, but trust your gut as some are pretty sleazy. The best bets for cheap accommodations are the endless chain motels that hug I-25 and I-40.
##### OLD TOWN
Böttger Mansion B&B $$
( 505-243-3639, 800-758-3639; www.bottger.com; 110 San Felipe St NW; r incl breakfast $104-179; ) A friendly and informative proprietor gives this well-appointed Victorian-era B&B an edge over some tough competition. The eight-bedroom mansion, built in 1912, is a one-minute walk from Old Town Plaza. The honeysuckle-lined courtyard is a favorite with bird-watchers. Famous past guests in the home include Elvis, Janis Joplin and Machine Gun Kelly.
Casas de Sueños B&B $$
( 505-247-4560; www.casasdesuenos.com; 310 Rio Grande Blvd SW; r incl breakfast from $159; ) This lovely and peaceful place with luscious gardens and a pool has 21 adobe casitas featuring handcrafted furniture and original artwork. Some casitas have a kitchenette, fireplace and/or private hot tub – a couple are even outside in a private garden.
##### DOWNTOWN
Andaluz BOUTIQUE HOTEL $$
( 505-242-9090; www.hotelandaluz.com; 125 2nd St NW; r $140-240; ) Albuquerque's top hotel will wow you with style and attention to detail, from the dazzling lobby – where six arched nooks with tables and couches offer alluring spaces to talk and drink in public-privacy – to the Italian-made hypoallergenic bedding. The restaurant is one of the best in town, and there's a beautiful guest library and a rooftop bar. The hotel is so 'green' you can tour its solar water heating system – the largest in the state. You'll get big discounts booking online. It's one block north of Central Ave in the heart of downtown.
Route 66 Hostel HOSTEL $
( 505-247-1813; www.rt66hostel.com; 1012 Central Ave SW; dm $20, r from $25; ) With discounts for HI-USA members, this 42-person hostel is clean, fun, cheap and conveniently located between downtown and Old Town. A kitchen and library are available for guest use. Just west of the downtown business district.
Mauger Estate B&B B&B $$
( 505-242-8755, 800-719-9189; www.maugerbb.com; 701 Roma Ave NW, cnr 7th St NW; r incl breakfast $99-195, ste $160-205; ) This restored Queen Anne mansion (Mauger is pronounced 'major') has comfortable rooms with down comforters, stocked refrigerators and freshly cut flowers. Kids are welcome and there's one dog-friendly room complete with Wild West decor and a small yard ($20 extra).
Hotel Blue HOTEL $
( 877-878-4868; www.thehotelblue.com; 717Central Ave NW; r incl breakfast $60-99; ) Well positioned beside a park on the western edge of downtown, the art-deco 134-room Hotel Blue has Tempur-Pedic beds and a free airport shuttle. Bonus points awarded for the good-size pool and 40in flat-screen TVs.
##### NOB HILL & UNM AREA
Hiway House MOTEL $
( 505-268-3971; www.hiwayhousemotel.com; 3200Central Ave SE; s/d $35/40; ) Hiway was once a prolific Southwest chain, and this was the last one built in the 1950s. Just beyond the heart of the UNM and Nob Hill neighborhood, it's a 60-room place with the original 1958 neon sign and colonial-style architecture, but has been updated, with wi-fi. Not the cleanest, but an OK budget bet.
##### METROPOLITAN ALBUQUERQUE
Los Poblanos B&B $$$
( 505-344-9297, 866-344-9297; www.lospoblanos.com; 4803 Rio Grande Blvd NW; r $130-360; ) This amazing 20-room B&B, set among 25 acres of gardens, lavender fields (blooming mid-June through July) and an organic farm, is a registered National Historic Place. Los Poblanos is a five-minute drive from Old Town and is within walking distance of the Rio Grande and open-space trails. Organic eggs and produce from the farm are served for breakfast, and rooms feature kiva fireplaces.
Cinnamon Morning B&B B&B $$
( 800-214-9481; www.cinnamonmorning.com; 2700 Rio Grande Blvd NW; r $109-225; ) This wired B&B near Old Town has four rooms, a two-bedroom guesthouse and an outdoor hot tub. Lots of Southwest charm and common areas make it a relaxing and homey place to slumber.
Casita Chamisa B&B B&B $$
( 505-897-4644; www.casitachamisa.com; 850 Chamisal Rd NW; r $105-125; ) Accommodations here include a two-bedroom guesthouse equipped with a kitchenette and vibrant greenhouse; a large bedroom in the main house; and a studio with a kitchenette. The friendly host, Arnold Sargeant, offers valuable advice about the area, including the archaeological site where the B&B is located. In the North Valley; turn east on Chamisal Rd from Rio Grande Blvd.
Albuquerque North Bernalillo KOA CAMPGROUND $
( 505-867-5227; www.koa.com; 555 S Hill Rd, Bernalillo; tent sites $23-30, RV sites $34-52, cabins $38-48; ) About 15 miles north of the Albuquerque city limits, the better of the city's two KOA franchises has wi-fi and is within easy exploring distance of city attractions. Take exit 240 or 242 off I-25; S Hill Rd is close to the interstate.
#### Eating
Albuquerque offers the region's widest variety of international cuisines while serving up some good New Mexican grub. However, it's not a foodie destination like Santa Fe, and many restaurants geared to tourists are less than outstanding. If you're not sure what you want, head to Nob Hill and browse a variety of spots ranging from hip to homey until one catches your eye.
##### OLD TOWN
The plaza is surrounded by average eateries serving average food at premium prices. Consider walking a few blocks for a better selection.
Golden Crown Panaderia BAKERY $
( 505-243-2424; www.goldencrown.biz; 1103 Mountain Rd NW; mains $5-20; 7am-8pm Tue-Sat, 10am-8pm Sun) Who doesn't love a friendly neighborhood bakery? Especially one with gracious staff, fresh-from-the-oven bread and pizza, fruit-filled empanadas, smooth coffee and the frequent free cookie. Call ahead to reserve a loaf of quick-selling green chili bread. Go to their website to check out their 'bread cam'.
Garcia's Kitchen NEW MEXICAN $
(1736 Central Ave SW; mains $6-8; 7am-9pm Sun-Thu, to 10pm Fri & Sat) Part of a small local chain, this place just east of Old Town has some of the best New Mexican food in Albuquerque. The red vinyl booths and eclectic crowd give it a pure local feel. It's a great spot for breakfast.
Church St Cafe NEW MEXICAN $$
(2111 Church St NW; mains $7-15; 8am-4pm Sun-Wed,to 8pm Thu-Sat) The food is good for the plaza area, and the cafe is historic and huge, with a nice patio. Try the Spanish hot chile dip or the veggie fajitas.
Seasons Rotisserie & Grill MODERN AMERICAN $$$
( 505-766-5100; www.seasonsabq.com; 2031 Mountain Rd NW; lunch $9-16, dinner $17-31; 11:30am-2:30pm Mon-Fri, 5-9:30pm Sun-Thu, 5-10:30pm Fri & Sat) With bright-yellow walls, high ceilings, fresh flowers and a creative menu, this contemporary place provides welcome relief from the usual Old Town atmosphere. Try the house-made raviolis or fresh grilled fishes and meats.
Antiquity STEAKHOUSE $$$
( 505-247-3545; 112 Romero St NW; mains $17-26; 5-10pm) With just 14 tables in an atmosphere of rustic elegance, Antiquity specializes in steak, seafood and fine wine. The desserts list isn't long, but it doesn't need to be. This is a favorite of locals and visitors alike.
##### DOWNTOWN
Slate Street Café & Wine Loft MODERN AMERICAN $$
( 505-243-2210; www.slatestreetcafe.com; 515 Slate St; mains breakfast $6-12, lunch $9-15, dinner $11-27; 7:30am-3pm Mon-Fri, 9am-2pm Sat & Sun, 5-9pm Tue-Sat) This downtown establishment is usually packed with people who come to sample the clever Southwestern/American fare in the cafe and drink merlot in the upstairs wine loft. The wine-tasting menu changes regularly and offers 30 different wines by the bottle from all over the world. It is located off 6th St NW, just north of Lomas Blvd.
Artichoke Café MODERN AMERICAN $$$
( 505-243-0200; www.artichokecafe.com; 424 Central Ave SE; lunch mains $8-16, dinner mains $19-30; 11am-2:30pm Mon-Fri, 5-9pm daily) Elegant and unpretentious, this popular bistro does creative gourmet cuisine with panache and is always high on foodies' lists of Albuquerque's best. It's on the eastern edge of downtown, between the bus station and I-40.
##### NOB HILL & UNM AREA
In the grand tradition of university neighborhoods, this is the best area for cheap, healthy and vegetarian meals. But you can also find a number of swanky places to nosh.
Street Food Asia ASIAN $$
(www.streetfoodasiaabq.com; 3422 Central Ave SE; mains $12; 11am-10pm) One of the newest additions to the Nob Hill scene, this restaurant will take you on a culinary tour of the street stalls of Asian capitals, from Beijing to Bangkok to Kuala Lumpur. The concept – and the taste – is fresh and creative. There's even a stir-fry noodle bar.
Frontier NEW MEXICAN $
(www.frontierrestaurant.com; 2400 Central Ave SE; mains $3-8; 5am-1am; ) Get in line for enormous cinnamon rolls (made with, like, a stick of butter each!) and some of the best huevos rancheros in town. The food, people-watching and Western art are all outstanding.
Annapurna INDIAN $
(www.chaishoppe.com; 2201 Silver Ave SE; mains $7-12; 7am-9pm Mon-Sat, 10am-8pm Sun; ) This awesome vegetarian and vegan cafe has some of the freshest, tastiest healthy food in town, including delicately spiced ayurvedic delights that even carnivores love. Dishes are complemented by authentic Indian (read: _real_ ) chai.
### LITERARY NEW MEXICO
In the year leading up to New Mexico's 2012 centential celebration, the New Mexico Book Co-op polled librarians, authors and the general public to compile a list of the 100 best New Mexico books of all time. Their top 10:
» _Bless Me, Ultima_ by Rudolfo Anaya
» _Milagro Beanfield War_ by John Nichols
» _A Thief of Time_ by Tony Hillerman
» _Death Comes for the Archbishop_ by Willa Cather
» _Red Sky at Morning_ by Richard Branford
» _Lamy of Santa Fe_ by Paul Hordan
» _House Made of Dawn_ by N Scott Momaday
» _Ben-Hur: A Tale of the Christ_ by Lew Wallace
» _The Rounders_ by Max Evans
» _First Blood_ by David Morrell
Obviously _Ben-Hur_ (which became the epic film starring Charlton Heston) and _First Blood_ (the inspiration for Sylvester Stallone's _Rambo_ dynasty) are not about New Mexico, but are by authors who have called the state home.
Il Vicino Pizzeria ITALIAN $
(3403 Central Ave NE; mains $7-9; 11am-11pm, to midnight Fri & Sat) Sure, you can come for simple Italian fare like wood-fired pizza, salads and pasta. But the real bread and butter here is spectacular, award-winning microbrewed beer, including the Wet Mountain IPA and Slow Down Brown.
Flying Star Café AMERICAN $
(3416 Central Ave SE; mains $6-12; 6am-11:30pm; ) This incredibly popular local chain draws flocks with perennial favorites alongside innovative main courses. There's an extensive breakfast menu, sumptuous desserts, free wi-fi and creative, comfortable decor. It's pushed over the top of the groovy scale with organic, free-range and antibiotic-free ingredients.
##### METROPOLITAN ALBUQUERQUE
The following Albuquerque options are worth the little trek it takes to reach them.
Saigon Far East VIETNAMESE $
(901 San Pedro SE; mains $4-8; 11am-8:30pm Thu-Tue, to 8pm Sun; ) Albuquerque has a bunch of great Southeast Asian restaurants, but this Vietnamese cheapie is our favorite. Don't be deterred by the dodgy-looking exterior. Inside is a friendly, family-run place that's one of the best dining values in town. From Central Ave, head south on San Pedro to the intersection with Kathryn St.
Rudy's Bar-B-Q BARBECUE $
(2321 Carlisle NE; mains $4-16; 10am-10pm; ) Mosey on into this barnlike structure filled with long picnic tables and benches, and your nose will tell you you've arrived in the land of serious barbecue. You don't order sandwiches here – you order meat by weight, then add bread. The brisket is so succulent it seems to melt in your mouth. Totally casual, it's great for families. Just north of I-40.
Loyola's Family Restaurant NEW MEXICAN $
(4500 Central Ave SE; mains $6-8; 6am-2pm Tue-Fri, 6am-1pm Sat, 7am-1pm Sun) Pure Route 66 style, baby, Loyola's has been serving fine, no-frills New Mexican fare since before there was even a song about the Mother Road. Some say it has the best chile in town. Just over 500yd east of Nob Hill.
#### Drinking
In addition to the places listed here, try the Slate Street Café & Wine Loft downtown for Albuquerque's best wine tasting. Il Vicino Pizzeria has excellent microbrews. Bars are generally open from 4pm to 2am Monday through Saturday, and until midnight on Sunday.
Satellite Coffee CAFE
(2300 Central Ave SE; 6am-11pm; ) Albuquerque's answer to Starbucks lies in these hip coffee shops – look for plenty of locations around town, including in the UNM and Nob Hill areas – luring lots of laptop-toting regulars. Owned by the same brilliant folks who started the Flying Star.
Kelly's Brewery BREWERY
(www.kellysbrewpub.com; 3226 Central Ave SE; 8am-midnight) Come to this former Route 66 service station for patio dining, lots of local microbrews and 20-somethings hanging out. You can even mix up your own batch with the help of one of Kelly's brewmasters – but you have to come back two weeks later to bottle it.
Downtown Distillery BAR
(406 Central Ave SW) Smack in the heart of downtown, the Distillery has a casual crowd, pool and a jukebox, so you can be your own DJ.
Copper Lounge LOUNGE
(1504 Central Ave SE) Just west of the UNM campus, you'll find a friendly, mixed crowd and daily drink specials at this place, which has a casual patio and a dark lounge area.
#### Entertainment
For a comprehensive list of Albuquerque's diverse nightspots and a detailed calendar of upcoming events, get _Alibi_ (www.alibi.com), a free weekly published every Tuesday. The entertainment sections of Thursday evening's _Albuquerque Tribune_ and the Friday and Sunday _Albuquerque Journal_ are helpful, too.
###### Nightclubs & Live Music
Downtown has a great bar scene, and Nob Hill's scene is pretty good, too, because of UNM. The theme seems to be atomic alien.
Caravan East LIVE MUSIC
(7605 Central Ave NE) Put on your cowboy boots and 10-gallon hat and hit the dance floor to practice your line dancing and two-stepping at this classic Albuquerque country-and-western music bar. Live bands perform and the ambience is friendly.
El Rey LIVE MUSIC
(www.elreytheater.com; 620 Central Ave SW, Downtown) A fabulous venue for local and national rock, blues and country acts. Over the years, it's hosted such stars as Ella Fitzgerald, Etta James and Arlo Guthrie. It also does national poetry slams and occasionally hosts CD launch parties.
Launch Pad LIVE MUSIC
(www.launchpadrocks.com; 618 Central Ave SW, Downtown) This retro-modern place is the hottest stage for local live music, and still allows smoking inside – wow, now that's old school.
###### Cinemas
Guild Cinema CINEMA
(www.guildcinema.com; 3405 Central Ave NE, Nob Hill; admission $7) This is the only independently owned, single-screen theater in town, and it always has great indie, avant-garde, Hollywood fringe, political and international features. Stick around when there are discussions following select films.
###### Performing Arts
Popejoy Hall (www.popejoyhall.com; Central Ave at Cornell St SE) and the historic KiMo Theater (www.cabq.gov/kimo; 423 Central Ave NW, Downtown) are the primary places to see big-name national acts, as well as local opera and theater. The Pit (www.unmtickets.com; 1111 University Blvd SE, UNM Arena) and Tingley Coliseum (300 San Pedro NE) also host major events.
The New Mexico Ballet Company (www.newmexicoballet.org; tickets $15-20) performs from October to April. The New Mexico Symphony Orchestra folded in April, 2011, but by the time you read this the newly formed New Mexico Philharmonic may be playing (www.nmphil.org).
###### Sports
About those Albuquerque Isotopes (www.albuquerquebaseball.com; Isotopes Park, Ave Cesar Chavez & University SE). First of all: yes, the city's baseball team really was named for the episode of _The Simpsons,_ 'Hungry, Hungry Homer,' when America's favorite TV dad tried to keep his beloved Springfield Isotopes from moving to Albuquerque. The 'Topes sell more merchandise than any other minor league team. They sometimes win, too.
The UNM Lobos (www.golobos.com) have a full roster of teams, but are best known for basketball (men's and women's) and women's volleyball.
#### Shopping
The most interesting shops are in Old Town and Nob Hill.
Mariposa Gallery ARTWORK
(www.mariposa-gallery.com; 3500 Central Ave SE, Nob Hill) Beautiful and funky arts, crafts and jewelry, mostly by regional artists.
IMEC JEWELRY
(www.imecjewelry.net; 101 Amherst SE, Nob Hill) Around the corner from Mariposa, you'll find more artistic fine jewelry at IMEC.
Palms Trading Post ARTS & CRAFTS
(1504 Lomas Blvd NW; 9am-5:30pm Mon-Sat) Has Native American crafts and informed salespeople.
Silver Sun JEWELRY
(116 San Felipe St NW; 9am-4:30pm) A reputable spot for turquoise.
Page One BOOKS
(www.page1books.com; 11018 Montgomery Blvd NE; 9am-10pm Mon-Sat, to 8pm Sun) A huge and comprehensive selection of books, some secondhand.
#### Information
###### Emergency
Police ( 505-764-1600; 400 Roma Ave NW)
###### Internet Access
Albuquerque is wired. The Old Town Plaza, Sunport, downtown Civic Plaza, Aquarium and Botanic Gardens have free wi-fi, as do Rapid Ride buses.
###### Internet Resources
Albuquerque Online (www.abqonline.com) Exhaustive listings and links for local businesses.
Albuquerque.com (www.albuquerque.com) Information on attractions, hotels and restaurants.
City of Albuquerque (www.cabq.gov) Public transportation, area attractions and more.
###### Medical Services
Presbyterian Hospital ( 505-841-1234, emergency 505-841-1111; 1100 Central Ave SE; 24hr emergency)
UNM Hospital ( 505-272-2411; 2211 Lomas Blvd NE; 24hr emergency) Head here if you don't have insurance.
###### Post
Post office (201 5th St SW)
###### Tourist information
Albuquerque Convention & Visitors Bureau ( 505-842-9918; www.itsatrip.org; 20 First Plaza; 9am-4pm Mon-Fri) At the corner of 2nd St and Copper Ave.
Old Town Information Center ( 505-243-3215; 303 Romero Ave NW; 10am-5pm Oct-May, to 6pm Jun-Sep)
#### Getting There & Away
###### Air
New Mexico's largest airport, the Albuquerque International Sunport ( 505-244-7700; www.cabq.gov/airport; 2200 Sunport Blvd SE) is served by multiple airlines and car-rental companies.
###### Bus
The Alvarado Transportation Center (100 1st St SW, cnr Central Ave) is home to Greyhound ( 505-243-4435, 800-231-2222; www.greyhound.com; 320 1st St SW), which serves destinations throughout the state and beyond.
###### Train
Amtrak's Southwest Chief stops at Albuquerque's Amtrak Station ( 505-842-9650, 800-872-7245; 320 1st St SW; ticket office 10am-5pm), heading east to Chicago (from $194, 26 hours) or west to Los Angeles (from $101, 16½ hours), once daily in each direction.
A commuter line, the New Mexico Rail Runner Express (www.nmrailrunner.com), shares the station, with eight Santa Fe departures (1½ hours; one-way/day pass $7/8) weekdays, four on Saturday and two on Sunday. At the time of writing, plans were being made to reduce weekday service.
#### Getting Around
###### To/From the Airport
ABQ Ride bus No 250 provides free service between the Sunport and the downtown area, including the Rail Runner station, four times a day, weekdays only. The Sunport Shuttle ( 505-866-4966; www.sunportshuttle.com) runs to local hotels and other destinations; theSandia Shuttle ( 888-775-5696; www.sandiashuttle.com) runs to Santa Fe (one-way/round-trip $25/45) hourly between 8:45am and 11:45pm.
###### Bicycle
Contact Parks & Recreation ( 505-768-2680; www.cabq.gov/bike) for a free map of the city's elaborate system of bike trails, or visit the website. All ABQ Ride buses are equipped with front-loading bicycle racks.
###### Bus
ABQ Rides ( 505-243-7433; www.cabq.gov/transit; 100 1st St SW; adult/child $1/35¢; day pass $2) is a public bus system covering most of Albuquerque on weekdays and major tourist spots daily. Maps and schedules are available on the website; most lines run till 6pm. Rapid Ride buses (which run on hybrid diesel engines and have free wi-fi!) service the BioPark, downtown, Nob Hill, the fairgrounds and Old Town; No 66 goes up and down Central Ave.
### NEW MEXICO'S PUEBLOS
New Mexico is home to 19 Native American pueblos, with the greatest concentration found outside of Santa Fe. For a compelling overview of these communities, stop by Albuquerque's Indian Pueblo Cultural Center (Click here). Operated by the Puebloans themselves, the museum traces the development of Pueblo cultures, including Spanish influence, and features exhibits of the arts and crafts created in each pueblo.
One unique aspect of New Mexico's pueblos, compared to many other Indian reservations in the rest of the country, is that most are located right where they've been for centuries. While some are populated with descendants of refugees whose pueblos were destroyed by the Spanish, most Pueblo Indians were not radically displaced and have long and deep ties to their lands.
Don't expect all pueblos to be tourist attractions: many offer little for visitors outside of festival weekends. Most are just communities where people live. Many pueblos make money by running casinos (you can gamble on the Indian reservations, but not elsewhere in the state). Note that most casinos don't serve alcohol. Many pueblos charge visitor fees (not for casinos) and photography fees, so check regulations before you start walking around taking pictures.
Our pick of the top three pueblos for visitors:
Taos Pueblo (Click here) The most famous pueblo in New Mexico, in a gorgeous spot below Pueblo Peak.
Zuni Pueblo (Click here) Less touristy than other Pueblos, with creative jewelry and wild scenery; it's 35 miles outside of Gallup.
Acoma Pueblo (Click here) Dramatic mesa-top location; along with Taos Pueblo and Arizona's Hopi villages, it's one of the oldest continually inhabited spots in America.
For more information on etiquette when visiting Indian reservations, see Click here. Note that all the Pueblos in this section are mapped on Click here. The consortium of pueblos north of Santa Fe is called Eight Northern Pueblos (www.enipc.org).
###### Car & Motorcycle
Albuquerque is an easy city to drive around. Streets are wide and there's usually metered or even free parking within blocks, or sometimes steps, from wherever you want to stop.
New Mexico's largest city is also motorcycle friendly: the town has its share of biker bars and you are more likely to hear a 'hog' thundering down the street than not.
###### Taxi
In general you must call for a taxi, though they do patrol the Sunport, and the Amtrak and bus stations.
Albuquerque Cab ( 505-883-4888; www.albuquerquecab.com)
Yellow Cab ( 505-247-8888)
### Albuquerque Area Pueblos
There are a number of pueblos north of Albuquerque on the way to Santa Fe.
##### ISLETA PUEBLO
This Pueblo (www.isletapueblo.com), 16 miles south of Albuquerque at I-25 exit 215, is best known for its church, the San Augustine Mission. Built in 1613, it's been in constant use since 1692. A few plaza shops sell local pottery, and there's gambling at the flash Hard Rock Hotel & Casino (www.hardrockcasinoabq.com; 8am-4am Mon-Thu, 24hr Fri-Sun). On Saint Augustine's Day (September 4), ceremonial dancing is open to the public.
##### SANTA ANA PUEBLO
This Pueblo (www.santaana.org; US 150) is _posh._ Really posh. It boasts two great golf courses ( 505-867-9464, 800-851-9469; www.santaanagolf.com; green fees $45-80): the Santa Ana Golf Club, with three nine-hole courses, and the extravagant Twin Warriors Golf Club, with 18 holes amid waterfalls. Santa Ana Star Casino ( 505-867-0000; US 150; 8am-4am Sun-Wed, 24hr Thu-Sat) has a staggering buffet, 36 lanes of bowling and live entertainment ranging from Michael Jackson impersonators to Bob Dylan (the real one).
### SALINAS PUEBLO MISSIONS
Smack in the center of New Mexico you'll find a mostly empty region of hills and plains. But 350 years ago, the Salinas Valley was one of the busiest places in the Pueblo Indian world. Some 10,000 people lived there, and it bustled with trade between local pueblos, the Rio Grande Valley, Acoma, Zuni, the Spaniards and the Apaches.
Conquistadors arrived in the last years of the 16th century, valuing the Salinas region for the vast quantities of salt available nearby, as well as the chance to convert lots of Indians to Christianity. Impressive churches were built of stone and wood, and what remains of them and the pueblos are preserved within Salinas Pueblo Missions National Monument (www.nps.gov/sapu; admission free; 9am-5pm, until 6pm in summer). The visitor center is in the town of Mountainair, about 1½ hours by car from Albuquerque, but the monument itself is split into three separate sites, each with interpretive trails. Abo, off of Hwy 60, 9 miles west of Mountainair, is known for the unusual buttressing of its church, rarely seen in buildings from that period. Quarai, 8 miles north of Mountainair along Hwy 55, features the most intact church within the monument. Gran Quivera, 25 miles south of Mountainair along Hwy 55, has the most extensively excavated Indian ruins, along with exhibits about Salinas pueblo life. The most scenic way to get to Salinas Pueblo Missions from Albuquerque is to take Hwys 337 and 55 south along the eastern side of the Manzano Mountains.
If you're interested in ancient pottery and up for some off-the-beaten-path adventure, the swath of state land west of Gran Quivera is littered with shards of centuries-old black-on-white ceramics. Just be sure you're not on private property before you go poking around.
The Stables at Tamaya ( 505-771-6037; 2hr trail ride $75 9:30am-3:30pm) offers trail rides and lessons ($75) through the woods, which the pueblo has recently restored. And ancient tradition has survived the modern glitz; there are Corn Dances on June 24 and July 26.
The luxurious Hyatt Tamaya ( 800-633-7313; www.tamaya.hyatt.com; 1300 Tayuna Trail; r from $159; ), hidden in the desert landscape with expansive views, has three pools, three restaurants and a small spa.
##### SANDIA PUEBLO
About 13 miles north of Albuquerque, this Pueblo (www.sandiapueblo.nsn.us; I-25 exit 234) was established around the year 1300. It opened one of the first casinos in New Mexico and subsequently used its wealth to successfully lobby for legislation preventing further development of Sandia Crest, the Sandia people's old sacred lands, appropriated by Cibola National Forest. Sandia Casino ( 800-526-9366; www.sandiacasino.com; 8am-4am Mon-Thu, 24hr Fri-Sun) boasts an elegant outdoor venue, the Sandia Casino Amphitheater, hosting everything from symphony orchestras to boxing matches to Bill Cosby.
Bien Mur Marketplace (100 Bien Mur Dr NE), across the road from the casino, claims to be the largest Native American–owned trading post in the Southwest, which is probably true. The tribe invites visitors to Marketfest (late October), when Native American artists show their work, as well as to corn dances during Feast Day (June 13).
## ALBUQUERQUE TO SANTA FE
Two main routes connect New Mexico's two major cities: it takes a speedy hour to get from Albuquerque to Santa Fe along the semi-scenic I-25; or about 90 minutes on the much lovelier NM 14, known as the Turquoise Trail.
### Along I-25
There are a couple of worthwhile stops off the interstate, including one fantastic place to hike.
##### CORONADO STATE MONUMENT
At Exit 242, about 1.7 miles west of I-25, you'll find Coronado State Monument (www.nmmonuments.org; US 550; adult/under 17yr $3/free, 8:30am-5pm Wed-Mon) and the ruins of Kuaua Pueblo. It's no Chaco Canyon, but the paintings are considered prime examples of precontact mural art in North America: various Pueblo gods (Kachinas) are depicted as personifications of nature, including the Corn Mother, who gave the Pueblo people corn. The murals have been artfully restored inside the visitor centerand underground kiva. There's also a campground (tent/RV sites $14/18) with shade shelters and showers.
##### SAN FELIPE PUEBLO
Though best known for the spectacular San Felipe Feast Green Corn Dances (May 1), this conservative Keres-speaking Pueblo (I-25 exit 252) now has a couple more claims to fame. The Casino Hollywood (www.sanfelipecasino.com; I-25 exit 252; 8am-4am Sun-Wed, 24hr Thu-Sat) isn't just for gambling: this themed venue takes full advantage of its location to pull in acts like Los Lobos and Julio Iglesias. The Pueblo opens to the publicon May 1 every year. Visitors are also invited to the San Pedro Feast Day (June 29) and the Arts & Crafts Fair in October.
##### SANTO DOMINGO PUEBLO
Now officially called Kewa Pueblo (Hwy 22; 8am-dusk), this nongaming pueblo has long been a seat of inter-Pueblo government: the All Indian Pueblo Council still meets here annually. Several galleries and studios at the pueblo abut the plaza in front of the pretty 1886 Santo Domingo Church, with murals and frescoes by local artists. The tribe is most famous for _heishi_ (shell bead) jewelry, as well as huge Corn Dances (August 4) and a wildly popular Arts & Crafts Fair in early September.
The Pueblo is on Hwy 22, 6 miles northwest from I-25 exit 259, about halfway between Albuquerque and Santa Fe.
##### COCHITI PUEBLO
About 10 miles north of Santo Domingo on NM 22, this Pueblo (www.pueblodecochiti.org) is known for its arts and crafts, particularly ceremonial bass drums and storyteller dolls. Several stands and shops are usually set up around the plaza and mission (built in 1628); dances open to the public are held on the Feast Day of San Buenaventura (July 14) and other occasions throughout the summer, plus December 25. There's no photography allowed here, but visitors can snap away at the golf course (Pueblo de Cochiti Golf Course; 505-465-2239; www.golfcochititoday.com; 5200 CochitiHighway; 9/18 holes $28/57), considered thestate's most challenging, or splash in Cochiti Lake, favored by swimmers and boaters (no motors allowed).
##### KASHA-KATUWE TENT ROCKS NATIONAL MONUMENT
The bizarre and beautiful Kasha-Katuwe Tent Rocks National Monument (www.blm.gov/nm/tentrocks) is a favorite hiking spot for Santa Fe and Albuquerque residents. At this surreal geologic realm, volcanic ash from the ancient Jemez Mountain volcanoes has been sculpted into tipi-like formations and steep-sided, narrow canyons that glow astrange light orange, sometimes with tiger stripes. Hike up a dry riverbed through the piñon-covered desert to the formations, where sandy paths weave through the rocks and canyons. You'll need a couple of hours to drive the desert dirt road to get here and to hike around a bit, but it's well worth it.
Take I-25 exit 264; follow Hwy 16 west to Hwy 22, then right onto Tribal Rte 92. At the time of research, dogs were banned from Tent Rocks.
### Turquoise Trail
The Turquoise Trail has been a major trade route since at least 2000 BC, when local artisans began trading Cerrillos turquoise with communities in present-dayMexico. Today it's the scenic back road between Albuquerque and Santa Fe, lined with quirky communities and other diversions. For info, see www.turquoisetrail.org.
##### CEDAR CREST
Located northeast of Albuquerque, on the eastern side of the Sandia Mountains, and just a bit up Sandia Crest Rd (NM 165) from Cedar Crest, the Tinkertown Museum (www.tinkertown.com; 121 Sandia Crest Rd; adult/child $3/1; 9am-5:30pm Apr-Nov; ) is one of the weirdest museums in New Mexico. Huge, detailed handcarved dioramas of Western towns, circuses and other scenes come alive with a quarter. Woodcarver and wisdom collector Ross J Ward built it and surrounded it with antique toys, 'junque' (aka fancy junk) and suggestions that you eat more mangoes naked.
The nearby Museum of Archaeology (22 Calvary Rd; adult/child $3.50/1.50; noon-7pm Apr-Oct; ), off NM 14, has an 'archaeological site' outdoors (kids dig this) and local Indian artifacts inside. It also runs the adjacent Turquoise Trail Campground ( 505-281-2005; www.turquoisetrailcampground.com; tent/RV sites $17.50/27, cabins $36-58), which has hot showers and cool shade. There's national forest access for guests.
##### MADRID
Madrid (pronounced _maa_ -drid) is about 30 miles south of Santa Fe on Hwy 14. A bustling company coal-mining town in the 1920s and '30s, it was all but abandoned after WWII. In the mid-1970s, the company's heirs sold cheap lots to tie-dyed wanderers who have built a thriving arts community with galleries and wacky shops. Though it's become a lot more touristy over the years, beneath the surface its old outlaw heart still beats, remaining a favorite stop on Harley rallies.
There are dozens of galleries and shops in this one-horse town, but pay special attention to The Crystal Dragon (www.thecrystaldragon.com; 2891 NM 14), one of Madrid's original galleries, with unique handcrafted jewelry at really reasonable prices; Seppanen & Daughters Fine Textiles (www.finetextiles.com; 2879 NM 14), with its tactile and colorful Oaxaca, Navajo and Tibetan rugs; and Range West (www.rangewest.com; 2861 NM 14), with its elegant water fountains carved from monolithic granite chunks.
The Old Coal Mine Museum (2814 NM 14; adult/child $5/3; 11am-5pm Fri-Mon) preserves plenty of old mining equipment, pretty much right where the miners left it. It also hosts the Madrid Melodrama & Engine House Theatre (www.themineshafttavern.com; adult/child $10/4; 3pm Sat & Sun May-Oct), starring a steam locomotive, lots of Wild West desperados, scoundrels and vixens, and stories that leave you feeling good. Admission includes a six-shooter loaded withmarshmallows to unload at the villains. At the time of research, the Theatre was closed due to fire-code violations, but will hopefully get those sorted out soon.
Both are attached to the Mine Shaft Tavern (www.themineshafttavern.com 2846 NM 14; mains $8-12; 11:30am-7:30pm Sun-Thu, to 9pm Fri & Sat, bar open late daily) to meet locals, listen to live music on weekends and experience the 'longest stand-up bar in New Mexico.' The bar was built in 1946 and has been Madrid's favorite attraction ever since. The sign inside tells you everything you need to know about the place: 'Madrid has no town drunk; we all take turns.'
Mama Lisa's Ghost Town Kitchen (2859 NM 14; snacks $6-10; 11am-4:30pm Fri-Sun) serves good quesadillas and a great red-chile chocolate cake.
Overnight at Java Junction B&B ( 505-438-2772; www.java-junction.com; 2855 Hwy 14; ste $89-129; ), which has a charming Victorian suite just upstairs from a cafe where they take their brew seriously.
##### CERRILLOS
A few miles north of Madrid on Hwy 14, Cerrillos still has one foot in the Old West. With unpaved streets threading through an adobe town relatively unchanged since the 1880s, this is the home of the first mine in North America, built to extract turquoise around AD 100.
In a region chock full of artists and galleries, one of the most unique and subtly mind-blowing is the Thomas Morin Studio ( 505-474-3147; 8 First St; 10am-4pm Mon-Sat, Apr-Nov), where you can watch the master sculptor work with his current medium of choice: used sandpaper belts. His pieces are absolutely exquisite; even if you're just planning on driving by on Hwy 14, do not miss this gallery. Call ahead if you don't want to leave a visit to chance. If you're on a tight budget, lock your checkbook in the car before going in.
The Cerrillos Turquoise Mining Museum & Petting Zoo (17 Waldo St; admission $3; 9am-sunset) packs five rooms with Chinese art, pioneer-era tools, mining equipment dating to 3000 BC, bottles and antiques excavated from an abandoned area hotel, and anything else the owners thought was worth displaying. For $2 more you can feed the goats, llamas and exotic chickens. Hours vary.
Broken Saddle Riding Co ( 505-424-7774; www.brokensaddle.com; off County Rd 57; rides $55-100) offers one- to three-hour horseback rides through juniper-dotted hills and abandoned mines, including a special sunset/moonlight ride. Along the way, you'll learn about local history and geology. Call in advance. Just down the road is Cerrillos Hills State Park (www.nmparks.com; per vehicle $5; sunrise-sunset) where 5 miles of hiking trails link historic mining sites.
## SANTA FE
Welcome to 'the city different,' a place that makes its own rules yet never forgets its long and storied past. Walking among the historic adobe neighborhoods, and even around the tourist-filled plaza, there's no denying that Santa Fe has a timeless, earthy soul. Founded around 1610, Santa Fe is the second-oldest city and the oldest state capital in the USA. It's got the oldest public building and throws the oldest annual party in the country (Fiesta). Yet the city is synonymous with contemporary chic, boasting the second-largest art market in the nation, gourmet restaurants, great museums, spas and a world-class opera. It's a beacon of progressive thought and creative culture. The UN named it 'most creative city' in 2005, a fitting honor for a city that is committed to the arts like few other places in the country.
At 7000 feet above sea level, Santa Fe is also the highest state capital in the US. Sitting at the foot of the Sangre de Cristorange, the city is a fantastic base for hiking, mountain biking, backpacking and skiing. When you come off the trails, you can indulge in chile-smothered local cuisine, then shop for turquoise and silver directly from the Native American jewelers who sell their work around the plaza, visit some of the most unique churches in the country, orsimply wander along centuries-old, cottonwood-shaded lanes and fantasize about moving here.
The city is home to a motley crew of characters, including traditional and avant-garde artists, New Age hippie transplants, Spanish families that have called the city home for centuries, undocumented Mexican immigrants, retirees from both coasts, and more than a few Hollywood producers and movie stars. All have come for the relaxed attitude, the space, the unbeatable climate and that certain something that gives Santa Fe a singularly alluring essence.
### SANTA FE IN...
#### Two Days
After breakfast at Cafe Pasqual's, art up at the Georgia O'Keeffe Museum. Stroll around the plaza, checking out the Native American jewelry being sold on the sidewalk, on your way to the lovely St Francis Cathedral. Have a classic (and cheap) New Mexican lunch at Tia Sophia's. Check out the the Loretto Chapel on your way over to Canyon Rd, stopping at numerous galleries there. For dinner, hit the Tune Up Café for casual local dining.
The next morning, chow down at the Santa Fe Baking Co. Head over to Museum Hill –don't miss the Museum of International Folk Art. Pop into Harry's Roadhouse for lunch, then take a scenic drive up Ski Basin Road, where there are loads of hiking and biking trails. Have dinner and catch some live flamenco at the city's oldest tavern, El Farol. Olé!
#### Three Days
After two days in town, grab breakfast at the Tesuque Village Market, then head on up to Bandelier National Monument, to hike in the gorgeous gorges and climb ladders into ancient cliffside kivas. Then it's back to Santa Fe for a dinner of barbecue brisket quesadillas and a Mescal margarita at the Cowgirl Hall of Fame.
#### Sights
Most downtown galleries, museums, sights and restaurants are either on or east of Guadalupe St and are within walking distanceof the plaza, the center of the action.
Downtown Santa Fe
Top Sights
Georgia O'Keeffe Museum D2
Loretto Chapel F4
St Francis Cathedral F3
Sights
1 78th St Gallery H4
2 Absolute Nirvana Spa & Tea Room H3
Avanyu Spa (see 28)
3 Economos/Hampton Galleries H5
4 Gerald Peters Gallery G5
LewAllen Gallery (see 29)
Marc Navarro Gallery (see 3)
Morning Star Gallery (see 58)
5 Museum of Contemporary Native Arts F3
6 Nedra Matteucci Galleries G6
7 New Mexico History Museum E2
8 New Mexico Museum of Art E2
9 Palace of the Governors F2
10 San Miguel Mission F5
Santa Fe Clay (see 16)
11 Santuario de Guadalupe C3
12 Shiprock F3
13 SITE Santa Fe A6
Tai Gallery (see 39)
Activities, Courses & Tours
14 High Desert Angler C5
15 Sangre de Cristo Mountain Works B4
16 Santa Fe Clay A5
17 Santa Fe School of Cooking E3
18 Santa Fe Southern Railway B4
Sleeping
19 El Paradero C5
20 Garrett's Desert Inn F4
21 Hotel St Francis E3
22 Inn & Spa at Loretto F4
23 Inn of the Anasazi F2
24 Inn of the Five Graces E4
25 Inn of the Governors D4
26 Inn on the Alameda G4
27 La Fonda F3
28 La Posada de Santa Fe H3
29 Sage Inn A6
Eating
30 Cafe Pasqual's E3
31 Cleopatra Cafe C4
32 Cowgirl Hall of Fame C3
33 Coyote Café E3
34 Del Churro Saloon E4
35 Flying Star Café A5
French Pastry Shop (see 27)
36 Guadalupe Cafe E5
37 Il Vicino D2
Raaga (see 38)
38 Ristra B3
39 Santa Fe Farmers Market A5
40 SantaCafé F1
41 Shed F3
42 Tia Sophia's D2
43 Tomasita's B4
44 Zia Diner B4
Drinking
45 Aztec Café C3
Bell Tower Bar (see 27)
46 Dragon Room Bar F5
47 Evangelo's E3
48 Marble Brewery Tap Room E3
49 Ore House E3
50 Second St Brewery A5
Entertainment
51 Lensic Performing ArtsTheatre D2
52 Santa Fe Playhouse E4
Santa Fe Symphony (see 51)
53 Vanessie of Santa Fe C2
Shopping
54 Garcia Street Books H6
55 Kowboyz B5
56 Nambé Foundry Outlet E3
57 Nambé Foundry Outlet G5
58 Nathalie H5
59 Seret & Sons D3
60 Travel Bug G4
While you're here in one of the top-rated cultural towns in the United States, plan tospend time in some of the city's museums. The art museums alone can keep you busy for a while, covering genres including Native American, Spanish Colonial, modern and contemporary, and international folk art.
Most museums are clustered in two locations – around the downtown plaza and on Museum Hill, where four excellent museums, a research library and a recommended cafe are all linked by a sculpture-lined trail. Since it's almost 3 miles southwest of the plaza, unless you're really up for the walk, drive or take the M Line – a Santa Fe Trails bus geared toward visitors – that winds through historical neighborhoods.
Many museums and other attractions offer discounts to senior citizens and discounts or free admission to New Mexico residents, at least on certain days of the week. Also, log on to www.museumhill.org for special-events calendars and links to all four Museum Hill institutions. If you're on a tight budget and can't splurge on many museums, remember that Santa Fe's gazillion art galleries are free, as is the fine collection at the State Legislature building.
The Plaza PLAZA
Santa Fe's Plaza is the heart of the town, and dates back to the city's beginning over 400 years ago. Between 1822 and 1880 the Plaza served as the end of the Santa Fe Trail, and traders from as far away as Missouri drove here in their wagons laden with goods. Today, Native Americans sell their jewelry and pottery beneath the portico of the Palace of the Governors; kids skateboard and play hackeysack; and tourists weighed down with cameras and purchases wander through the grassy center on their way to the next shop, museum or margarita. The food stalls here are a great place to grab a snack.
Georgia O'Keeffe Museum MUSEUM
( 505-946-1000; www.okeeffemuseum.org; 217 Johnson St; adult/child $10/free; 10am-5pm, to 8pm Fri) The renowned painter first visited New Mexico in 1917 and lived in Abiquiú, a village 45 minutes northwest of Santa Fe, from 1949 until her death in 1986 (see Click here). Possessing the world's largest collection of her work, this museum showcases the thick brushwork and luminous colors that don't always come through on ubiquitous posters; take your time to relish them here firsthand. The museum is housed in a former Spanish Baptist church with adobe walls that has been renovated to form 10 skylighted galleries. Tours of O'Keeffe's house an hour away in Abiquiú require advance reservations.
Museums of New Mexico MUSEUM
(single museum adult/child $8/free, 4-day pass to all 4 museums adult/child $18/free; 10am-5pm Tue-Sun) This is a collection of four very different museums – two of them on Museum Hill and two on the Plaza – which also offersseminars, musical events and a variety of guided tours with historic or artistic focuses,many designed for children. Both the Palace of the Governors and the New Mexico Museum of Art, the two located on the Plaza, are free on Friday from 5pm to 8pm. All the museums have fabulous gift shops.
_Museum of International Folk Art_
(www.internationalfolkart.org; 706 Camino Lejo) On Museum Hill, this museum houses more than 100,000 objects from more than 100 countries and is arguably the best museum in Santa Fe. The exhibits are at once whimsical and mind-blowing, as the world's largest collection of folk art spills across the galleries in festive presentations. There are dolls, masks, toys, garments and entire handmade cities on display. The historical and cultural information is concise and thorough; try to hit the incredible International Folk Art Market, held here each June.
_Museum of Indian Arts & Culture_
(www.indianartsandculture.org; 710 Camino Lejo) This museum opened on Museum Hill in 1987 to display artifacts unearthed by the Laboratory of Anthropology, which must confirm that any proposed building site in New Mexico is not historically significant. Since 1931 it has collected over 50,000 artifacts. Rotating exhibits explore the historical and contemporary lives of the Pueblo, Navajo and Apache cultures. One of the most complete collections of Native American arts anywhere, it's a perfect companion to the nearby Wheelwright Museum.
_New Mexico Museum of Art_
(www.nmartmuseum.org; 107 W Palace Ave) This museum features works by regional artists and sponsors regular gallery talks and slide lectures. It was built in 1918, and the architecture is an excellent example of the original Santa Fe–style adobe. With more than 20,000 pieces – including collections of the Taos Society of Artists, Santa Fe Society of Artists and other legendary collectives – it's a who's who of the geniuses who put this dusty town's art scene on a par with those of Paris and New York.
_Palace of the Governors_
( 505-476-5100; www.nmhistorymuseum.org; 105 W Palace Ave) This is one of the oldest public buildings in the country. Built in 1610 by Spanish officials, it housed thousands of villagers when the Indians revolted in 1680 and was home to the territorial governors after 1846. It displays a handful of regional relics, but most of its holdings are now shown in an adjacent exhibition space called the New Mexico History Museum (113 Lincoln Ave), a glossy, 96,000-sq-ft expansion that opened in 2009. Volunteers lead free, highly recommended palace tours throughout the day; call for exact times.
St Francis Cathedral CHURCH
(www.cbsfa.org; 131 Cathedral Pl; 8:30am-5pm, Mass 7am & 5:15pm Mon-Sat, 8am, 10am, noon & 5:15pm Sun) Jean Baptiste Lamy was sent to Santa Fe by the pope with orders to tame the Wild Western outpost town through culture and religion. Convinced that the town needed a focal point for religious life, he began construction of this cathedral in 1869. Lamy's story was the inspiration for Willa Cather's classic _Death Comes for the Archbishop._ Inside the cathedral is a small chapel, housing the oldest Madonna statue in North America. Carved in Mexico, the statue was brought to Santa Fe in 1625, but when the Indians revolted in 1680, the villagers took it into exile with them. When Don Diego de Vargasretook the city in 1692, he brought it back, and legend has it that its extraordinary powers are responsible for the reconquest of the city.
Loretto Chapel CHURCH
(www.lorettochapel.com; 207 Old Santa Fe Trail; admission $3; 9am-5pm Mon-Sat, 10:30am-5pm Sun) The Gothic chapel is modeled on Sainte Chapelle in Paris, and was built between 1873 and 1878 for the Sisters of Loretto, the first nuns to come to New Mexico. Sainte Chapelle has a circular stone staircase, but when the Loretto Chapel was being constructed, no local stonemasonswere skilled enough to build one and the young architect didn't know how to design one of wood. The nuns prayed for help and a mysterious traveling carpenter, whom the nuns believed afterward to be St Joseph, arrived. He built what is known as the Miraculous Staircase, a wooden spiral staircase with two complete 360-degree turns and no central or visible support. He left without charging for his labors and his identity remains unknown.
Today the chapel is a museum popular with tourists who come to snap photos of St Joseph's Miraculous Staircase and check out the intricate stations of the cross lining the aisle to the very Catholic main altar. The gift shop is packed with Catholic kitsch.
The chapel is one of the top places to get married in Santa Fe (it's nondenominational). After the ceremonies (which are not open to the public) the newlyweds are often led across the plaza to the tunes and dancing of a colorfully costumed mariachi band, a true Santa Fe tradition.
San Miguel Mission CHURCH
(401 Old Santa Fe Trail; admission $1; 9am-5pm Mon-Sat, 10am-4pm Sun, Mass 5pm Sun) The original construction of this mission was started in 1625, and it served as a mission church for the Spanish settlers' Tlaxcalan Indian servants, who had been brought from Mexico. Though considered the oldest church in the United States, much of the original building was destroyed during the Pueblo Revolt of 1680; it was rebuilt in 1710, with new walls added to what remained. The mix of Spanish and Indian artwork inside is well worth a peek!
Santuario de Guadalupe CHURCH
(100 Guadalupe St; 9am-4pm Mon-Sat) The adobe church is the oldest extant shrine to Our Lady of Guadalupe, the patroness of Mexico. It was constructed between 1776 and 1796, with several additions and renovations since. The oil-on-canvas Spanish baroque _retablo_ (altar painting) inside the chapel was painted in Mexico in 1783 by José de Alzíbar. For the trip to Santa Fe, the painting had to be taken apart and transported up the CaminoReal in pieces on mule back. This is just one of the many cultural treasures housed here, including the Santa Fe Archdiocese's collection of _santos_ – wood-carved portraits of saints, for which New Mexican artisans are famous.
Museum of Contemporary Native Arts MUSEUM
(www.iaia.edu/museum; 108 Cathedral Pl; adult/child $10/free; 10am-5pm Mon & Wed-Sat, noon-5pm Sun, closed Tue) Primarily showing work by the students and faculty of the esteemed Institute of American Indian Arts, this place also has the finest contemporary offerings of Native American artists from tribes across the US. It's an excellent place to see cutting-edge art and understand its role in modern Native American culture.
Wheelwright Museum of the
American Indian MUSEUM
(www.wheelwright.org; 704 Camino Lejo; 10am-5pm Mon-Sat, 1-5pm Sun) In 1937 Mary Cabot established this museum, part of Museum Hill, to showcase Navajo ceremonial art. While its strength continues to be Navajo exhibits, it now includes contemporary Native American art and historical artifacts, too. The gift store has an extensive selection of books and crafts.
State Capitol MUSEUM
( 505-986-4589; cnr Paseo de Peralta & Old Santa Fe Trail; 7am-6pm Mon-Fri, 9am-5pm Sat in summer, guided tours by appt) Locally referred to as the Roundhouse, the State Capitol is the center of New Mexico's government and was designed after the state symbol, the Zia sign. It also has one of the best (free) art collections in New Mexico. You can walk through by yourself, or call the number above or email Christal Branch (christal.branch@nmlegis.gov) to set up a guided tour.
### LA VILLA REAL DE LA SANTA FÉ DE SAN FRANCISCO DE ASIS
When a tiny settlement at the base of the Sangre de Cristo Mountains was made the capital of New Mexico in 1610, the newly appointed Spanish governor named it _La Villa Real de Santa Fé_ – The Royal Town of Holy Faith. For many years after its founding, it was known simply as 'La Villa.' Sometime during your stay, you may hear that the city's original name was actually _La Villa Real de la Santa Fé de San Francisco de Asís_ – The Royal Town of the Holy Faith of St. Francis of Assisi. But the exhaustively researched _Place Names of New Mexico_ disagrees. Its author, Robert Julyan, suggests the St. Francis part was tacked on in more modern times, thanks to 'tourist romanticism.'
Rancho de las Golondrinas MUSEUM
(www.golondrinas.org; 334 Los Pinos Rd, La Cienega; adult/child $6/free; 10am-4pm Wed-Sun Jun-Sep; ) The 'Ranch of the Swallows' has been around nearly as long as the city of Santa Fe. It was built as a stop along the Camino Real; now it's a 200-acre living museum, carefully reconstructed and populated with historical re-enactors. You can watch bread being baked in an _horno_ (traditional adobe oven), visit the blacksmith, the molasses mill or traditional crafts workshops. There are orchards, vineyards and livestock. Festivals are held throughout the summer. This is one of the best places to learn something about the history of the area while the kids are having a blast. To get there, take I-25 south to exit 276, then follow the signs.
SITE Santa Fe MUSEUM
(www.sitesantafe.org; 1606 Paseo de Peralta; adult/child $10/free; 10am-5pm Thu & Sat, 10am-7pm Fri, noon-5pm Sun, tours 6pm Fri, 2pm Sat & Sun) An enormous, whitewashed space, the 8000-sq-ft SITE Santa Fe is a nonprofit art museum dedicated to presenting world-class contemporary art to the community. From radical installation pieces to cutting-edge multimedia exhibitions, this hybrid museum-gallery takes art to the next level. It also hosts wine-splashed openings, artist talks, movie screenings and performances of all kinds. Admission is free on Fridays.
Santa Fe
Sights
Adobe Gallery (see 2)
1 Body C1
2 Chalk Farm Gallery D1
GF Contemporary (see 2)
3 Museum of Indian Arts & Culture D2
4 Museum of International Folk Art D2
5 Pushkin Gallery D1
6 Santa Fe Children's Museum C1
7 Wheelwright Museum of the American Indian D2
Activities, Courses & Tours
8 Mellow Velo C1
9 Santa Fe Workshops D2
Sleeping
10 Inn of the Turquoise Bear C1
11 Santa Fe International Hostel B1
12 Silver Saddle Motel A2
Eating
13 Compound D1
14 El Farol D1
15 Geronimo D1
16 Santa Fe Baking Co C1
17 Tune-Up Café B1
Drinking
18 Second Street Brewery B2
Tea House (see 14)
Entertainment
El Farol (see 14)
Shopping
19 Jackalope A2
Shidoni Foundry GARDENS, GALLERY
(www.shidoni.com; 1508 Bishop's Lodge Rd, Tesuque; 10am-5pm Mon-Sat; ) Five miles north of Santa Fe in Tesuque, Shidoni has an 8-acre grassy sculpture garden, a great place for a picnic or for the kids to run around among some funky artwork. There's also an indoor gallery and an on-site glassblowing studio. Every Saturdayyou can watch 2000°F molten bronze being poured into ceramic shell molds, one of several steps in the complex lost-wax casting technique ($2).
#### Activities
Although Santa Fe's museums, churches, galleries and shops are top-notch, visitors do not live by art appreciation alone. Get thee to the great outdoors. The best one-stop spot to peruse your options is the Public Lands Information Center, which is inconveniently located south of town off of Hwy 14. If you don't feel like schlepping out there, the folks at Santa Fe's gear shops – like Sangre de Cristo Mountain Works ( 505-984-8221; www.sdcmountainworks.com; 328 S Guadalupe St; 10am-7pm Mon-Fri, 10am-6pm Sat, noon-5pm Sun) – know a ton about the area; their website is also packed with details about where to hike, climb, bike and camp.
Before you head out for any strenuous activities, remember the elevations you're dealing with; make sure you've taken time to acclimatize and watch for signs of altitude sickness if you're going high. Weather changes rapidly in the mountains, and summer storms are frequent, especially in the afternoons, so keep an eye on the sky and hike prepared. Most trails are usually closed by snow in winter, and higher trails may be closed through May.
The best area overview map for trails and outdoor action is the Santa Fe/Bandelier/Los Alamos map published by Sky Terrain.
###### Skiing
Though downhill gets most of the attention around here, there are also numerous cross-country ski trails in both the Sangre de Cristo and Jemez Mountains.
Ski Santa Fe SKIING
( 505-982-4429, snow report 505-983-9155; www.skisantafe.com; lift ticket adult/child $63/43; 9am-4pm late Nov-Apr) Often overlooked for its more famous cousin outside of Taos, the Santa Fe ski area boasts the same fluffy powder (though usually a little less of it), with an even higher base elevation (10,350ft) and higher chairlift service (12,075ft). Briefly admire the awesome desert and mountain vistas, then fly down powder glade shoots, steep bump runs or long groomers. The resort caters to families and expert skiers alike with its varied terrain. The quality and length of the ski season can vary wildly from year to year depending on how much snow the mountain gets, and when it falls (you can almost always count on a good storm in late March).
On autumn weekends, the chairlift takes passengers up through the shimmering golden foliage of the aspen forest (one-way/round-trip $7/10, small children free); there's also an extensive system of hiking trails off of the parking lot. To get there, take Hwy 475 –known first as Artist Rd, then Hyde Park Rd, then Ski Basin Rd – from just north of the plaza.
Though the ski area rents gear, lots of people prefer to pick up skis, poles, boots and boards at Cottam's ( 505-982-0495; www.cottamsskishops.com; 740 Hyde Park Rd) On the way to the slopes, it has reasonable prices on gear packages (from adult/child $22/16) and also rents snowshoes ($13.50). Reserve online and get a discount.
###### Mountain Biking
Some of the best intermediate single track in New Mexico is found on the North and South Dale Ball Trail System, which encompasses more than 20 miles of paved and unpaved bike and hiking trails with fabulous views of mountains and deserts. Trails vary in length and difficulty – the South Dale Ball Trails are the most challenging. To get to the south trails, follow Upper Canyon Rd north to the well-signed parking lot at Cerro Gordo Rd – there is a great dog park across the street. The ride from this parking lot is a favorite, but beware it starts with a super-long, hard and rocky single-track climb, followed by a series of harrowing switchbacks. You'll be rewarded richly, however, with loads of supreme isolation and outstanding views.
### TOP FIVE SPAS
Many Santa Fe spas offer spectacular natural settings, mountain views and world-class pampering. Below are our top choices.
Absolute Nirvana Spa & Tea Room ( 505-983-7942; www.absolutenirvana.com; 106 Faithway St; 10am-6pm Sun-Thu, to 8pm Fri & Sat) Rose-petal baths and sumptuous Indonesian- and Thai-style massage ($105 to $190 per treatment) await you here.
Avanyu Spa ( 505-986-0000; www.laposada.rockresorts.com; 330 E Palace Ave; 7am-8pm) Choose from a range of sophisticated therapies, including craniosacral, reiki, polarity and shiatsu ($135 to $200), at this swanky spot within the La Posada Hotel.
Body ( 505-986-0362; www.bodyofsantafe.com; 333 Cordova Rd; 7am-9pm) Aimed at local clientele, Body offers high-quality massages with fewer frills for less money ($80). Drop your kids at the supervised play room ($6 per hour) while you de-stress.
Encantado Resort ( 877-262-4666; www.encantadoresort.com; 198 State Rd 592, Tesuque; 9am-9pm) Everything from ayurvedic treaments ($155 to $300) to acupuncture ($150) to crystal chakra balancing ($245) – oh, and traditional massage ($150) and facials ($165 to $225).
Ten Thousand Waves ( 505-982-9304; www.tenthousandwaves.com; 3451 Hyde Park Rd; communal tubs $19, private tubs per person $29-49; 2-10:30pm Tue, 9am-10:30pm Wed-Mon Jul-Oct, reduced hours Nov-Jun) This gorgeous Japanese spa offers a host of attractive public and private outdoor soaking tubs, kitted out in a smooth Zen style with cold plunges and saunas. A host of treatments – from prenatal, hot stone and Thai massages to herbal wraps – are offered. Massages start at $99.
The Winsor Trail (No 254;) is one of the most popular intermediate bike routes in the state. The scenery – particularly in the fall – is outstanding. The trail wends through Hyde State Park and Santa Fe National Forest, and serves as the spine of several other multi-use trails, including the bike-friendly Chamisa Loops. The downhill ride on the Winsor from up near the ski area is unforgettable!
### CANYON RD & AROUND: SANTA FE GALLERY-HOPPING
Once a footpath used by Pueblo Indians, then the main street through a Spanish farming community, Santa Fe's most famous art avenue, Canyon Rd (www.canyonroadarts.com), began its current incarnation in the 1920s, when artists led by Los Cinco Pintores (a group of five painters who fell in love with New Mexico's landscape) moved in to take advantage of the cheap rent.
Today Canyon Rd is a must-see attraction. More than 100 of Santa Fe's 300-plus galleries are found here, and it has become the epicenter of the city's vibrant art scene, with everything from rare Indian antiquities to Santa Fe School masterpieces to wild contemporary work. Gallery-hopping can seem a bit overwhelming, so we'd suggest not worrying and just wandering. Exhibitions are constantly changing, so have a peek in the window; you'll quickly tell what you like and don't like.
Friday nights are particularly fun: that's when the galleries put on glittering openings, starting around 5pm. Not only are these great social events, but you can also browse while nibbling on cheese, sipping Chardonnay or sparkling cider and chatting with the artists.
Below is just a sampling of our Canyon Rd (and around) favorites. For more, pick up a handy, free _Santa Fe & Canyon Road Walking Map_ or check out the Santa Fe Gallery Association's website, www.santafegalleries.net. More galleries are concentrated around the Railyard and along Lincoln Ave just north of the Plaza.
Adobe Gallery (www.adobegallery.com; 729 Canyon Rd) This gallery includes pieces by the 'Five Matriarchs' of the Pueblo pottery renaissance: Maria Martinez, Margaret Tofoya, Maria Nampeyo, Lucy Lewis and Helen Cordero, among many other famed Southwestern Indian artisans.
Chalk Farm Gallery (www.chalkfarmgallery.com; 558 Canyon Rd) This gallery is filled with irresistibly fantastical pieces – mostly paintings, but also sculpture, kaleidoscopes and fine-art furniture.
Economos/Hampton Galleries (500 Canyon Rd) Museums come here to purchase fantastic examples of ancient Native American art, pre-Columbian Mexican pieces and much, much more, all crammed onto two huge floors swirling with history.
GF Contemporary (www.gfcontemporary.com; 707 Canyon Rd) Contemporary paintings and mixed-media creations lure with thought-provoking content and presentation.
Marc Navarro Gallery (520 Canyon Rd) Collectors come here to find antique Spanish and Mexican silver pieces, including jewelry studded with onyx and amethyst.
Morning Star Gallery (www.morningstargallery.com; 513 Canyon Rd) Of all the Canyon Rd shops dealing Indian antiquities, this remains the best: weavings, jewelry, beadwork, kachina dolls and even a few original ledger drawings are just some of the stars at this stunning gallery, which specializes in pre-WWII Plains Indian ephemera. Some artifacts here are finer than those in most museums – like the 1775 Powhoge ceramic storage jar that sold for $225,000 and the 1860 Nez Perce war shirt that went for $220,000.
Pushkin Gallery (www.pushkingallery.com; 550 Canyon Rd) Owned by the family of poet Alexander Pushkin, this gallery shows Russian masters including Nikolai Timkov and Vasily Golubev, who are outshone by newcomer Alexy Smirnov Vókressensky. Museum-quality Orthodox icons and lacquer boxes are also on display.
The following galleries are off Canyon Rd but worth visiting for their unique mediums and creations:
78th St Gallery ( 505-820-0250; www.78thstreetgallery.com; 357 E. Alameda St) Open by appointment only, this gallery just off Canyon Rd features unique paintings by local and international artists that focus on color, movement and spirit. Also check the website.
Gerald Peters Gallery (www.gpgallery.com; 1011 Paseo de Peralta) Santa Fe's preeminent restaurant and real-estate tycoon Gerald Peters' gallery, two blocks from Canyon Rd, carries a collection of fine art that few museums can touch, with all the Southwest masters: Nicolai Fechin, Charles Russell, Edward Borein, Woody Gwyn and many more. The back room has treasures the Museum of Fine Arts can't even afford.
Shiprock (www.shiprocktrading.com; 53 Old Santa Fe Trail, on Plaza) In a second-floor loft at the northeast corner of the Plaza, Shiprock has an extraordinary collection of Navajo rugs. Run by a fifth-generation Indian country trader, the vintage pieces are the real deal.
Nedra Matteucci Galleries (www.matteucci.com; 1075 Paseo de Peralta) Works by the Taos Society (Click here) are on display at this top gallery, which shows the best work of Joseph Henry Sharp, Ernest Blumenschein and the rest of the gang. Don't miss the beautiful gardens out back, which have monumental sculptures in stone and bronze, including work by Vietnam Women's Memorial designer Glenna Goodacre.
For something less alpine, race the trains on the Santa Fe Rail Trail. Beginning at the Santa Fe Southern Railway Depot, this 15-mile trail follows the rail line clear to Lamy. The trail is unpaved until you hit Agua Fria St, then paved the rest of the way, though mountain bikers can take a dirt turnoff at the intersection with US 285 to avoid following CR 33 into Lamy.
For bike rental and repair, and more route info, see the kind gentlemen at Mellow Velo ( 505-982-8986; www.mellowvelo.com;621 Old Santa Fe Trail; rentals per day from $35; 9am-5:30pm Mon-Sat). Their website also has a really useful page with trail maps.
###### Rafting
The two rivers worth running near Santa Fe are the Rio Grande – for white-water thrills –and the Rio Chama – which is mellower, but better for multiday trips and arguably more scenic.
As soon as it's marginally warm enough, rafting outfits head to the Rio Grande to crash through rapids on the renowned Class V Taos Box, which traverses 16 miles of spectacular wilderness gorge. It's fantastically fun but not for the faint of heart, and commercial companies require passengers to be at least 12 years old. Flows in this stretch of the river are usually too low to boat beyond early summer.
Less extreme but still exciting is the Class III Racecourse, also on the Rio Grande. It's fine for kids over six or seven (depending on the company), and the put-in is much closer to Santa Fe than the launch point for the Box. The season here usually runs from May to October, depending on water levels. This is also a classic playground for kayakers.
The Rio Chama has a few Class III rapids, but most of it is fairly flat, making it a fantastic choice for families, especially if you were wondering how you were going to get your kids or lazy spouse out into the backcountry for a couple of nights. Parts of the canyon are sublime.
Outfitters offer a number of variations on the above themes, so check in with them for all the options. Some reliable companies:
Santa Fe & Around
Sights
1 Cleveland Roller Mill Museum D4
2 Cochiti Pueblo A6
3 El Santuario de Chimayo B4
4 Kasha-Katuwe Tent Rocks National Monument A6
La Cueva Mill (see 10)
5 Nambé Pueblo B5
6 Ohkay Owingeh Pueblo B4
7 Picuris Pueblo C3
8 Pojoaque Pueblo B5
9 Rancho de Las Golondrinas A6
10 Salman Ranch D4
11 San Felipe Pueblo A6
12 San Ildefonso Pueblo B5
13 San Miguel Mission D7
14 Santa Clara Pueblo B4
15 Santo Domingo Pueblo A6
16 Shidoni Foundry B5
17 Taos Pueblo C3
Tapetes de Lana Weaving Center (see 19)
18 Tesuque Pueblo B5
19 Victory Ranch D4
Activities, Courses & Tours
20 Cottam's Ski Shop B5
21 Hermit Peak Trailhead D5
22 Pajarito Mountain Ski Area A5
Raven's Ridge Trailhead (see 24)
23 Sipapu Ski Area C4
24 Ski Santa Fe B5
Stables at Bishop's Lodge (see 27)
Upper Winsor Trailhead (see 24)
25 Winsor Trailhead B5
Sleeping
26 Abiquiú Inn A3
27 Bishop's Lodge Resort & Spa B5
28 Rancheros de Santa Fe Campground B6
29 Santa Barbara Campground C4
Eating
Bobcat Bite (see 28)
30 Casa de Teresa's Tamales D4
31 Harry's Roadhouse B6
32 San Marcos Café B6
Entertainment
33 Santa Fe Brewing Co B6
34 Santa Fe Opera B5
Shopping
Tesuque Flea Market (see 34)
Santa Fe Rafting Co RAFTING
( 888-988-4914; www.santaferafting.com; per person Taos Box $110-120; Racecourse $65; 3-day Chama $595) Pickup from Santa Fe or meet at the river.
New Wave Rafting Co RAFTING
( 800-984-1444; www.newwaverafting.com; perperson Taos Box $116; Racecourse adult/child $57/50; 3-day Chama $525) Now based near Pilar; meet at or near the river.
Kokopelli Rafting Adventures RAFTING
( 800-879-9035; www.kokopelliraft.com; per person Taos Box $110-120; Racecourse adult/child $53/42; 3-day Chama $449) Pickup from Santa Fe or meet near the river.
###### Horseback Riding
No Western fantasy is complete without hopping into a saddle, and there's some great riding to be done around Santa Fe. The Stables at Bishop's Lodge ( 505-819-4013; www.bishopslodge.com; 1297 Bishop's Lodge Rd; 8am-5pm; ) has a long menu of themed trail rides to choose from, including a sunset ride on Tuesdays and Thurdays.
Other highly recommended scenic rides are further from town, like those offered down in Cerrillos by Broken Saddle (Click here) and at Ghost Ranch (Click here), near Abiquiú.
If you're looking for lessons – Western or English – head a half-hour north to Española, where you'll find the affable Erlene Seybold-Smythe, one of the best instructors and horse trainers in the area, at Roy-El Morgan Farm ( 505-753-3696; www.roy-elmorgans.com; 1302 McCurdy Rd, Española; ), a champion Morgan facility.
###### Hiking & Backpacking
Some of the best hiking and backpacking in New Mexico is right outside of Santa Fe, in Santa Fe National Forest. The heart of the national forest is the undeveloped Pecos Wilderness, with nearly 1000 miles of trails leading through spruce and aspen forest, across grassy alpine meadows, and up to several peaks surpassing 12,000ft. The quickest way to get above treeline is to drive to the ski basin, hop on the Winsor Trail, and trudge up the switchbacks. For more on the Pecos Wilderness, see Click here. For top day hikes in the area, see box.
The most immediately accessible hiking trails are on the city's Dale Ball Trail System, just east of downtown. Also close to downtown, the Randall Davey Audubon Center ( 505-983-4609; www.nm.audubon.org; 1800 Upper Canyon Rd; trail use $2; 9am-4pm Mon-Fri, to 2pm Sat) offers a few trails, including the 3-mile Bear Canyon Trail. Free guided bird walks are given each Saturday at 8:30am.
###### Fishing
New Mexico's most outstanding fishing holes are better accessed from Taos and the Enchanted Circle, but there are plenty of opportunities out of Santa Fe, includingAbiquiú and Nambé Lakes and the Rio Chama. You'll need a license (one-day/five-day $12/24). For gear, fly-fishing lessons and guided trips around northern NM, look no further than High Desert Angler ( 505-988-7688; www.highdesertangler.com; 460 Cerrillos Rd; 8am-6pm Mon-Sat, 11am-4pm Sun mid-May–mid-Sep, 10am-6pm Mon-Sat, 11am-4pm Sun mid-Sep–mid-May)
### TOP FIVE SANTA FE DAY HIKES
There are a ton of trails around Santa Fe. Whether you're looking for all-day adventure or just a relaxing stroll through a special landscape, you'll find it. Trailheads for all the hikes in this list are within an hour's drive from the Plaza. The first two hikes start from the ski basin parking lot, beginning along the same trail.
Backcountry trails at Bandelier National Monument (see Click here) are also suberb.
Raven's Ridge No trail has better views than this one. After hiking the first steep mile of the Upper Winsor Trail, Raven's Ridge cuts east, more or less following the Pecos Wilderness boundary high above treeline to the top of Lake Peak (12,409ft). You can see forever from up here. Make a loop by hiking back down the ski slopes to the parking lot. It's a strenuous hike at substantial elevation, but well worth it if your body can take it. About 4 miles round trip.
Upper Winsor to Puerto Nambe After the first mile or so of steep switchbacks, the trail mellows out, essentially contouring around forested slopes with a moderate uphill section toward the end. Puerto Nambe (11,050ft) is a huge and beautiful meadow in the saddle between Santa Fe Baldy (12,622ft) to the north and Penitente Peak (12,249ft) to the south. It's a great place for picnic. The round-trip is about 10 miles.
Aspen Vista The premier path for immersing yourself in the magic of the fall foliage, this trail lives up to its name. The first mile or so is supereasy, gaining little elevation and following an old dirt road. It gets a little more difficult as you go along. Just go as far as you want, then turn back. The trailhead is at about 10,000ft, along the road to the ski basin; it's marked 'Trail No 150'. Mountain bikers love this one too.
Tent Rocks For something surreal, Kasha-Katuwe Tent Rocks National Monument (Click here) has a couple of short trails that meander through a geologic wonderland. The Cave Loop is 1.2 miles long; Veterans Memorial is a mile-long loop that's wheelchair accessible; the Canyon Trail round-trip is about 3 miles. Located 40 miles southwest of Santa Fe.
Valles Caldera A couple of remarkable trails circle small peaks in a massive basin that's really the crater of an ancient supervolcano. Elevations are between 9000ft and 10,000ft. This one pushes the one-hour drive time right to the edge, and is much closer to Los Alamos. You must call Valles Caldera National Preserve (see Click here) in advance to reserve a hiking permit.
#### Courses
Santa Fe School of Cooking COOKING
( 505-983-4511; www.santafeschoolofcooking.com; Plaza Mercado) If you develop a love for New Mexican cuisine, try cooking lessons at this cooking school which specializes in Southwestern cuisine. Classes are three hours long and cost between $60 and $80, including the meal.
Santa Fe Workshops PHOTOGRAPHY
( 505-983-1400; www.santafeworkshops.com; Mt Carmel Rd; courses $1075-1700) Develop your inner Ansel Adams awareness at these legendary weeklong traditional photography and digital imagery workshops. Course fees do not include meals and lodging.
Santa Fe Clay CERAMICS
( 505-984-1122; www.santafeclay.com; 545 Camino de la Familia) During summer, this premier ceramics gallery offers an array of four-day clay workshops ($525), taught by master potters. In winter and spring, weekend workshops are occasionally held. Though courses go way beyond throwing pots, most are open to aspiring ceramic artists of all levels.
Wise Fool CIRCUS
( 505-992-2588; www.wisefoolnewmexico.org; 2778-D Agua Fria St) Ever want to learn the arts of trapeze, juggling, or just plain clowning around? Wise Fool has drop-in classes ($20) and multiday intensives for adults ($175), plus weeklong summer camps for kids ($100).
#### Tours
Several companies offer walking and bus tours of Santa Fe and northern New Mexico. Others organize guided trips to the pueblos,as well as air tours and biking, hiking, rafting and horseback-riding trips.
Santa Fe Southern Railway SCENIC
( 505-989-8600; www.sfsr.com; 410 S Guadalupe St) Offers several scenic rides using the old spur line. The most popular run, a four-hour day trip (adult $32 to $45, child $18 to $32) on Friday (11am) or Saturday (noon), takes you past the Galisteo Basin and to the fairly ghostly town of Lamy. Several other themed trips are offered on other days. Note that the old downtown depot will no longer be home to the railway, but trains will still leave from behind it and tickets will be sold on the platform.
A Well-Born Guide/Have PhD, Will Travel WALKING
( 505-988-8022; www.swguides.com; tours from $22) If the name doesn't lure you in, then the tours will. Run by Stefanie Beninato, an informative local historian who has a knack for good storytelling, these lively trips receive excellent feedback from past participants. Stefanie offers a variety of themed hikes and walks around Santa Fe that focus on everything from bars and former brothels to ghosts, architecture and, of course, art. Multiday trips around New Mexico are also offered.
Seven Directions GENERAL
( 877-992-6128; www.sevendirections.com) Specializes in French-, Italian- and Spanish-language tours of the city and the state.
### LOCAL MAGIC: CHRISTMAS EVE ON CANYON RD
On the night before Christmas, Santa Fe is an ethereal site. The city's thousands of adobe buildings glow a warm yellow from the lights of thousands of _farolitos –_ real candles nestled in greased brown paper bags – lining streets, entranceways and even the roofs of the adobe homes and shops.
Walking down Santa Fe's most famous gallery avenue, Canyon Rd, on Christmas Eve is a uniquely Santa Fe experience, and in our book a magical must. There's something overwhelmingly graceful and elegant about the taste of the frosty air, the look of miles of glowing pathways of tiny candles and comradely quiet, the way the night sky meets softly lit gallery windows filled with fine art.
The magic comes partly from the intoxicating sights and scents of small piñon and cedarwood bonfires that line the road, offering guiding light and unforgettable memories. Partly it's a few equestrians prancing on horseback, jingle bells jingling, clackity-clacking along the narrow street, evoking memories of early Santa Feans who led their burros up the 'Road of the Canyon' to gather firewood in mountain forests. Partly it's the silhouettes of 250-year-old adobes softly lit by rows of twinkling _farolitos_.
Dress warmly and arrive early – say, by 6pm – if you want to beat the crowds. As night falls, the streets fill with human revelers and their canine friends, all giddy with the Christmas spirit. Small groups of carolers sing remarkably in tune. Join them, then pop into a gallery for a cup of spiced cider and a quick perusal of post-communist Russian art to warm up.
Pink Lady Tours WALKING
( 505-699-4147; www.wildwackytours.com) Walking tours of Santa Fe, with the guide who strives for the most laughs per minute.
Loretto Line HISTORICAL
( 505-983-3701; www.toursofsantafe.com) Cruisearound in an open-air tram and learn about the history and culture of Santa Fe from experienced guides.
#### Festivals & Events
The Santa Fe Visitors Bureau (www.santafe.org) provides an excellent list of events, musical and theatrical productions and museum shows. Some of the biggies:
ARTfeast ART
(www.artfeast.com) Eat your way around Santa Fe's galleries during this weekend-long festival in late February that incorporates art, food, wine and fashion and benefits art programs for Santa Fe children.
Pride on the Plaza GAY PRIDE
(www.santafehra.org) Drag queens, parades, floats, a film festival, music, comedy and more; area bars and restaurants throw special bashes for a full week in mid-June, here in the city ranked 'second gayest in America' by the _Advocate_ magazine.
Rodeo de Santa Fe CULTURAL
(www.rodeodesantafe.org; adult/child from $17/10) For more than half a century, wranglers, ranchers and cowpokes, along with plenty of rhinestone cowpersons, have been gathering to watch those bucking broncos, clowns in barrels, lasso tricks and fancy shooting. A pre-rodeo parade takes it all downtown. Held in late June.
International Folk Art Market CULTURAL
(www.folkartmarket.org) The largest folk art market in the world brings over 130 artists from 50 countries around the world to the Folk Art Museum for a festive weekend of craft shopping and cultural events in early July. Things get off to a fun start with a free World Music concert at the Railyard.
Spanish Market CULTURAL
(www.spanishcolonial.org) Traditional SpanishColonial arts, from _retablos_ and _bultos_ to handcrafted furniture and metalwork, make this juried show in late July an artistic extravaganza, second only to the Indian Market. Another Spanish Market is held in early December at the Sweeny Convention Center.
Santa Fe Indian Market CULTURAL
(www.swaia.org) Only the best get approved to show their work at this world-famous juriedshow (held the weekend after the third Thursday in August), where more than 1000 artists from 100 tribes and Pueblos exhibit. As if that's not enough, 100,000 visitors converge on the Plaza, at open studios, gallery shows and the Native Cinema Showcase. Get there Friday or Saturday to see pieces competing for the prestigious top prizes (they get snapped up by collectors), but wait until Sunday if you want to try bargaining.
### SANTA FE FOR CHILDREN
Check 'Pasatiempo,' the Friday arts and entertainment section of the _Santa Fe New Mexican,_ for its 'Bring the Kids' column, which has a rundown on area events for children. Also look for the free local newspaper, _New Mexico Kids,_ published six times a year, for great day-by-day event calendars.
The Santa Fe Children's Museum (www.santafechildrensmuseum.org; 1050 Old Pecos Trail; admission $9, $5 on Sun; 10am-6pm Tue-Sat, noon-5pm Sun; ) features hands-on exhibits on science and art for young children, but adults will enjoy it as well. The museum runs daily two-hour programs, led by local scientists, artists and teachers, that tackle subjects like solar energy and printmaking.
The amazing Museum of International Folk Art (Click here) has a fantastic big indoor play area with books, Lego and other toys. It is perfect rainy-day entertainment for your little one.
If you're traveling with a budding thespian, check out the backstage tours of the Santa Fe Opera (Click here) during opera season. They're interesting, and free for folks under 17.
Most restaurants, except those that are seriously upscale, are happy to host your kids, and most have special menus – but only the Cowgirl Hall of Fame (Click here) has a playground _and_ a full bar. One of Santa Fe's top breakfast spots, Cafe Pasqual's (Click here), is also very child-friendly.
If you want to get out on your own, Magical Happenings Babysitting ( 505-982-9327) can have sitters stay with your kids in your hotel room; it's $18 an hour for one child or $20 an hour for two, with a four-hour minimum, and reservations should be made in advance, particularly during the high season.
Santa Fe Fiesta CULTURAL
(www.santafefiesta.org) Two weeks of events in early September celebrate the September 4, 1692, resettlement of Santa Fe, including concerts, a carnival, a candlelight procession and the kids' favorite – the Pet Parade. Everything kicks off with the bizarrely pagan and slightly terrifying torching of Zozobra – a 50-foot-tall effigy of Old Man Gloom – as the mob gathered in Fort Marcy Park shouts 'Burn him!'
Wine & Chile Fiesta FOOD
(www.santafewineandchile.org) It's a gourmet's fantasy fiesta, with wine tastings and fine cuisine; dinner events sell out early. Late September.
#### Sleeping
Rates vary from week to week and day to day. Generally, January and February offer the lowest rates – cut by as much as 50% from what's listed here. September, October, March and April generally have midrange rates. In December and during the summer (particularly during Indian Market in August and on opera nights), expect to pay premium prices. Make reservations well in advance. Remember: prices do not include taxes and other add-ons of 11% to 15%.
Many agencies can help with reservations, including Santa Fe Stay ( 800-995-2272; www.santafestay.com), specializing in home stays, ranch resorts and casitas.
Most of the low-budget and national chain options line Cerrillos Rd between I-25 and downtown.
When it comes to luxury accommodations, Santa Fe has more than its share of intimate hotels and posh B&Bs ready to cater to your every whim. Book through an internet consolidator for the best rates.
Santa Fe National Forest and Hyde State Park are the best places around for car camping. Stop by the Public Lands Information Center for maps and detailed information.
##### DOWNTOWN SANTA FE
La Fonda HISTORIC HOTEL $$$
( 800-523-5002; www.lafondasantafe.com; 100 E San Francisco St; r/ste from $140/260; ) Staff artist Ernest Martinez has been painting thousands of windows and other fixtures since 1954, giving La Fonda its unique folk-art character. Claiming to be the original 'Inn at the end of the Santa Fe Trail,' here since 1610, the hotel also features Southwest murals and paintings commissioned in the 1920s and '30s. The top-floor luxury suites in the Terrace are lovely, and sunset views from the rooftop Bell Tower Bar are the best in town.
El Paradero B&B $$
( 505-988-1177; www.elparadero.com; 220 W Manhattan Ave; r $125-200; ) Just a few blocks from the Plaza, this 200-year-old adobe B&B is one of Santa Fe's oldest inns. Each room is unique and loaded with character; our favorite is No 6. The full breakfasts satisfy. The owners also offer an off-site casita ($350) that sleeps six, with a gorgeous Southwestern-style kitchen and peaceful garden.
Inn of the Five Graces BOUTIQUE HOTEL $$$
( 505-992-0957; www.fivegraces.com; 150 E DeVargas St; ste $340-900; ) Much more than an ordinary luxury getaway, this one-of-a-kind exquisite, exclusive gem offers an upscale gypsy-style escape. Sumptuous suites are decorated in a lavish Persian/Indian/Asian fusion theme, complete with fireplaces, beautifully tiled kitchenettes and a courtyard behind river-rock walls. They also rent the Luminaria House (per night $2500), with two master bedrooms, five fireplaces and all the luxury you'd expect for the price.
Inn on the Alameda HOTEL $$
( 888-984-2121; www.innonthealameda.com; 303 E Alameda St; r $125-245; ) Handmade furniture, kiva fireplaces, luxe linens, elegant breakfasts and afternoon wine-and-cheese receptions bring B&B-style elegance to a pleasantly efficient hotel. The staff can also arrange cooking classes, fly-fishing, outdoor adventures and more, all with local experts. The inn is perfectly positioned between Canyon Rd and the Plaza. Small dogs are welcome for an extra $30 per night.
La Posada de Santa Fe LUXURY HOTEL $$$
( 505-986-0000; www.laposada.rockresorts.com; 330 E Palace Ave; r from $200; ) Your every need is catered to on this beautiful, shady, 6-acre property a few blocks from the Plaza. Elegantly furnished adobe casitas are outfitted with gas fireplaces. More historical (and smaller) rooms, some with views, are located in the Staab House. On-site Avanyu Spa (see Click here) is deservedly fabulous, while the cigar-friendly Staab House Lounge (open 11:30am to 11pm) is a local favorite for its leather-chaired ambience and single-malt scotch.
Inn of the Anasazi LUXURY HOTEL $$$
( 800-688-8100; www.innoftheanasazi.com; 113 Washington Ave; r $200-525; ) Ancient blends seamlessly with ultramodern in this elegant, Navajo-themed property half a block off the Plaza. Details are meticulously attended to. The interior waterfall has been named one of the 'thousand things to see before you die' – though we're not sure why – on one of those lists that declare those kinds of things.
Inn & Spa at Loretto LUXURY HOTEL $$$
( 505-988-5531; www.hotelloretto.com; 211 Old Santa Fe Trail; r from $180; ) Modeled after the Taos Pueblo, this gorgeous old hotel has large, luxurious rooms with a Native American theme that includes local art hanging on dark-red walls. Modern amenities include iPod docking stations and huge flat-screen TVs. In-room minibars feature small oxygen tanks, in case you need a quick boost. Have a drink in the lobby bar and look up at the ceiling – each panel is hand-painted.
Hotel St Francis HISTORIC HOTEL $$
( 505-983-5700; www.hotelstfrancis.com; 210 Don Gaspar Ave; r $120-300; ) Recently renovated, the St. Francis has traded some of its faded charm for modern upgrades. All in all, it's retained its historic ambience, blending luxurious touches with a nicely underplayed Spanish missionary theme.
Inn of the Governors HOTEL $$
( 505-982-4333; www.innofthegovernors.com; 101 W Alameda St; r from $130; ) You can't beat the location, just blocks from the Plaza. Rooms are elegantly decorated with kiva fireplaces, warm-hued bedspreads and Southwestern-style doors and windows. It's an intimate place to slumber. Don't miss the adjoining Del Charro Saloon, with some of the cheapest eats downtown.
Garrett's Desert Inn HOTEL $$
( 505-982-1851; www.garrettsdesertinn.com; 311 Old Santa Fe Trail; r $80-170; ) An old motor court–style place, Garrett's has been popular with travelers for half a century now. Rooms are in good shape, and the location is great. The heated pool is a plus. Families can book into one of the large suites and pets stay free.
##### CERRILLOS RD & METRO SANTA FE
Ten Thousand Waves Japanese Resort & Spa RESORT $$$
( 505-982-9304; www.tenthousandwaves.com; 3451 Hyde Park Rd; r $200-270; ) This Japanese spa 4 miles from the Plaza features 13 gorgeous, Zen-inspired freestanding guest houses. Most come with fireplaces and either a deck or courtyard, and all are within walking distance of the mountainside hot tubs and massage cabins. Make reservations two months in advance. Pets are welcomed with custom-size beds, bones and treats!
Bishop's Lodge Resort & Spa RESORT $$$
( 800-419-0492; www.bishopslodge.com; 1297 Bishops Lodge Rd; r from $160; ) Come play (upscale) cowgirl on 450 acres of almost untouched piñon wilderness just 3 miles from the Plaza. This family-friendly destination resort has huge, luxurious rooms and casitas, many with patios, kitchenettes, fireplaces and more. From yoga classes at its spa to a magnificent outdoor pool overlooking the mountains to horseback riding through the mountains, there truly is something for everyone. The on-site restaurant, Las Fuentes, has a lavish Sunday brunch that has been voted best in Santa Fe. Free shuttles take you downtown.
Inn of the Turquoise Bear B&B $$
( 800-396-4104; www.turquoisebear.com; 342 E Buena Vista St; r $110-245; ) Visitors enjoy the quiet now, but this expansive adobe palace, built by local legend Witter Bynner and partner Robert Hunt, was once home to legendary parties hosting Thornton Wilder, Robert Oppenheimer, Edna St Vincent Millay, Robert Frost and many, many others. It's now a B&B surrounded by an acre of sculpted gardens, combining authentic ambience and modern amenities.
Sage Inn HOTEL $$
( 505-982-5952; www.santafesageinn.com; 725 Cerrillos Rd; r $78-125; ) With more appeal than a chain hotel but not as much as boutique accommodations, the Sage Inn is a nice compromise in terms of quality, service and location. It's modern and clean and a good place for budget-minded families. There's a guest laundromat, pets are OK ($25), and it's right next to Whole Foods.
Silver Saddle Motel MOTEL $
( 505-471-7663; www.silversaddlemotelllc.com; 2810 Cerrillos Rd; r from $45; ) Some rooms here have attractively tiled kitchenettes, and all have shady wooden arcades outside and comfortable cowboy inspired decor inside. For a bit of kitsch, request the Kenny Rogers or Wyatt Earp rooms. This is the best budget value in town; rates include continental breakfast.
Santa Fe International Hostel HOSTEL $
( 505-988-1153; www.hostelsantafe.com; 1412 Cerrillos Rd; dm $18, r $25-35; ) If you're looking for a true-blue old hippie hostel, you can't beat this experience in communal living – including the refrigerator full of free, donated food. It's not the cleanest place in Santa Fe, but it's definitely the cheapest, and there's usually an interesting array of other travelers to meet. Rooms are simple but big, with metal beds with tired mattresses and fading but freshly washed linens. Rooms facing the main road are a bit noisy. They take cash only, and short daily chores are required.
Rancheros de Santa Fe Campground CAMPGROUND $
( 505-466-3482; www.rancheros.com; 736 Old Las Vegas Hwy; tent/RV sites $23/39; Mar-Oct; ) Eight miles southeast of the Plaza, off exit 290 from I-25 North, Rancheros has nice views, a convenience store and free wireless internet. Plus, its sites are shady and big. Enjoy hot showers, cheap morning coffee and evening movies.
#### Eating
Food is another art form in Santa Fe, and some restaurants are as world-class as the galleries. From spicy, traditional Southwest favorites to cutting-edge cuisine, it's all here. Reservations are always recommended for the more expensive venues, especially during summer and ski season. All Santa Fe restaurants and bars are nonsmoking.
Check for current reviews in the _Santa Fe Reporter,_ which often has coupons for area eateries, or the free monthly _Local Flavor_ , with reviews and news about area restaurants.
##### THE PLAZA & CANYON RD
If you're on a budget downtown, one of the cheapest and tastiest places to eat lunch or an early dinner is at the takeaway, city-licensed stalls on the Plaza lawn. The beef fajitas with fresh guacamole is our favorite. Tacos and burritos are also offered.
Coyote Café MODERN SOUTHWESTERN $$$
( 505-983-1615; www.coyotecafe.com; 132 Water St; mains $28-56; 5:30-9pm) Serious foodies return year after year for stellar interpretations of New Mexico cuisine. Now in the capable hands of chef Eric DiStefano, the menu at Santa Fe's most celebrated restaurant changes frequently, featuring creative interpretations of wild game, seafood and steaks. Delish margaritas come in a rainbow of flavors. For more affordable and casual options from the same kitchen, eat upstairs on the roof at the Coyote Cantina (mains $7-18; 11:30am-9pm Apr-Oct; ), which also serves lunch.
El Farol TAPAS, SPANISH $$$
( 505-983-9912; www.elfarolsf.com; 808 Canyon Rd; lunch mains $8-18, dinner mains $25-50; 11:30am-late; ) This popular restaurant and bar, set in a rustically authentic adobe, has live music nightly. Although El Farol does excellent steaks, most people come to sample the extensive list of tapas ($8). The flamenco dinner show (most nights 6:30pm, $25) is lively and perfect for birthdays or special occasions. Kids will also dig it.
Cafe Pasqual's INTERNATIONAL $$$
( 505-983-9340; www.pasquals.com; 121 Don Gaspar Ave; breakfast & lunch mains $8-15, dinner mains $20-40; 7am-3pm & 5:30-9pm; ) Make reservations for dinner if you'd like, but definitely wait in line to enjoy the famous breakfasts. We highly recommend _huevos motuleños_ , made with eggs and black beans, sautéed bananas, feta cheese and more; _tamale dulce_ , a sweet corn tamalewith fruit, beans and Mexican chocolate; or the enormous Durango ham-and-cheese omelet. They're all served up in a festive, if crowded, interior. Grab a seat faster by sitting at the community table, where tourists and locals mix it up daily.
Guadalupe Cafe NEW MEXICAN $$
(442 Old Santa Fe Trail; mains $8-15; 7am-2pm & 5-9pm Tue-Fri, 8am-2pm & 5-9pm Sat; 8am-2pm Sun) With a few dining rooms spread around a cozy old house, and an inviting outdoor patio, this reliable restaurant goes beyond the usual list of New Mexican specialties (try the chicken breast _rellenos_ ). Breakfasts are hearty and the salads are immense.
Tia Sophia's NEW MEXICAN $
(210 W San Francisco St; mains $7-10; 7am-2pm Mon-Sat; ) Local artists and visiting celebrities outnumber tourists at this longstanding Santa Fe favorite that's always packed. Breakfast is the meal of choice, with fantastic burritos and other Southwestern dishes. Lunch is pretty damn tasty too; try the perfectly prepared _chile rellenos_. The shelf of kids' books helps little ones pass the time.
Geronimo MODERN AMERICAN $$$
( 505-982-1500; 724 Canyon Rd; mains $28-44; 5:45-10pm Mon-Thu, to 11pm Fri & Sat) Housed in a 1756 adobe, Geronimo is among the finest and most romantic restaurants in town. The short but diverse menu currently includes honey-grilled prawns with fiery sweet chile and peppery elk tenderloin with applewood-smoked bacon.
SantaCafé MODERN SOUTHWESTERN $$$
( 505-984-1788; www.santacafe.com; 231 Washington Ave; lunch mains $11-15, dinner mains $19-33; 11:30am-2pm Mon-Sat, 5:30-9pm daily; ) Chef David Sellars is practically an international celebrity because of dishes like roasted poblano _chile rellenos_ with three-mushroom quinoa and chipotle cream ($19). Housed in an 1850s adobe built by the infamous Padre Gallegos, Santacafé also has the best courtyard in town for summertime dining. Lunch is a deal, the wine list flawless and the dining room historical. In short, perfection.
Compound MODERN AMERICAN $$$
( 505-982-4353; www.compoundrestaurant.com; 635 Canyon Rd; lunch mains $12-20, dinner mains $28-34; noon-2pm Mon-Sat, 6-9pm daily) A longtime local foodie favorite, the Compound features the contemporary American creations of Mark Kiffin, recognized by the James Beard Foundation as the Best Chef of the Southwest in 2005. The acclaimed seasonal menu draws on the elegant flavors of Southwestern and Mediterranean cooking. Ingredients are always fresh, and the presentation perfect. Come when there's reason to celebrate: the wine list includes several top-notch champagnes.
Del Charro Saloon PUB $
(Inn of the Governors, 101 W Alameda St; mains under $6; 11:30am-midnight) Attached to Inn of the Governors, this popular pub is an atmospheric place with copper-topped tables, lots of vegetation and a blazing fire in the winter. In summer the patio opens up and tables spill onto the sidewalk. It serves giant, inexpensive margaritas and delicious pub grub well into the night.
French Pastry Shop CREPERIE $
(La Fonda Hotel, 100 E San Francisco St; mains $6-9; 6:30am-5pm) Serving delicious French bistro food inside La Fonda hotel, including crepes – filled with everything from ham and cheese to strawberries and cream –along with a host of quiches, sandwiches, cappuccinos and, of course, pastries.
Il Vicino ITALIAN $
(www.ilvicino.com/santafe; 321 W San Francisco St; mains $6-9; 11am-10pm Sun-Thu, until 11pm Fri & Sat; ) For a break from chile, come to Il Vicino, where you'll find brick-oven pizzas, pastas and salads a quick walk from the Plaza.
Shed NEW MEXICAN $$
(www.sfshed.com; 113½ E Palace Ave; lunch mains $8-11, dinner mains $11-17; 11am-2:30pm & 5:30-9pm Mon-Sat; ) Superconvenient to the Plaza and with a fun ambience. The food, however, is seriously overrated, aiming straight for the perceived middle-of-the-road tourist palate. There's a nice patio.
##### GUADALUPE ST AREA
Off the Plaza but easily walkable from there, this funky little neighborhood is home to some quirky dining and drinking options frequented by Santa Fe's young and hip crowd.
Santa Fe Farmers Market MARKET $
( 505-983-4098; Paseo de Peralta, 55yd west of Guadalupe St; 7am-noon Sat & Tue Apr-Nov; ) Local produce, much of it heirloom and organic, is on sale at these spacious digs, alongside homemade goodies, inexpensive food, natural body products and arts and crafts.
Ristra MODERN AMERICAN $$$
( 505-982-8608; www.ristrarestaurant.com; 548 Agua Fria St; mains $20-40; 11:30am-2:30pm & 5:30-9:30pm Tue-Sat) Ristra attracts a regular clientele who come for its casual intimacy and excellent food. The contemporary-American menu is influenced by the flavors of France and the Southwest, and changes seasonally. The steaks here are always fantastic, the wine list is lengthy and there are plenty of bottles of bubbly to toast those special occasions.
Cowgirl Hall of Fame BARBECUE $$
(www.cowgirlsantafe.com; 319 S Guadalupe St; mains $8-18; 11am-midnight Mon-Fri, 10am-midnight Sat, 10am-11pm Sun; ) A fun place for all ages, thanks to the great playground in the back, wacky Western-style feminist flair, outside patio and live music, this restaurant has fabulous food and awesome margaritas. Everything is tasty, but the Cowgirl is known for its barbecue brisket – order it in a quesadilla with green chile. After dark, order smoky mescal margaritas and play a game of pool in the new billiard room.
Zia Diner AMERICAN $
(366 S Guadalupe St; mains $6-12; 11am-10pm; ) Voted Best Comfort Food by locals, this cozy diner is known for its meatloaf, buffalo burgers and yummy homemade pies. Have a beer and watch pink-haired hipsters and graying progressives coo over their blue-plate specials (served weekdays only). It's one of the few places open late on Sundays.
Tomasita's NEW MEXICAN $$
( 505-983-5721; 500 S Guadalupe St; mains $7-15; 11am-10pm Mon-Sat; ) Sure it's touristy, but it's good! The menu sticks to traditional New Mexican fare like burritos and enchiladas, and there are huge blue-plate specials. It's a raucous place, good for families hauling exuberant kids. Prepare to wait; the restaurant is always packed.
Cleopatra Cafe MIDDLE EASTERN $
(Design Center, 418 Cerrillos Rd; mains $5-12; 6am-8pm Mon-Sat, to 6pm Sun; ) Makes up for lack of ambience with taste and value: big platters of delicious kebabs, hummus, falafel and other Middle Eastern favorites.
Raaga INDIAN $$
(www.raagacuisine.com; 544 Agua Fria St; mains $13-18; 11:30am-2pm & 5-9:30pm, to 10pm Fri & Sat; ) An awesome new Indian restaurant with delicious curries, biryanis and tandoori specialties. Only one flaw: the chai is lame.
Flying Star Café AMERICAN $
(www.flyingstarcafe.com; 500 Market St; mains $7-13; 7am-9pm Sun-Thu, to 10pm Fri & Sat; ) The Santa Fe branch of this casual, Albuquerque-based diner chain, located at the Railyard, has quickly become a local favorite, especially for families with kids.
##### METRO SANTA FE
Some of the best places to eat aren't right in the center of town. These are worth traveling for.
San Marcos Café NEW MEXICAN $
( 505-471-9298; www.sanmarcosfeed.com; 3877 Hwy 14; mains $7-10; 8am-2pm; ) About 10 minutes' drive south on Hwy 14, this country-style cafe is well worth the trip. Aside from the down-home feeling and the best red chile you'll ever taste, turkeys and peacocks strut and squabble outside and the whole place is connected to a feed store, giving it some genuine Western soul. The pastries and desserts – especially the bourbon apple pie – sate any sweet tooth. Make reservations on weekends.
Tune-Up Café INTERNATIONAL $$
(www.tuneupcafe.com; 1115 Hickox St; mains $7-14; 7am-10pm Mon-Fri, from 8am Sat & Sun; ) Santa Fe's newest favorite restaurant is casual, busy and does food right. The chef, from El Salvador, adds a few twists to classic New Mexican and American dishes while also serving fantastic Salvadoran _pupusas_ (stuffed corn tortillas), huevos and other specialties. The molé colorado enchiladas and the fish tacos are exceptional.
Horseman's Haven NEW MEXICAN $
(4354 Cerrillos Rd; mains $6-12; 8am-8pm Mon-Sat, 8:30am-2pm Sun; ) Hands down, the hottest green chile in town! (The timid should order it on the side). Service is friendly and fast, and their enormous 3D burrito might be the only thing you need to eat all day.
### RAILYARD RENAISSANCE
After years of municipal wrangling over how to develop the dormant Railyard District (www.railyardsantafe.com), its grand opening was held in 2008. It's already come into its own as a lively multi-use area that merges with the Guadalupe St District. Aside from the welcoming drinking joints & restaurants here, such as Second Street Brewery and Flying Star Café, it's also home to the Santa Fe Farmers Market. One end is devoted to a park with gardens, a few things to climb and play on and an outdoor performance space; it's no Tuileries, but if it's good enough for pot-smoking high school kids, it's good enough for us.
The Railyard is also making a real play at being the epicenter of Santa Fe's contemporary art scene, with 10 galleries and SITE Santa Fe. A few you won't want to miss:
Santa Fe Clay (www.santafeclay.com; 545 Camino de la Familia) Fine art ceramics that range from innovative functionality to cutting-edge sculpture.
Tai Gallery (www.taigallery.com; 1601B Paseo de Peralta) Featuring fine bamboo crafts by Japanese masters, along with work by Japanese photographers and textile arts from around the world.
LewAllen Galleries (www.lewallengalleries.com; 1613 Paseo de Peralta) Probably the most prominent modern contemporary art gallery in town, LewAllen also shows Modernist masters.
Harry's Roadhouse AMERICAN, NEW MEXICAN $
( 505-989-4629; www.harrysroadhousesantafe.com; 96 Old Las Vegas Hwy; mains breakfast $5-8, lunch $7-11, dinner $9-16; 7am-10pm; ) This longtime favorite on the southern edge of town feels like a rambling cottage. And, seriously, _everything_ is good here. Especially the desserts! The mood is casual, it's family-friendly and has a full bar. If you're with six or more, call for reservations.
Santa Fe Baking Company AMERICAN $
(www.santafebakingcompanycafe.com; 504 W Cordova Rd; mains $5-11; 6am-8pm Mon-Sat, to 7pm Sun; ) A bustling cafe serving burgers, sandwiches and big breakfast platters all day. There's also a full-on smoothie bar. This is a great spot to get a glimpse of the human melting pot that is Santa Fe. Need proof? The local radio station, KSFR, broadcasts a talk show from here each weekday morning.
Bobcat Bite BURGERS $
(www.bobcatbite.com; 420 Old Las Vegas Hwy; mains $6-23; 11am-7:50pm Wed-Sat, 11am-5pm Sun) Often voted as serving the Best Burger in Santa Fe by locals, this relaxed roadhouse beneath the neon really does an outstanding green chile cheeseburger ($7). The steaks are pretty darn good too.
Tesuque Village Market CAFE $$
(www.tesuquevillagemarket.com; 138 Tesuque VillageRd, Tesuque; mains $8-20; 7am-9pm) Once hole-in-the-wall, now country-hip, this is a hot spot on weekend mornings for folks heading to or from the Tesuque Flea Market. If you're hungry and in a hurry, grab a handheld burrito and take it with you – the breakfast burritos will start your day right, and the _carne adovada_ is some of the best anywhere. Take Bishops Lodge Rd or Hwy 285 north to Exit 168.
#### Drinking
###### Bars
Talk to 10 residents and you'll get 10 different opinions about where to find the best margarita. You'll just have to sample the lot to decide for yourself.
Evangelo's BAR
(200 W San Francisco St) Everyone is welcome in this casual, rowdy joint owned by the Klonis family since 1971 (ask owner/bartender Nick about his father's unusual fame). Drop in, put on some Patsy Cline and grab a draft beer – it's the perfect escape from Plaza culture.
Second Street Brewery BREWERY
(www.secondstreetbrewery.com) Railyard (Railyard); 2nd Street (1814 2nd St) Santa Fe's favorite brewery is the perfect spot to stop for a pint after a long hike. It serves handcrafted English-style beers – brewed on the premises – and also offers a hearty selection of better-than-average pub grub. Sit outside on the big patio or inside the brewery. There's live music nightly. We like the newer Railyard location better than the original.
Bell Tower Bar BAR
(100 E San Francisco St; 5pm-sunset Mon-Thu, from 2pm Fri-Sun May-Oct) In summer this bar atop La Fonda hotel is the premier spot to catch one of those patented New Mexican sunsets while sipping a killer margarita. After dark, retire to the hotel's lobby Fiesta Bar for live country and folk music.
Dragon Room Bar BAR
(406 Old Santa Fe Trail) This 300-year-old adobe is a consistent top fave for locals and Hollywood-famous visitors alike. Drop by for a signature Black Dragonmargarita. Visit after 9pm on Tuesday, Thursday or Saturday if you want it served with live music (flamenco guitar, Latin jazz and the like).
Ore House BAR
(50 Lincoln Ave) We think this place makes the best fresh lime (no sweet and sour) margarita in town, and with more than 40 different types to choose from, there's bound to be a margarita for everyone. Choose from the seats on the heated balcony overlooking the Plaza or a table inside. The steaks here make it worth staying for dinner.
Marble Brewery Tap Room PUB
(60 E San Francisco St) With microbrews on tap and an espresso bar, this upstairs place covers both ends of the legal substance spectrum. An outdoor patio overlooks the Plaza, a leather-couched lounge has big flat-screens to watch whatever game is on, and they serve pizza.
###### Cafes
Aztec Cafe CAFE
(www.azteccafe.com; 317 Aztec St; 7am-7pm Mon-Sat, from 8am Sun, closes daily at 6pm in winter; ) Our pick for best local coffeehouse, the Aztec welcomes all kinds to its low-key indoor art space and outdoor patio.
Tea House CAFE
(www.teahousesantafe.com; 821 Canyon Rd; 8am-7pm; ) If you're feeling ambivalent, prepare for a dilemma when confronted with the list of 150 types of tea. They have coffee, too, and breakfast and lunch. A perfect stop when you're done with the galleries on Canyon Rd.
#### Entertainment
###### Performing Arts
Patrons from the world's most glittering cities are drawn to Santa Fe in July and August because of opera, chamber music, performance and visual arts, an area in which Santa Fe holds its own against anywhere on the globe. The opera may be the belle of the ball – clad in sparkling denim –but there are lots of other highbrow and lowbrow happenings every week. Let the searchable, exhaustive online Events Calendar (www.santafe.com/calendar) becomeyour new best friend. Plan ahead to score coveted seats, lodging and gourmet meals.
Santa Fe Opera OPERA
( 505-986-5900; www.santafeopera.org; Hwy 84/285, Tesuqu; late Jun–late Aug) Many come to Santa Fe for this and this alone: the theater is an architectural marvel,with nearly 360-degree views of wind-carved sandstone wilderness crowned with sunsets and moonrises, and at center stage the world's finest talent performs Western civilization's masterworks. It's still the Wild West, though; you can even wear jeans – just try _that_ in New York City.
Gala festivities begin two hours before the curtain rises, when the ritual tailgate party is rendered glamorous in true Santa Fe style right in the parking lot. Bring your own caviar and brie, make reservations for the buffet dinner and lecture or a picnic dinner, or have your own private caterer – several customize the menu to the opera's theme – pour the champagne. Prelude Talks, free to all ticket holders, are offered in Stieren Orchestra Hall one hour and two hours before curtain to accommodate various dining schedules. Shuttles run to and from the event from Santa Fe and Albuquerque; reserve through the opera box office.
Youth Night at the Opera offers familiesa chance to watch dress rehearsals a few nights each summer, for bargain rates; one precedes the run of each of the season's operas – with brief talks aimed at audience members ages 6 to 22. Backstage tours (adult/child $5/free; 9am Mon-Fri Jun-Aug) offer opportunities to poke around the sets, costumeand storage areas.
Lensic Performing Arts Theater PERFORMING ARTS
( 505-984-1370; www.lensic.com; 211 W San Francisco St) A beautifully renovated 1930 movie house, the theater hosts a weekly classic film series and eight different performance groups, including the Santa Fe Symphony Orchestra & Chorus.
Santa Fe Playhouse THEATER
( 505-988-4262; www.santafeplayhouse.org; 142 E De Vargas St; 8pm Thu-Sat, 2pm Sun) The state's oldest theater company performs avant-garde and traditional theater and musical comedy. On Sunday, admission is as much as you can afford.
Santa Fe Chamber Music Festival CLASSICAL MUSIC
( 505-982-1890; www.sfcmf.org; Jul & Aug) This is the other big cultural event, known for filling elegant venues like the Lensic with Brahms, Mozart and other classical masters. It's not just world-class acts like violinist Pinchas Zukerman and pianist Yuja Wang defining the season; top-notch jazz, world music and New Music virtuosos round out the menu.
Santa Fe Desert Chorale LIVE MUSIC
( 505-988-2282, 800-244-4011; www.desertchorale.org) Twenty lauded professional singers from around the country come together in July, August and the winter holidays to perform everything from Gregorian chants and gospel to Renaissance madrigals and modern love songs at venues like St Francis Cathedral and Loretto Chapel.
###### Live Music & Dance Clubs
La Fonda and the Inn & Spa at Loretto are just two of many hotel bars offering live music most nights. Check the _Santa Fe Reporter_ and the 'Pasatiempo' section of Friday's _New Mexican_ for a thorough listing of what's going on in Santa Fe – clubs here change faster than the seasons.
El Farol TRADITIONAL DANCE, LIVE MUSIC
(www.elfarolsf.com; 808 Canyon Rd) Aside from the Flamenco dinner shows, there's a regular Latin soul show and other entertainment.
Santa Fe Brewing Co LIVE MUSIC
(www.santafebrewing.com; 35 Fire Pl) One of Santa Fe's best venues for out-of-town bands, especially reggae masters. Enjoy a handcrafted microbrew, from pilsner to porter to stout. Out on Hwy 14, just south of town.
Vanessie of Santa Fe CABARET
(434 W San Francisco St) You don't really come to Vanessie for the food, though there's nothing wrong with it. No, the attraction here is the piano bar, featuring blow-dried lounge singers who bring Neil Diamond and Barry Manilow classics to life in their own special way.
Warehouse 21 LIVE MUSIC
(www.warehouse21.org; 1614 Paseo de Peralta) This all-ages club and arts center in a 3500-sq-ft warehouse is the perfect alcohol-free venue for edgy local bands, plus a fair number of nationally known acts, or for just showing off the latest in multihued hairstyles.
#### Shopping
Besides the Native American jewelry sold directly by the artists under the Plaza _portales_ , there are enough shops for youto spend weeks browsing and buying in SantaFe. Many venues are gallery-and-shop combos. The focus is mainly on art, from Native American jewelry to wild contemporary paintings. For the gallery lowdown, see Click here.
### TOP TIP: SHOPPING FOR NATIVE AMERICAN ART IN SANTA FE
The best place for shopping is the under the _portales_ (overhangs) in front of the Palace of Governors. This is where Indians come – some from as far as 200 miles away – to sell their gorgeous handmade jewelry. It's a tradition that began in the 1880s, when Tesuque artisans began meeting the train with all manner of wares. Today up to 1200 members, representing almost every New Mexican tribe, draw lots for the 76 spaces under the vigas each morning. Those lucky enough to procure the desirable spots display their work – bracelets, pendants, fetishes (small statues) and thick engraved silver wedding bands – on colorful woven blankets. The classic turquoise and silver jewelry is the most popular, but you'll find many other regional stones in a rainbow of colors. The artists are generally happy to tell you the story behind each piece in his or her open-air gallery – and most are one-of-a-kinds. Not only are the prices better here than in a store but the money goes directly back to the source: the artist. It's best not to barter, unless it's suggested, as the artists may find this insulting.
Seret & Sons HANDICRAFTS
( www.seretandsons.com; 224 Galisteo St) Feel like you've stepped into an Asian or Arabian bazaar at this giant art-and-sculpture warehouse. It has a vast and fascinating collection of fine carpets, giant stone elephants, Tibetan furniture, pillars and solid teak doors. Of course getting all this home takes a bit of effort (or shipping money), but it's fun just to browse too.
Kowboyz CLOTHING
(www.kowboyz.com; 345 W Manhattan Ave) This secondhand shop has everything you need to cowboy up. Shirts are a great deal at $10 each; the amazing selection of boots, however, demands top dollar. Movie costumers looking for authentic Western wear often come in here.
Nambé Foundry Outlet HOMEWARES
(www.nambe.com; 104 W San Francisco St) A unique metal alloy that contains no silver, lead or pewter (but looks like silver) was discovered in 1951 to the north of Santa Fe, near Nambé. Fashioned into gleaming and elegant pieces, Nambéware designs are individually sand-cast and have become an essential element of Santa Fe style. Another, larger outlet (924 Paseo de Peralta) is near the start of Canyon Rd.
Nathalie CLOTHING
(www.nathaliesantafe.com; 503 Canyon Rd; 10am-6pm Mon-Sat) Come here for exquisite cowboy and cowgirl gear, including gemstone-studded gun holsters, handmade leather, denim couture and lingerie for that saloon girl with a heart of gold. The Spanish Colonial antiques are stunning.
Tesuque Flea Market MARKET
(www.pueblooftesuquefleamarket.com; US Hwy 84/285; 8am-4pm Fri-Sun Mar-Nov) An outdoor market a few minutes' drive north of Santa Fe at Tesuque Pueblo, it has everything from high-quality rugs, turquoise rings and clothing to the best used (read: broken-in) cowboy boots in the state. Nowadays, most booths are like small shops; there aren't many individuals left who come to sell funky junk.
Jackalope HANDICRAFTS
(www.jackalope.com; 2820 Cerrillos Rd; 10am-6pm) Essential pieces of Southwest decor can be yours for a song. Start with a cow skull like the ones Georgia O'Keeffe made famous, snap up a kiva ladder, add some colorful pottery and Navajo pot holdersand you'll be set. Don't leave without watching live prairie dogs frolic in their 'village.'
Travel Bug MAPS
(www.mapsofnewmexico.com; 839 Paseo de Peralta; 7:30am-5:30pm Mon-Sat, 11am-4pm Sun; ) This shop has one of the most complete selections of travel books and maps you'll find anywhere; you can even have topo maps printed on demand on waterproof paper. Local travelers, including some authors and photographers, give slide shows about their adventures Saturdays at 5pm. There's also a coffee bar, wi-fi, and computer terminals.
Garcia Street Books BOOKS
(www.garciastreetbooks.com; 376 Garcia St; 9:30am-6pm) Scavengers are rewarded with excellent bargains as well as the town's best selection of art books, and such rarities as the wood engraving prints of Willard Clark.
#### Information
EMERGENCY Police ( 505-955-5000; 2515 Camino Entrada)
INTERNET ACCESS Travel Bug ( 505-992-0418; 839 Paseo de Peralta; ) Free wi-fi and internet from on-site terminals.
MEDICAL SERVICES St Vincent's Hospital ( 505-983-3361; 455 St Michael's Dr) Has 24-hour emergency care.
Walgreens ( 505-982-4643; 1096 S St Francis Dr) A 24-hour pharmacy.
MONEY It's a tourist town, and all-too-convenient ATMs are everywhere. Wells Fargo ( 505-984-0424; 241 Washington Ave) changes foreign currency.
POST Post office (120 S Federal Pl)
TOURIST INFORMATION New Mexico Tourism Bureau ( 505-827-7440; www.newmexico.org; 491 Old Santa Fe Trail; 8am-5pm; ) Housed in the historic 1878 Lamy Building (site of the state's first private college), this friendly place is very helpful.
Public Lands Information Center ( 505-438-7542; www.publiclands.org; 1474 Rodeo Rd; 8:30am-4:30pm Mon-Fri) This place is very helpful, with maps and information on public lands throughout New Mexico.
Visitor Center ( 505-955-6200, 800-777-2489; www.santafe.org; 201 W Marcy St; 8am-5pm Mon-Fri) Conveniently located at the Sweeny Convention Center.
WEBSITES Lonely Planet (www.lonelyplanet.com/usa/santa-fe) Planning advice, author recommendations, traveler reviews and insider tips.
#### Getting There & Away
American Eagle ( 800-433-7300; www.aa.com) flies in and out of Santa Fe Municipal Airport ( 505-955-2900; www.santafenm.gov; 121 Aviation Dr), with three daily flights to/from Dallas (DFW) and one daily flight to/from Los Angeles (LAX).
If you're flying into Albuquerque, Sandia Shuttle Express ( 505-242-0302; www.sandiashuttle.com) runs between Santa Fe and the Albuquerque Sunport ($27); make advance reservations. North Central Regional Transit (www.ncrtd.org) provides free shuttle bus service from downtown Santa Fe to Española, where you can transfer to shuttles to Taos, Los Alamos, Ojo Caliente and other northern destinations. Downtown pick-up/drop-off is by the Santa Fe Trails bus stop on Sheridan St, a block northwest of the Plaza. There's also an express shuttle (www.taosexpress.com; one-way $10; Fri-Sun) to Taos on weekends from the corner of Guadalupe & Montezuma Sts, by the Railyard. Santa Fe Trails ( 505-955-2001; www.santafenm.gov; one-way adult/senior & child $1/50¢, day pass $2/1) provides local bus service.
The Rail Runner (www.nmrailrunner.com) commuter train has multiple daily departures for Albuquerque – with connections to the airport and the zoo. The trip takes about 1½ hours. Board at the Railyard or the South Capital Station. Amtrak ( 800-872-7245; www.amtrak.com) services Lamy station, from where buses continue 17 miles to Santa Fe.
If you need a taxi, call Capital City Cab ( 505-438-0000).
Despite these options, most visitors will want to have their own car.
## AROUND SANTA FE
Don't get too comfortable in Santa Fe, because there's plenty to explore nearby. Whichever direction you head, you'll be traveling through some of New Mexico's finest scenery, from pine forests to rainbow-colored canyons, from mesa lands to mountain views. This area also offers the state's best hot-spring resort, streams made for fly-fishing, endless hiking trails, and museums celebrating everything from Pueblo crafts to the building of the atom bomb. Small towns reveal unexpected treasures – from beautiful old adobe churches to fabulous local restaurants to art studios where the artists and artisans create and sell their work.
### Pecos
When the Spanish arrived, they found a five-story pueblo with almost 700 rooms that was an important center for trade between the Pueblo Indians of the Rio Grande and the Plains Indians to the east. The Spaniards completed a church in 1625, but it was destroyed in the Pueblo Revolt of the 1680s. The remains of the rebuilt mission, completed in 1717, are the major attraction. The Pueblo itself declined, and in 1838 the 17 remaining inhabitants moved to Jemez Pueblo (see Click here).
At the Pecos National Historical Park Visitor Center ( 505-757-6414; www.nps.gov/peco; adult/child $3/free; 8am-5pm), a museum and short film explain more about the area's history. From Santa Fe, take I-25 north for about 25 miles and follow signs.
### Tesuque Pueblo
Nine miles north of Santa Fe along Hwy 285/84 is Tesuque Pueblo, whose members played a major role in the Pueblo Revolt of 1680. Today, the reservation encompasses more than 17,000 acres of spectacular landscape, including sections of the Santa Fe National Forest. If driving through on the highway, look for the aptly named Camel Rock on the west side of the road, more or less opposite Camel Rock Casino (www.camelrockcasino.com; 8am-2am Mon-Thu, 24 hrsFri-Sun). San Diego Feast Day (November 12) features dancing; the Deer and Buffalo dances in December are known for their costumes and attention to ritual detail. The flea market held here is well worth checking out (see Click here).
### Pojoaque Pueblo
Although this Pueblo's history predates the Spaniards, a smallpox epidemic in the late 19th century killed many inhabitants and forced the survivors to evacuate. No old buildings remain. The few survivors intermarried with other Pueblo people and Hispanics, and their descendants now number about 300 (most people who live onthe Pueblo's land are not Native American). In 1932, a handful of people returned to the Pueblo and they have since worked to rebuild their people's traditions, crafts and culture.
The Poeh Cultural Center & Museum (www.poehcenter.com; 10am-4pm Mon-Sat), on the east side of Hwy 84/285, features exhibits on the history and culture of the Tewa-speaking people. Next door, check out the large selection of top-quality crafts from the Tewa Pueblos at the visitor center ( 505-455-9023; 96 Cities of Gold Rd). The Pueblo also runs the giant Buffalo Thunder Resort ( 505-455-5555; www.buffalothunderresort.com; r from $190; ), with luxurious rooms and suites, four 9-hole golf courses, a spa and casino.
The Pueblo public buildings are 16 miles north of Santa Fe on the east side of Hwy 84/285, just south of Hwy 502. The annual Virgin de Guadalupe Feast Day on December 12 is celebrated with ceremonial dancing.
### San Ildefonso Pueblo
Eight miles west of Pojoaque along Hwy 502, this ancient Pueblo ( 505-455-3549; per vehicle $4, camera/video/sketching permits $10/20/25; 8am-5pm) was the home of Maria Martinez, who in 1919, along with her husband, Julian, revived a distinctive traditional black-on-black pottery style. Her work, now valued at tens of thousands of dollars, has become world famous and is considered by collectors to be some of the best pottery ever produced.
Several exceptional potters (including Maria's direct descendants) work in the Pueblo, and many different styles are produced, but black-on-black remains the hallmark of San Ildefonso. Several gift shops and studios, including the Maria Poveka Martinez Museum (admission free; 8am-4pm Mon-Fri), sell the Pueblo's pottery. The Pueblo Museum, with exhibits on the Pueblo's history and culture and a small store, is next to the visitor center.
Visitors are welcome to Feast Day (January 23) and corn dances, which are held throughout the summer.
### STUDIO TOURS
In case you need more reasons to explore the region around Santa Fe, check out any of the many studio tours held throughout the year. Artists along the various routes open up their homes and personal studios to the public and show their work; often the houses themselves are as interesting as the artwork. Most tours feature locally cooked foods to sample, too. For a complete statewide list, visit www.newmexico.org. Among the best:
Dixon Studio Tour (www.dixonarts.org) New Mexico's original studio tour is still going strong; it's held the first weekend in November in scenic Dixon (Click here), one hour north of Santa Fe.
Galisteo Studio Tour (www.galisteostudiotour.org) Held in the historic abode village of Galisteo, 25 minutes south of Santa Fe, in mid-October.
High Road Art Tour (www.highroadnewmexico.com) From Chimayo to Truchas to Peñasco plus villages between and beyond, the High Road to Taos (Click here) opens its doors the last two weekends in September.
Abiquiú Studio Tour (www.abiquiustudiotour.org) In Georgia O'Keeffe's former home town along the lovely Chama River, the Abiquiú (Click here) tour runs on Columbus Day weekend. It's 50 minutes from Santa Fe.
Eldorado Studio Tour (www.eldoradostudiotour.org) Over 100 artists show in this Santa Fe–style suburb, just 10 minutes from town, in mid-May.
For an art-themed excursion further afield, head south to the Lincoln County Art Loop (www.artloop.org) studio tour, held the first weekend after July 4, which links towns throughout the beautiful Lincoln area (Click here).
### Santa Clara Pueblo
The Pueblo entrance is 1.3 miles southwest of Española on Hwy 30. Several galleries and private homes sell intricately carved black pottery, but stop first at Singing Water Gallery ( 505-753-9663; www.singingwater.com; Hwy 30; 11:30am-5pm), right outside the main Pueblo. In addition to representing 213 of some 450 Santa Clara potters, owners Joe and Nora Baca also offer tours of the Pueblo on weekends ($12), pottery demonstrations ($30) and classes, and can arrange feast meals ($15) with 48 hours' notice.
On the reservation at the entrance to Santa Clara Canyon, 5.7 miles west of Hwy 30 and southwest of Española, are the Puye Cliff Dwellings ( 888-320-5008; www.puyecliffs.com; tours adult/child $20/18; hourly 9am-5pm May-Sep, 10am-2pm Oct-Apr) where you can visit ancestral Puebloan cliffside and mesa-top ruins abandoned sometime around 1500.
Santa Clara Feast Day (August 12) and St Anthony's Feast Day (June 13) feature the Harvest and Blue Corn Dances. Both are open to the public; the governor's office (Hwy 30; 8am-4:30pm Mon-Fri) issues photo and video permits ($5).
### Los Alamos
The top-secret Manhattan Project sprang to life in Los Alamos in 1943, turning a sleepy mesa-top village into a busy laboratory of secluded brainiacs. Here, in the 'town that didn't exist,' the first atomic bomb was developed in almost total secrecy. Humanitycan trace some of its greatest achievements and greatest fears directly to this little town. Los Alamos National Laboratory still develops weapons, but it's also at the cutting edge of other scientific discoveries, including mapping the human genome and making mind-boggling supercomputing advances.
The Lab dominates everything here and gives Los Alamos County the highest concentration of PhDs per capita in the US, along with the highest per-capita income in the state. You only have to be here for five minutes before realizing it's a place unto itself that feels very little like anywhere else around. It's in a beautiful spot atop a series of mesas and hugged by national forest,much of which unfortunately burned in the 48,000-acre Cerro Grande fire of 2000, leaving the hills behind town eerily barren.
More of the surrounding forest was ablaze in 2011, as the fire around Las Conchas scorched over 150,000 acres – the largest ever recorded in New Mexico. Fortunately, the fire narrowly missed the Lab.
#### Sights & Activities
Entering from the east on Hwy 502, Central Ave is the main axis and is where you'll find most places of interest. To connect to Hwy 4, heading to Bandelier National Monument or into the Jemez Mountains, head west on Trinity, Central or Canyon, then take Hwy 501 south for 5 miles.
Most of the town's sights are related to the atomic bomb project. Outside of town, there's some good rock climbing (with plentyof top-roping), including the Overlook and the Playground in the basalt cliffs east of Los Alamos.
Bradbury Science Museum MUSEUM
(www.lanl.gov/museum; 1350 Central Ave; admission free; 10am-5pm Tue-Sat, from 1pm Sun & Mon) You can't actually visit the Los Alamos National Laboratory, where the first atomic bomb was conceived, but the Bradbury Science Museum has compelling displays on bomb development and atomic history, along with medical and computer sciences. There's even a room where you can twist your brain into a pretzel with hands-on problem-solving games. Pop into the Otowi Station Museum Shop and Bookstore next door for a great selection of science-y books, gifts and toys.
Los Alamos Historical Museum MUSEUM
(www.losalamoshistory.org; 1050 Bathtub Row; 10am-4pm Mon-Fri, from 11am Sat, from 1pm Sun) Pop-culture artifacts from the atomic age are on display at the interesting Los Alamos Historical Museum. It also features exhibits on the social history of life 'on the hill' during the secret project. Pick up one of the self-guided downtown walking-tour pamphlets.
Pajarito Mountain Ski Area SKIING, MOUNTAIN BIKING
(www.skipajarito.com; lift tickets adult/child $57/34; Fri-Sun Dec-Mar) Ever wanted to ski down the rim of a volcano? Look no further: this ski area, 7 miles west of downtown, has 40 runs –from easy groomers to challenging mogul steeps – plus a terrain park for snowboarders. The area is open daily around Christmas and New Year's. In summer, lifts run on weekends ($25) for some serious mountain-biking action, including courses with jump ramps and log rides.
### SCENIC DRIVE: JEMEZ MOUNTAIN TRAIL
To the west of Los Alamos, Hwy 4 twists and curves through the heart of the Jemez Mountains, on a sublime scenic drive that's made even better by all the places to stop.
At the time of writing, Las Conchas Trail (between mile markers 36 & 37) was closed due to fire damage. It's a lovely place to hike and there's some great rock climbing along the path, so we hope it reopens soon (call 575-834-7235 for current conditions).
A few miles further along, you'll enter the Valles Caldera National Preserve ( 866-382-5537; www.vallescaldera.gov; permits adult/child $10/5), which is basically what the crater of a dormant supervolcano looks like 1,250,000 years after it first blows. (The explosion was so massive that chunks were thrown as far away as Kansas.) The 89,000-acre bowl – home to New Mexico's largest elk herd – is simply breathtaking, with vast meadows from which hills rise like pine-covered islands. Though there are two trails on the edge of the preserve with free, open hiking, you should make reservations for the limited number of permits given out to hike within the caldera on any given day. Access to those trailheads is only possible by shuttle bus from the visitor center. If you want to gape at the lay of the land but aren't up for high-altitude exertion, take a van tour. It's also possible to bike, ride horseback, fish, hunt, and cross-country ski here. There's an information center in Jemez Springs.
Continuing along Hwy 4, there are a number of natural hot springs to hike into. One of the most accessible is Spence Hot Springs, between Miles 24 and 25. The temperature's about perfect, and the inevitable weird naked guy adds authenticity to the experience.
The pretty village of Jemez Springs (www.jemezsprings.org) was built around a cluster of springs, as was the ruined pueblo at the small Jemez State Monument (www.nmmonuments.org; NM 4; adult/child $3/free; 8:30am-5pm Wed-Sun). You can experience the waters yourself at rustic Jemez Springs Bath House ( 575-829-3303; 62 Jemez Springs Plaza; per hr $17; 10am-7pm), which has private tubs, massages and more. In winter, bliss out in the hot-spring pools – bathing suits required; sorry, weird naked guy – at Bodhi Manda Zen Center ( 575-829-3854; www.bmzc.org; $10 suggested donation; 9am-5pm Tue-Sat). At other times they run intensive Zen meditation programs – see their website for details.
Eat at Los Ojos Restaurant & Saloon (www.losojossaloon.com; Hwy 4; mains $5-11; 11am-9:30pm Mon-Fri, from 8am Sat & Sun, bar open late; ), which has a surprising variety of vegetarian fare considering the number of animal heads on the walls. And if you're not traveling with kids or pets, stay at Cañon del Rio B&B ( 575-829-4377; www.canondelrio.com; $140-150; ), which has gorgeous canyon views, a pool, hot tub and day spa, killer breakfasts and terrific hosts.
Ten miles south of Jemez Springs, the Walatowa Visitor Center (7413 Hwy 4; 8am-5pm) at Jemez Pueblo houses the small, sort-of-interesting Museum of Pueblo Culture (admission free). If you're into wine, take a little detour to Ponderosa Valley Winery (www.ponderosawinery.com; 3171 Hwy 290; 10am-5pm Tue-Sat, from noon Sun) for a bottle of late-harvest riesling or pinot noir, before emerging onto Hwy 550, between Bernalillo and Cuba. From there, continue on to Albuquerque, back to Santa Fe, or up towards Chaco Canyon and the Four Corners.
Art Center at Fuller Lodge MUSEUM
(www.fullerlodgeartcenter.org; 2132 Central Ave; 10am-4pm Mon-Sat) The Art Center mounts mixed-media shows of local and nationalartists. Fuller Lodge, built in 1928 to serve as the dining hall for the local boys' school, was purchased by the US government for the Manhattan Project. Inside are two small but good museums.
#### Sleeping
Adobe Pines B&B B&B $
( 505-661-8828; www.losalamoslodging.com; 1601Loma Linda Dr; s/d $87/94; ) Adobe Pines offers five distinct rooms in an adobe building. Each is a little different. Try the 2nd-floor East Room, which comes with a king-size bed, private sitting area and a balcony to enjoy the city lights by evening or Jemez Mountains by day. The Sun Room has plate-glass doors, a wooden four-poster bed and white linens, giving it airy appeal.
Best Western Hilltop House Hotel HOTEL $$
( 505-662-1118; www.bestwesternlasalamos.com;400 Trinity Dr; r incl breakfast from $86; ) This is the nicest hotel in Los Alamos. Guests are greeted with a welcome drink in the hotel lounge, and rooms are spacious and recently upgraded, with lots of amenities. There is a workout room and spa on-site, plus an indoor heated pool.
#### Eating
Hill Diner DINER $$
(1315 Trinity Dr; mains $8-15; 11am-8pm) Those craving some home-cooked American classics, like chicken-fried steak and white country gravy, won't be disappointed by the array of American diner fare served daily at this popular place. There are good salads and other veggie options, too.
Blue Window Bistro AMERICAN $$
(labluewindowbistro.com; 813 Central Ave; lunch mains $10-12, dinner mains $10-27; 11am-2:30pm & 5-8:30pm Mon-Sat; 9:30am-2:30pm Sun, closed Sat lunch) On the north side of the shoppingcenter, this brightly colored cafe offers lunchtime gyros and poached salmon, and dinners like Southwestern chicken and double-cut pork chops.
Central Avenue Grill FUSION $$
(1789 Central Ave; mains $10-26; 11am-8:30pm Mon-Sat) For a more upscale and contemporary setting, try this spot, with high ceilings and big windows that open onto downtown Los Alamos. It serves satisfyingif rather pricey dishes like shrimp fajitas, green-curry chicken and Asian-spiced salmon.
#### Information
Chamber of Commerce ( 505-662-8105, 800-444-0707; www.visit.losalamos.com; 109 Central Park Sq; 9am-5pm Mon-Fri, 9am-4pm Sat, 10am-3pm Sun)
Hospital ( 505-662-4201; 3917 West Rd; 24hr)
Post office (1808 Central Ave)
### Bandelier National Monument
The sublime, peach-colored cliffs of Frijoles Canyon are pocked with caves and alcoves that were home to Ancestral Puebloans untilthe mid-1500s. Today, they're the main attraction at Bandelier National Monument (www.nps.gov/band; per vehicle $12; 8am-6pm summer, 9am-5:30pm spring & fall, 9am-4:30pm winter). This is one of the most popular day trips from Santa Fe, rewarding whether you're interested in ancient Southwestern cultures or just want to walk among pines and watch the light glowing off the canyon walls. The Ceremonial Cave, 140ft above the ground and reached by climbing four ladders, is a highlight of a visit. The more adventurous can strike out on rugged trails that traverse 50 sq miles of canyon and mesa wilderness dotted with archaeologicalsites; backpackers should pick up a free backcountry permit from the visitor center.
The park, 12 miles from Los Alamos, has a good bookstore that sells trail maps and guidebooks.
Juniper Campground (campsites $12), set among the pines near the monument entrance, has about 100 campsites, drinking water, toilets, picnic tables and fire grates, but no showers or hookups.
13 miles north of the visitor center on Hwy 4 (about 20 minutes closer to Santa Fe by road), Bandelier's satellite site, Tsankawi (admission free) is less impressive than Frijoles Canyon but still nice, with a 1.5-mile loop trail that cuts across a mesa top and winds down a cliffside past a few small caves. Views of the Sangres are full on.
### Española
Founded by conquistador Don Juan de Oñate in 1598, Española (www.espanolaonline.com) is at a major fork in the road between Santa Fe and points north, including Taos, Ojo Caliente, and Abiquiú. There's not much to appeal to visitors here, unless you're in search of a Super Wal-Mart or the best chicken-guacamole tacos on the planet.
It's still known as the 'Low Rider Capital of the World' and you're sure to see some seriously pimped-up rides cruising through Española on summer weekend nights, but there are far fewer on the streets these days than when it first claimed its title. For some of the craziest stories you'll ever read, pick up a copy of the Rio Grande Sun, the local paper; be sure to check out the police blotter.
Just north of Española is Ohkay Owingeh Pueblo, which was visited in 1598 by Juan de Oñate, who named it San Gabriel and made it the short-lived first capital of New Mexico. The Oke Oweenge Crafts Cooperative ( 505-852-2372; Hwy 74; 9am-4:30pm Mon-Sat) has a good selection of traditional red pottery, seed jewelry, weavings and drums. Public events include the Basket Dance (January), Deer Dance (February), Corn Dance (June 13), San Juan Feast Day (June 23–24) and a seriesof Catholic and traditional dances and ceremonies from December 24 to 26.
#### Sleeping & Eating
There's no compelling reason to stay in Española, unless it happens to be convenient for you for some reason.
Santa Claran CASINO HOTEL $$
( 877-505-4949; www.santaclaran.com; 460 N Riverside Dr; r from $100; ) Run by SantaClara Pueblo, this is Española's nicest and most reliable hotel. The pueblo theme throughout adds some character. Even betterthan the casino is the 24-lane bowling center on the ground floor.
El Parasol NEW MEXICAN $
( www.elparasol.com; 603 Santa Cruz Rd; mains $2-5; 7am-9pm) As local as it gets. Line up outside of this tiny trailer that's the somehow more delicious offspring of the fancy-ishEl Paragua Restaurant next door. The chicken-guacamole tacos are a handful of greasy goodness (order at least two) and the carne adovada (pork in red chile) is the real deal. Though it's begun opening other branches, this is the original and best, and the only one where you're supposed to hang out in the shaded parking lot to eat your order.
#### Getting There & Around
The town sits at the junction of US 84/285 (Santa Fe Hwy/S Riverside Dr), leading southeast to Santa Fe; NM 30 (Los Alamos Ave), running southwest to Santa Clara Pueblo, Los Alamos and Bandelier; US 84 (Oñate St), heading northwest to Abiquiú and Ghost Ranch; NM 76 (Santa Cruz Rd; High Road to Taos), the back road to Taos, going through Chimayo; and N Riverside Dr/NM 68, heading north out of town as the Low Road to Taos.
### Abiquiú
The tiny community of Abiquiú (sounds like barbeque), on Hwy 84 about 45 minutes' drive northwest of Santa Fe, is famous because the renowned artist Georgia O'Keeffe lived and painted here. With the Rio Chama flowing through farmland, and spectacular rock formations, the ethereal landscape continues to attract artists, and many live and work here.
#### Sights & Activities
Georgia O'Keeffe Home HOUSE
( 505-946-1083; www.okeeffemuseum.org; tours $35-45; Tue, Thu & Fri mid-Mar–Nov, Sat Jun-Oct) Georgia O'Keeffe died in 1986, at age 98, and the Spanish Colonial adobe house she restored is open for limited visits. One-hour tours are often booked months in advance, so plan ahead.
Ghost Ranch OUTDOORS, MUSEUM
( 505-685-4333; www.ghostranch.org; US Hwy 84; ) Set amid the colorful canyonlands that were obviously inspirational for O'Keeffe, Ghost Ranch is now an education and retreat center run by the Presbyterian Church. Hiking trails – including the 4-mile round-trip trek into Box Canyon and the popular 3-mile round-trip to Chimney Rock – are open to the public, as is Piedra Lumbre Visitor Center ( 9am-5pm Tue-Sun, closed Dec–mid-Mar), with displays about the area's natural history. The Ruth Hall Museum of Paleontology ( 9am-5pm Mon-Sat, 1-5pm Sun) features exhibits on the trove of dinosaurs found right at Ghost Ranch. Horseback riding (adult/child from $40/20) is offered for riders of all levels, and for kids as young as four. Fun factoid: scenes from City Slickers were filmed here.
Christ in the Desert Monastery MONASTERY
(www.christdesert.org; 9:15am-5pm) Day visitors are welcome at this ecosustainable Benedictine monastery, in a secluded geological wonderland, for a one-of-a-kind spiritual-architectural experience. Take Forest Service Rd 151, a dirt road off of Hwy 84, just south of Echo Amphitheater and 5 miles north of Ghost Ranch, and drive 13 beautiful miles. Do not attempt this road if it's muddy.
### GEORGIA O'KEEFFE
Although classically trained as a painter at art institutes in Chicago and New York, Georgia O'Keeffe was always uncomfortable with traditional European style. For four years after finishing school, she did not paint, and instead taught drawing and did graphic design.
However, after studying with Arthur Wesley Dow, who shared her distaste for the provincial, O'Keeffe began developing her own style. She drew abstract shapes with charcoal, representing dreams and visions, and eventually returned to oils and watercolors. These first works caught the eye of her future husband and patron, photographer Alfred Stieglitz, in 1916.
In 1929 she visited Taos' Mabel Dodge Luhan Ranch and returned to paint 'The Lawrence Tree,' which still presides over the DH Lawrence Ranch (Click here). O'Keeffe tackled the subject of the San Francisco de Asis Church in Ranchos de Taos, painted by so many artists before her, in a way that had never been considered: only a fragment of the mission wall, contrasted against the blue of the sky.
It was no wonder O'Keeffe loved New Mexico's expansive skies, so similar to her paintings' negative spaces. As she spent more time here, landscapes and fields of blue permeated her paintings. During desert treks, she collected the smooth white bones of animals, subjects she placed against that sky in some of her most identifiable New Mexico works.
Telltale scrub marks and bristle impressions divulge how O'Keeffe blended and mixed her vibrant colors on the canvas itself. This is in direct contrast to photographs of her work, which convey a false, airbrush-like smoothness. At the Georgia O'Keeffe Museum (Click here), you can experience her work firsthand.
Dar Al Islam Mosque MOSQUE
(www.daralislam.org) Muslims worship at this adobe mosque that welcomes visitors. From Hwy 84, take Hwy 554 (southeast of Abiquiú) towards El Rito, cross the Rio Chama, take your first left on to County Rd 155 and follow it for 3 miles. The mosque is up a dirt road on the right.
Surrounded by red rock and high-desert terrain, Abiquiú Lake & Dam (Hwy 84; dawn-dusk) is a beautiful swimming spot.
#### Sleeping & Eating
Christ in the Desert Monastery MONASTERY $
(www.christdesert.org; off US Rte 84; r incl board suggested donation $50-75) When you really want to get away from it all, head west from US Hwy 84 onto the rough dirt Forest Service Rd 151, then follow it along the meandering Rio Chama for 13 inspirational miles to this isolated Benedictine monastery. Rates for the simple rooms, plus outrageous trails and peace and quiet, include vegetarian meals served without conversation. Chores are requested (not required) and include minding the gift shop or tending the garden.
Ghost Ranch HOSTEL $
( 505-685-4333; www.ghostranch.org; US Hwy 84; tent/RV sites $19/22, dm incl board $50, r with shared/private bath incl breakfast from $50/80) A friendly place to stay in an unbeatable setting, with lots to do (see above).
Abiquiú Inn HOTEL $$
( 505-685-4378, 800-447-5621; www.abiquiuinn.com; US Hwy 84; RV sites $18, r $140-200, 4-personcasitas $189) An area institution, this sprawling collection of shaded faux-dobes is peaceful and lovely; some spacious rooms have kitchenettes. The on-site Cafe Abiquiú (breakfast mains under $10, lunch & dinner mains $10-20; 7am-9pm) is the best restaurant around. Specialties include chipotle honey-glazed salmon and fresh trout tacos.
Bode's General Store DELI $
(www.bodes.com; US Hwy 84; mains $5-12; 6:30am-7pm Mon-Sat, to 6pm Sun; ) The hub of Abiquiú, Bode's (pronounced Boh-dees) has been around since 1919. This is the place to buy everything from artsy postcards to fishing lures to saddle blankets. Grab a sandwich or tamale at the deli and hang out with the locals.
#### Getting There & Around
Abiquiú is on Hwy 84, about 50 minutes' drive northwest of Santa Fe. It is best reached by private vehicle.
### Ojo Caliente
At 140 years old, Ojo Caliente Mineral Springs Resort & Spa ( 505-583-2233, 800-222-9162; www.ojospa.com; 50 Los Baños Rd; r $139-169, cottages $179-209, ste $229-349; ) is one of the country's oldest health resorts –and Pueblo Indians were using the springs long before then! Fifty miles north of Santa Fe on Hwy 285, the newly renovated resort has 10 soaking pools with several combinations of minerals (shared/private pools from $18/40). Hit the sauna and steam room beforeindulging in one of the superpampering spa treatments (massages $89-149, wraps $12-90, facials from $59, luxury packages from $125), a yoga class in a yurt, or hiking along one of the trails. If you're staying at the resort, admission to the pools is free. In addition to pleasant, if nothing-special, historic hotel rooms, the resort has added 12 plush, boldly colored suites with kiva fireplaces and private soaking tubs, and 11 New Mexican–style cottages.
The on-site Artesian Restaurant (breakfast mains $5-10, lunch mains $9-12, dinner mains $11-28; 7:30am-10:30am, 11:30am-2:30pm & 5-9pm Sun-Thu, to 9:30pm Fri & Sat) prepares organic and local ingredients with aplomb.
Other accommodations within walking distance of the springs include the slightly cheaper Inn at Ojo ( 505-583-9131; www.ojocaliente.com; Los Baños Dr; s/d $85/115; ), which is run by a former Los Alamos physicist, his wife and their daughter. It's a personable spot where rooms are decorated with 19th-century wardrobes.
For eats, try the Mesa Vista Café (Hwy 285; dishes $4-7; 8am-9pm; ), serving New Mexican diner food with lots of veggie options and a recommended red chile cheeseburger.
Ojo Caliente is about 50 miles north of Santa Fe on Hwy 285. It's a pretty drive.
Twelve miles south of Ojo Caliente is one of New Mexico's top lodging and dining experiences, Rancho de San Juan ( 505-753-6818; www.ranchodesanjuan.com; 34020 Hwy 285; half-board r/casita from $450/700; ). Set among 225 strikingly scenic acres, this little gem features first-class rooms, a spa, great service and a spectacular setting for dining on New Mexican classics at two nightly settings. Even if you can't afford to stay, it's worth coming to eat (prix fixe menu $85). Considered the number-one restaurant in New Mexico by many, Rancho de San Juan is so good that locals drive from Santa Fe just to dine. The meals are specially prepared but are planned in advance, so call a week ahead with any special dietary requirements. At the time of research, they were in the process of selling their liquor license, so their impressive wine list may no longer exist by the time you read this (and dinner prices will have dropped).
### High Road To Taos
Go on, take the high road. One of two routes between Santa Fe and Taos, the famous High Road isn't necessarily any prettier (although beauty is relative here; both are gorgeous) than the faster Low Road, but it's got a special rural mountain feeling that is classicnorthern New Mexico. The road winds through river valleys, skirts sandstone cliffs and traverses high pine forests, all beneath the gaze of the 13,000-ft Truchas Peaks. Villages along this route are filled with old adobe houses with pitched tin roofs. Massive firewood piles rise next to rusting, disassembled pick-up trucks in yards surrounded by grassy horse pastures. Many of these towns are home to art studios and traditional handicraft workshops.
Though many people drive the High Road north from Santa Fe to Taos, taking the Low Road back, you actually get more impressive vistas in both directions if you take the Low Road up and the High Road down. We've presented both High and Low routes from south to north. To follow the High Road from Santa Fe to Taos, take 84/285 to Pojoaque and turn right on Hwy 503, toward Nambé. From Hwy 503, take Hwy 76 to Hwy 75 to Hwy 518.
##### NAMBÉ PUEBLO
Perhaps because of the isolated location (or inspirational geology), Nambé Pueblo has long been a spiritual center for the Tewa-speaking tribes, a distinction that attracted the cruel attentions of Spanish priests intent on conversion by any means necessary. After the Pueblo Revolt and Reconquista wound down, Spanish settlers annexed much of their land.
Nambé's remaining lands have a couple of big attractions off of Hwy 503; the loveliest are two 20-minute hikes to Nambé Falls (per car per day $10). The steep upper hike has a photogenic overlook of the falls, while the easier, lower hike along the river takes in ancient petroglyphs. The most popular attraction, however, is Lake Nambé (Hwy 101; per car per day $10; camping $25; 7am-7pm Apr-Oct), created in 1974 when the US dammed the Rio Nambé, flooding historic ruins but creating a reservoir that attracts boaters (no motors allowed) and trout lovers.
Public events include San Francisco de Asis Feast Day (October 4) and the Catholic Mass and Buffalo Dance (December 24).
##### CHIMAYO
Twenty-eight miles north of Santa Fe is the so-called 'Lourdes of America,' El Santuario de Chimayo (www.elsantuariodechimayo.us; 9am-5pm Oct-Apr, to 6pm May-Sep), one of the most important cultural sites in New Mexico. In 1816, this two-towered adobe chapel was built over a spot of earth said to have miraculous healing properties. Even today, the faithful come to rub the tierra bendita – holy dirt – from a small pit inside the church on whatever hurts; some mix it with water and drink it. The walls of the dirt room are covered with crutches, left behind by those healed by the dirt. During Holy Week, about 30,000 pilgrims walk to Chimayo from Santa Fe, Albuquerque and beyond in the largest Catholic pilgrimage in the US. The artwork in the _santuario_ is worth a trip on its own.
This village is also famous for the arts and crafts created here. Chimayo has a centuries-old tradition of producing some of the finest weavings in the area and has a handful of family-run galleries. Irvin Trujillo, a seventh-generation weaver, whose carpets are in collections at the Smithsonian in WashingtonDC and the Museum of Fine Arts in SantaFe, works out of and runs Centinela Traditional Arts (www.chimayoweavers.com; NM 76; 9am-6pm Mon-Sat, 10am-5pm Sun). Naturally dyed blankets, vests and pillows are sold, and you can watch the artists weaving on handlooms in the back. Virtually across the road, the Oviedo family has been carving native woods since 1739, and today the Oviedo Gallery (www.oviedoart.com; Hwy 76; 10am-6pm) is housed in the 270-year-old family farm.
Stay for dinner at Rancho de Chimayo ( 505-984-2100; www.ranchodechimayo.com; County Rd 98; mains $7-15; 8:30am-10:30am Sat & Sun, 11:30am-9pm daily, closed Mon Nov-Apr), serving classic New Mexican cuisine, courtesy of the Jaramillo family's famed recipes.
Also highly recommended is the unpretentious Casa Escondida ( 505-351-4805; www.casaescondida.com; 64 County Rd 100; r $105-165; ), with eight beautiful rooms, a hot tub and big old cat named Griffin.
##### TRUCHAS
Rural New Mexico at its most sincere is showcased in Truchas, originally settled bythe Spaniards in the 18th century. Robert Redford's _The Milagro Beanfield War_ was filmed here (but don't bother with the movie – the book it's based on, by John Nichols, is waaaay better). Narrow roads, many unpaved, wend between century-old adobes. Fields of grass and alfalfa spread toward the sheer walls and plunging ridges that define the eastern flank of the Truchas Peaks. Between the run-down homes are some wonderful art galleries, which double as workshops for local weavers, painters, sculptors and other artists. The Cordovas Handweaving Workshop (www.la-tierra.com/busyles; Main Truchas Rd; 8am-5pm), is run by a friendly fourth-generation weaver namedHarry. You can watch him weaving in betweenbrowsing his beautiful blankets, placemats and rugs. The High Road Marketplace (www.highroadnewmexico.com; 1642 Hwy 76; 10am-5pm, to 4pm in winter) is a cooperative art gallery with a huge variety of work by area artists.
Rancho Arriba B&B ( 505-689-2374; www.ranchoarriba.com; Main Truchas Rd; s/d with shared bath $70/90, d $120; ), in a rusticadobe farmhouse on the edge of Pecos Wilderness, has horses and wood stoves, and will cook you dinner with advance notice. It was temporarily closed at the time of research, but there's a good chance it'll be open again by the time you read this.
If you drive through town, rather than taking the left turn for Taos, you'll find yourself heading up a valley at the base of the mountains, where there are trailheads into the Pecos Wilderness.
Six miles north of Truchas, turn left on County Rd 73 and follow the signs to Ojo Sarco Pottery (web.mac.com/ojosarco1; County Rd 73; 10am-5pm), where you can check out the fine clay creations of master potters Kathy Riggs and Jake Willson. The work of other local artists, from glass-crafters to bell-makers, is also shown here.
##### LAS TRAMPAS
Completed in 1780 and constantly defended against Apache raids, the Church of San José de Gracia (Hwy 76; 9am-5pm Fri & Sat) is considered one of the finest surviving 18th-century churches in the USA and is a National Historic Landmark. Original paintings and carvings remain in excellent condition, and self-flagellation bloodstains from Los Hermanos Penitentes (a 19th-century religious order with a strong following in the northern mountains of New Mexico) are still visible.
##### PICURIS PUEBLO
Located just off the High Road, this was once among the largest and most powerful Pueblos in New Mexico. The Picuris built adobe cities at least seven stories tall and boasted a population approaching 3000. After the Pueblo Revolt and Reconquista, when many retreated to Kansas rather than face De Vargas' wrath, the returning tribe numbered only 500. Between raids by the Spanish and Comanches, that number continued to dwindle.
The governor's office ( 505-587-2519; photo/video permits $5/10; 8am-5pm Mon-Fri) can, with advance notice, help arrange guidedPueblo tours that include their small buffalo herd, organic gardens, ruins from the old Pueblo site and the exquisite 1770 San Lorenzo de Picuris Church. The unique tower kiva is off-limits to visitors but makes an impression even from the outside. The tribe's Picuris Pueblo Museum ( 505-587-1099) displays tribal artifacts and local art. The best time to visit the Pueblo is duringthe popular San Lorenzo Feast Days (August 9 and 10), which sees food and craft booths, dances, races and pole climbs.
From Picuris Pueblo, follow Hwy 75 east and go north on Hwy 518 to connect with Hwy 68, the main road to Taos.
##### PEÑASCO
This scenic village along the Rio Santa Barbara and beneath Jicarita Peak (12,835ft) is the gateway to the less crowded northern side of the Pecos Wilderness. You'll find trailheads at nearby Santa Barbara Campground, which has 22 RV/tent sites (per day $15). From there, it's possible to access the Skyline Trail, a multiday backpacking loop that traverses above-treeline ridges and can easily include ascents of Truchas Peak (13,102ft), New Mexico's second-highest, and Jicarita; both are nontechnical walk-ups.
In town, the historic Peñasco Theatre (15046 Hwy 75) is part of Wise Fool (Click here), a collective of performance artists who blend clowning, trapeze, puppetry, music and other forms of storytelling, sometimes to explore complex social issues, other times just to have fun. The Theatre offers myriadprograms, concerts, movies and classes throughout the year, including weeklong youth circus camps in summer. Attached to the Theatre is Sugar Nymphs Bistro ( 575-587-0311; www.sugarnymphs.com; mains $10-15; 11am-2:30pm Wed-Sun, 5:30-7:30pm Thu-Sat), serving gourmet comfort food made mostly from local produce, including a great goat's cheese salad and desserts that often sell out.
Ten miles east of Peñasco, on Hwy 518 towards Mora, is the small, family-oriented Sipapu Ski Resort ( 800-587-2240; www.sipapunm.com; lift tickets adult/child/under 7 $39/29/free; ). The snow and terrain can't compare to Taos Ski Valley, but lift tickets are cheap and there are lots of special deals, making this a reasonable place to bring the kids. In summer, Sipapu has one of the top-ranked disc (Frisbee) golf courses in the country.
### Low Road To Taos
First the bad news about the Low Road: it passes through Española (Click here). But then you drive through the Rio Grande Gorge, between towering walls of granite, sculpted volcanic tuff and black basalt. The river tumbles by on your left, carrying tourist-packed white-water rafts downstream. Along the river are numerous pull-off and picnic spots –and Sugar's BBQ (1799 Hwy 68; mains $5-12; 11am-6pm Thu-Sun), a tin-clad trailer once named one of the top 10 roadside joints in America by _Gourmet_ Magazine. Brisket burritos = genius.
Ultimately, you'll emerge from the gorge onto the Taos Plateau. The first vista is truly awesome, with the Sangre de Cristos and the deep river canyon coming suddenly and simultaneously into view. To take the Low Road from Santa Fe, take Hwy 84/285 to Hwy 68. The following places are on the way.
##### DIXON
While driving through the Rio Grande Gorge, take a slight detour east on Hwy 75to this small farming and artist community, in the gorgeous Rio Embudo Valley, 24 miles south of Taos. Turn your radio dial to 96.5 FM and tune in to Dixon's own local station, KLDK. And don't miss the original New Mexico artist studio tour (Click here) if you're in the area on the first weekend of November. While Dixon is famous for its apple orchards, plenty of other crops are grown here too; try to catch the local farmers market on Wednesday afternoons in summer and fall, with food fresh from the fields.
At the junction of Hwy 68 and Hwy 75 you'll see Vivac Winery (www.vivacwinery.com; 10am-6pm Mon-Sat, from noon Sun), run by the genial Padberg brothers, both born and raised in Dixon. Their tasting room features a variety of vintages, including a highly rated Syrah – plus chocolates hand made by Chris's wife, Liliana. Don't drink too much here, though, because 2.5 miles down Hwy 75 you can sample more selections at La Chiripada Winery (www.lachiripada.com; NM 75; 11am-6pm Mon-Sat, from noon Sun), a frequently award-winning vintner that uses only New Mexican–grown grapes.
Ask at the local food co-op, and some kind soul might point you to the waterfalls, up a nearby dirt road.
If you're hungry, you're lucky, because Zuly's Cafe (www.zulyscafe.org; 234 Hwy 75; mains $5-11; 7:30am-3pm Tue-Thu, 7:30am-8pm Fri, 9am-8pm Sat) is here; it's a superfriendly place run by Dixon native Chalako Chilton, who serves some of the best green chile you'll find anywhere. You can even get an espresso! Reduced hours in winter.
For such a small village, there are plenty of great guesthouses, including the charming adobe La Casita ( 505-579-4297; www.vrbo.com/79296; casita $90; ), Rock Pool Gardens ( 505-579-4602; www.vrbo.com/107806; ste $90; ), with an indoor heated pool, and Tower Guest House ( 505-579-4288; www.vrbo.com/118083; cottage $95; ) on a working garlic farm along the Rio Embudo. Rooms must be booked well in advance during the studio tour.
##### RINCONADA AND PILAR
Grab a pint or a growler at the new Blue Heron Brewing Co. (www.blueheronbrews.com; 2214 Hwy 68; 11am-6pm Mon-Wed, 10am-8pm Thu-Sat, noon-6pm Sun) in the small community of Rinconada, just north of Dixon on Hwy 68, where local brewmasters pour handcrafted ales in an attractive art space that was once a veterinarian's office. A few more seconds up the road, Rift Gallery (www.saxstonecarving.com; Hwy 68; 10am-5pm Wed-Sun) showcases the work of sculptor Mark Saxe and Betsy Williams, a potter specializing in the Japanese Karatsu tradition. Each summer, the gallery hosts a highly regarded weeklong stone-carving workshop.
Seven miles further north, tiny Pilar is the base for summer white-water rafting on the Rio Grande Racecourse (see Click here). Though some outfits are run out of Santa Fe or Taos, others are based right here. Far Flung Adventures ( 800-359-2627; www.farflung.com; Pilar Yacht Club), runs full-day and half-day floats ($55 to $96) as well as more thrilling trips down the Taos Box. The Rio Grande Gorge Visitor Center (NM 68; 9am-4:30pm) has information on campsites and area hikes.
Take a detour on to Hwy 570 at Pilar and visit Stephen Kilborn's studio (www.stephenkilborn.com; 10am-5pm Mon-Sat, from 11am Sun), whose whimsically painted Southwestern-style pottery puts the 'fun' in functional; sometimes there are great deals on 'factory' seconds.
Keep going on Hwy 570, staying with the river, and you'll soon enter Orilla Verde Recreation Area (day-use $3, tent/RV sites $7/15). This popular stretch of the Rio Grande features flat water appreciated by fishers and inner-tubers who want a relaxing float downstream. For landlubbers, there are sheltered picnic tables and campsites along the river. A couple of trails climb from the river to the rim of the gorge; we like trail Old 570, a dirt road blocked by a landslide, with expansive vistas of the Taos Plateau and the Sangre de Cristos (tip: if you want to hike but others in your group don't, have them drop you off at the trailhead, then drive around and meet you at the top, where Old 570 connects to County Rd 110).
## TAOS
Taos is a place undeniably dominated by the power of its landscape: the 12,300-foot snowcapped peaks that rise behind town, a sage-speckled plateau that unrolls to the west before plunging 800 feet straight down into the Rio Grande Gorge. The sky can be a searing sapphire blue or an ominous parade of rumbling thunderheads so big they dwarf the mountains. And then there are the sunsets...
### TOP TEN TAOS
Taos Ski Valley (Click here) For champagne powder, tree glades and snowboarding!
El Monte Sagrado (Click here) For posh high-desert R & R.
Millicent Rogers Museum For a look at one of the best collections of Southwestern jewelry and art anywhere.
La Fonda de Taos (Click here) For a peek at DH Lawrence's 'Forbidden Art' and fabulous rooms.
Adobe Bar (Click here) For a potent margarita and live music.
Taos Pueblo (Click here) For Native American festivals and delicious fry bread.
Earthship Rentals (Click here) For sleeping off the grid.
Rafting the Taos Box (Click here) For sheer white-water thrills.
Rio Grande Gorge Bridge (Click here) For the view.
Taos Plaza For wandering.
Taos Pueblo, one of the oldest continuously inhabited communities in the United States and a marvel of adobe architecture, roots the town in a long history with a rich cultural legacy – including conquistadors, Catholicism, and cowboys. Kit Carson – legendary mountain man, soldier, and Indian enemy turned Indian advocate – was the first in a long line of celebrities to settle here, in 1842. His name is still found everywhere, from the main street in the historic district to the surrounding national forest to the local electric company.
A broken wagon wheel stranded a couple of artists in Taos in 1898. They stayed, and their reasons for staying soon got out; before too long an artists' enclave, drawn by light unencumbered by the weight of atmosphere, by colors at once subtle and brilliant, was formed. Today Taos is home to more than 80 galleries, and about 30% of people here call themselves artists.
This little town also became a magnet for writers and creative thinkers of all types. DH Lawrence hoped to build a utopia outside of town; Carl Jung was deeply affected by his visit to Taos Pueblo, which is also where Aldous Huxley found his inspiration for _Brave New World_ ; Dennis Hopper shot key scenes from _Easy Rider_ around Taos, and was so enchanted he moved here. It's not hard to see why.
Taos remains a relaxed and eccentric place, with classic mud-brick buildings, quirky cafes and excellent restaurants. Its 5000 residents include bohemians and hippies, alternative-energy aficionados and old-time Hispanic families. It's both rural and worldly, and a little bit otherworldly.
#### Sights
The best attraction in the Taos area is Taos Pueblo. Built around 1450 and continuously inhabited ever since, it is the largest existing multistoried pueblo structure in the USA and one of the best surviving examples of traditional adobe construction. Otherwise, for a village that gets as much tourist traffic as Taos, there aren't that many actual sights. Wander historic Ledoux St, Taos' art alley. Stop and pose for a picture by the life-size bronzes by Native American artist RC Gorman. Stroll under the verandas of the old adobes surrounding picturesque Taos Plaza.
With the Museum Association of Taos, the town's most important museums have united to offer a five-museum pass for $25, saving you $15 if you visit them all. The pass is good for a year and, in the true spirit of Taos, the Association actually encourages you to pass yours off to someone else if you haven't gotten around to each sight yourself! The museums covered include the Millicent Rogers, the Harwood, Taos Historic Museums, and the Art Museum & Fechin Institute.
Taos Area
Top Sights
1 Martinez Hacienda B5
2 Millicent Rogers Museum B4
3 San Francisco de Asfs Church B6
4 Taos Pueblo C4
Activities, Courses & Tours
5 HistoricTaosTrolleyTours B6
Native Sons Adventures (see 23)
Rio Grande Stables (see 8)
6 Taos Indian Horse Ranch C4
7 Taos Mountain Casino C4
8 Taos Ski Valley D1
Sleeping
9 Abominable Snowmansion B3
10 Adobe and Stars B&B C2
11 American Artists Gallery House B&B B5
12 Casa Europa B5
13 Old Taos Guesthouse C5
Snakedance Condominiums & Spa (see 8)
14 Sun God Lodge B6
Eating
15 Love Apple C5
16 Orlando's B4
17 Taos Cow C2
18 Taos Diner B5
19 Tewa Kitchen C4
Tim's Stray Dog Cantina (see 8)
20 Trading Post CaféB6
Drinking
21 Mondo Kultur B5
Entertainment
22 KTAO Solar Center B4
23 Storyteller Cinema B6
Shopping
24 Tony Reyna Indian Shop C4
Taos
Top Sights
Fechin Institute C2
Sights
1 Blumenschein Home & Museum B4
2 Harwood Foundation Museum A4
3 Kit Carson Home & Museum C3
4 Taos Art Museum C2
Activities, Courses & Tours
5 Cottam's Ski & Outdoor B4
6 Gearing Up Bicycle Shop B3
7 Mudd-n-Flood B3
8 Taos Mountain Outfitters B3
Sleeping
9 Casa Benavides Bed & Breakfast C3
10 Doña Luz Inn B3
11 El Monte Sagrado C4
12 El Pueblo Lodge D1
13 Historic Taos Inn C3
14 La Fonda de Taos B3
15 Mabel Dodge Luhan House D3
Eating
Doc Martin's(see 13)
16 Dragonfly Café & Bakery C1
17 El Gamal B3
18 Gorge Bar & Grill B3
19 Graham's Grille B3
20 Michael's Kitchen C2
Drinking
Adobe Bar(see 13)
21 Alley Cantina B3
Anaconda Bar(see 11)
22 Caffe Tazza C3
23 Eske's Brew Pub & Eatery B3
Entertainment
24 Taos Center for the Arts C3
Shopping
25 Buffalo Dancer B3
El Rincón Trading Post(see 10)
Millicent Rogers Museum MUSEUM
(www.millicentrogers.org; 1504 Millicent Rogers Museum Rd; adult/child $8/6; 10am-5pm, closed Mon Nov-Mar) This museum, about 4 miles from the plaza, is filled with pottery, jewelry, baskets and textiles from the private collection of Millicent Rogers, a model and oil heiress who moved to Taos in 1947 and acquired one of the best collections of Indian and Spanish colonial art in the USA. You want to know what a top-quality squash blossom necklace is supposed to look like? Look no further. Also displayed are contemporary Native American and Hispanic artworks.
Taos Art Museum & Fechin Institute MUSEUM
(www.taosartmuseum.com; 227 Paseo del Pueblo Norte; admission $8; 10am-5pm Tue-Sun) This museum was home to Russian artist Nicolai Fechin, who emigrated to New York City in 1922 at age 42 and moved to Taos in 1926. Today his paintings, drawings and sculptures are in museums and collections worldwide. Between 1927 and 1933, Fechin completely reconstructed theinterior of his adobe home, adding his own distinctly Russian woodcarvings. The Fechin house exhibits the artist's private collection, including much Asian art, and hosts occasional chamber music events. Five-day watercolor, sculpture and other arts workshops are offered from May to October at the nearby ranch.
Harwood Foundation Museum MUSEUM
(www.harwoodmuseum.org; 238 LedouxSt; adult/child $8/free; 10am-5pm Tue-Sat,noon-5pm Sun) Housed in a historic mid-19th-century adobe compound, the HarwoodFoundation Museum features paintings, drawings, prints, sculpture and photography by northern New Mexican artists, both historical and contemporary. Founded in 1923, the Harwood has been run by the University of New Mexico since 1936 and underwent a major renovation in 1997. It is the second-oldest museum in New Mexico, and one of its most important when it comes to art collections.
Taos Historic Museums MUSEUM
(www.taoshistoricmuseums.org; adult/child each museum $8/4; 10am-5pm Mon-Sat, noon-5pm Sun) The 1797 Blumenschein Home & Museum (222 Ledoux St) was the home of artist Ernest Blumenschein (one of the founding members of the Taos Society of Artists; see Click here) in the 1920s. Today it's maintained much as it would have been when the Blumenscheins lived here. The period furniture is interesting, and the art is spectacular. Down the road a bit (you'll want to drive), the Martínez Hacienda (708 Lower Ranchitos Rd), built in 1804, became the end of the line on the northern spur of the Camino Real. With 21 rooms, it's one of the best preserved New Mexican 'Great Houses' from that era. Cultural events are held here regularly.
Earthships NEIGHBORHOOD
(www.earthship.net; US Hwy 64; tours $5; 10am-4pm) Innovative and off-the-grid, Earthships are self-sustaining, environmentally savvy houses built with recycled materials like used automobile tires and cans. The community is the brainchild of architect Michael Reynolds, whose idea was to develop a building method that 'eliminates stress from both the planet and its inhabitants.' Buried on three sides by earth, the Earthships are designed to heat and cool themselves, make their own electricity and catch their own water. Sewage is decomposed naturally, and dwellers grow their own food. The Earthship 'tour' is a little disappointing – you pay five bucks basically to watch a short dvd and check out the visitor center. It's much more interesting to stay in an Earthship Rental overnight. The tour office is located 1.5 miles past the Rio Grande Gorge Bridge on US Hwy 64 West.
San Francisco de Asís Church CHURCH
(St Francis Plaza; 9am-4pm Mon-Fri) Four miles south of Taos in Ranchos de Taos, this iconic church was built in the mid-18th century and opened in 1815. Famed for the curves and angles of its adobe walls, it's been memorialized in Georgia O'Keeff e paintings and Ansel Adams photographs. Mass is held at 6pm the fi rst Saturday of the month, and usually at 7am, 9am and 11:30am every Sunday.
Rio Grande Gorge Bridge BRIDGE, CANYON
On US Hwy 64 about 12 miles northwest of Taos, the gorge bridge is the second-highest suspension bridge in the USA. Constructed in 1965, the vertigo-inducing steel bridge spans 500ft across the gorge and 650ft above the river below, and there's a walkway across it all. The views west over the emptiness of the Taos Plateau and down into the jagged walls of the Rio Grande will surely make you gulp as you gape. On the eastern side of the bridge you'll usually find a motley array of vendors selling jewelry, sage sticks and other souvenirs for good prices.
Kit Carson Home & Museum MUSEUM
(www.kitcarsonhomeandmuseum.com; 113 Kit Carson Rd; adult/child $5/3; 11am-5pm) Kit Carson (1809–68) was the Southwest's most famous mountain man, guide, trapper, soldier and scout. His home serves as an excellent introduction to Taos in the mid-19th century, housing such artifacts as Carson's rifles, telescope and walking cane. Built in 1825 with 30in adobe walls and traditional Territorial architecture, the home's 12 rooms are today furnished as they may have been during Carson's day, with exhibits on all periods of Taos history and mountain-man lore.
#### Activities
Hike, bike, raft, ski, fish...the variety of outdoor activities in the Taos area is exhaustive; consult www.taosoutdoorrecreation.com for an online rundown of all your options.
There are a number of well-respected local outfitters who can help you plan and execute your outdoor excursions. Native Sons Adventures ( 575-758-9342; www.nativesonsadventures.com; 1033 Paseodel Pueblo Sur; 7am-6pm) is a good one, guiding rafting and mountain-biking trips, renting gear, and running single-track shuttles; if they can't help you, they'll know who can.
If you need to pick up any gear, head to the Plaza for Taos Mountain Outfitters (www.taosmountainoutfitters.com; 114 S Plaza) or to Bent St for Mudd-n-Flood (134 Bent St). Both are well stocked and have substantial sale racks, and the folks behind the counters know what they're talking about.
###### Winter Sports
In winter it's all about skiing, and most of the action takes place at the Taos Ski Valley, which is not actually in the town of Taos; it's about 20 miles away. The ski (and newly minted snowboard) resort has a slew of lodging and eating options, so we've actually given it its own heading in this guide. Check out Click here for more on skiing in Taos.
The best in cross-country skiing is at the Enchanted Forest up by Red River (Click here), but there's also a great little area in Carson National Forest at Amole Canyon, 15 miles south of Taos on Hwy 518.
Just north of Amole Canyon along Hwy 518, US Hill – the primo sledding spot in the area – is the most popular place around for kids to get frostbitten and bruised and love every minute of it.
Cottam's Ski & Outdoor (www.cottamsskishops.com; 207a Paseo del Pueblo Sur), in town, is a reliable place to rent or buy whatever winter gear you need. They have another location at the ski valley.
###### Mountain Biking
Where else are you going to find biking this good, this close to the sky? Why bother looking elsewhere when an enormous network of mountain-bike and multi-use trails cover the region of the Carson National Forest between Taos, Angel Fire and Picuris Peak?
Standouts include the 9-mile West Rim Trail at Orilla Verde Recreation Area, suitable for strong beginners and intermediate cyclists to enjoy views of Rio Grande Gorge; and storied South Boundary Trail, considered one of the best mountain-bike trails in the nation – a 28-mile ride for experienced cyclists.
If you want to really challenge yourself, try the 84-mile Enchanted Circle loop. It makes a fine regional road-bike circuit once you've acclimatized to the altitude.
There's a surprising amount of information about mountain biking at the Taos Visitor Center. For more advice, talk to the good people at Gearing Up Bicycle Shop ( 575-751-0365; www.gearingupbikes.com; 129 Paseo del Pueblo Sur; 9am-6:30pm), where you can pick up trail maps, rent bikes (per day from $35) and racks ($7), and set up shuttles.
### TAOS SOCIETY OF ARTISTS
In 1893 artist Joseph Henry Sharp first visited Taos to produce for publication a group of illustrations depicting the Pueblo. Quite smitten with the scene, Sharp spread the word among his colleagues about his 'discovery,' and shortly afterward relocated here permanently.
Ernest Blumenschein, Bert Phillips and many more of his contemporaries followed, and in 1912 they, along with Oscar Berninghaus, Eanger Irving Couse and Herbert Dunton, established the Taos Society of Artists (TSA). The original six were later joined by other prominent painters, including Lucy Harwood, the only female member, and Juan Mirabol, from Taos Pueblo.
Early TSA paintings were inspired by the backdrop of the Sangre de Cristo Mountains as well as the buildings and people of Taos Pueblo. Set against the tonal shapes and neutral colors of earth, human figures act as flashes of color seen nowhere else in the desert. Pueblo architecture, with clusters of organic and sculptural block shapes reflecting the high desert light, also appealed to the Taos painters' artistic sensibilities.
The artists' styles were as diverse and experimental as the many philosophies of painting that defined the first half of the 20th century. From Sharp's illustrative and realistic approach and Blumenschein's impressionistic treatment of Southwestern themes to the moody art-deco spirit of Dunton's landscapes, the TSA portrayed the same subjects in infinite ways.
Only in later years would the TSA's contribution to contemporary art's development be fully recognized. Historically the paintings of the TSA are seen as a visual documentary of northern New Mexican cultures, which had not yet been so dramatically influenced by the industrial age.
###### Hiking & Hot Springs
While there are a number of day-use trails just outside of Taos, particularly on the south side of Hwy 64 east of town, the best day hiking and backpacking is a little ways away, around the Ski Valley, in the Latir Peak Wilderness (Click here) plus in and around the Pecos Wilderness (Click here).
One popular day hike heads into the Rio Grande Gorge and the Manby Hot Springs (aka Stagecoach Hot Springs). A worthy place of pilgrimage – this is where the hot-springs scenes were shot in _Easy Rider_ – the quality of the springs depends on the height of the river. To get there, ask a local to draw you a map. The more easily accessible Black Rock Hot Springs along the river are near the John Dunn Bridge, west of Arroyo Hondo, some 9 miles north of Taos.
###### Rafting
Perched between the Box and Racecourse sections of the Rio Grande, Taos is in a good position for acheiving some white-water satisfaction. Rafting companies run trips to the frothy Taos Box when there's enough water to boat it – usually in late spring and early summer. This stretch of river is not for the easily panicked; the rapids can hit Class V (most difficult but still possible, with Class VI being something like 'certain death'), and the remote feeling of the canyon makes it all that much more intense. From spring to fall, the Racecourse – downriver at Pilar (Click here) – is perpetually popular; it's exciting,but rarely feels death-defying.
Among the best Taos-based river outfits is Los Rios River Runners ( 800-544-1181; 4003 Hwy 68; www.losriosriverrunners.com; Box trips $100-115, Racecourse trips adult/child $50/40, 3-day Chama trips per person $490; 8am-6pm) Besides the Box (minimum age 12) and the Racecourse, they also run the scenic Chama. Unique twists include their 'Native Cultures Feast and Float,' which is accompanied by a Native American guide and includes a lunch homemade by a local Pueblo family.
###### Fishing
The creeks, rivers and lakes around Taos have enough variety to please experts and beginners alike, and scenery ranging from deep rocky canyons to high alpine meadows. Teach the kids at Eagle Nest Lake (Click here) or Orilla Verde Recreation Area (Click here); take your fly rod up to the Red River or down to the Rio Santa Barbara. Don't forget to pick up a one-day/five-day license for $12/24.
For the right flies for these waters, stop by Taos Fly Shop ( 575-751-1312; www.taosflyshop.com; 308c Paseo del Pueblo Sur) and find out what's hatching where. They have expert guides (half-/full day from $250/325) and offer fly-fishing instruction.
###### Horseback Riding
Rio Grande Stables HORSEBACK RIDING
( 575-776-5913; www.lajitasstables.com/taos.htm; mid-May–mid-Sep) Based up by the ski valley, this recommended ridingcompany offers one- to four-hour trips ($50 to $95), all-day rides (including one to the top of Wheeler Peak) and combination horseback/rafting/camping treks they'll customize just for you. Call in advance.
#### Tours
Historic Taos Trolley Tours HISTORICAL
( 575-751-0366; www.taostrolleytours.com; cnr Paseo del Pueblo Sur & Paseo del Cañon; adult/child $33/10; 10:30am & 2pm) Offers two different tours aboard red trolleys from the visitor center. One visits Taos Pueblo, San Francisco de Asís and the Plaza (where they'll also pick you up); the other takes in Millicent Rogers Museum and the Martínez Hacienda.
#### Festivals & Events
There are numerous athletic and cultural events all year, as well as visual arts workshops; the visitor center has details. Some of the most memorable and unique are held at Taos Pueblo. Check out Click here for info on the green Solar Music Festival in June, which has lately been in a constant state of flux. The Fiestas de Taos (www.fiestasdetaos.net; late July) rock with New Mexican music and dance, and fill the streets with parades. Christmas holiday celebrations include mass at San Francisco de Asís Church (Click here), plus carolers and _farolitos_ everywhere help keep everyone's spirits bright.
#### Sleeping
Taos offers a wide variety of accommodations, from free camping in national forests to gourmet B&Bs in historic adobes. Rates can fluctuate wildly depending on what week it is, though June to September and December to February are usually considered high season, with a major spike around Christmas.
Reservation services include the Taos Association of Bed & Breakfast Inns (www.taos-bandb-inns.com) and Taos Vacation Rentals ( 800-788-8267; www.taosvacationrentals.com).
Earthship Rentals QUIRKY $$
( 505-751-0462; www.earthship.net; US Hwy 64; r $120-160) Experience an off-grid night in a boutique-chic, solar-powered dwelling. A cross between organic Gaudí architecture and space-age fantasy, these sustainable dwellings are put together from recycled tires, aluminum cans and sand, with rain-catching and gray-water systems to minimize their footprint. Half-buried in a valley surrounding by mountains, they could be hastily camouflaged alien vessels – you never know...
Mabel Dodge Luhan House HISTORIC HOTEL $$
( 505-751-9686; www.mabeldodgeluhan.com; 240 Morada Lane; r $100-195; ) Every inch of this place exudes elegant-meets-rustic beauty. The 'Patroness of Taos,' Mabel Dodge Luhan (by equal measures graceful and grand, scandalous and unbearable) built this fabulous mansion to welcome everyone from Emma Goldman and Margaret Sanger to Carl Jung for a nice chat. You can sleep in rooms where Georgia O'Keeffe, Ansel Adams or Willa Cather once laid their heads, or where DH Lawrence added artful touches. It also runs art workshops.
### ANDEAN-ESQUE ADVENTURE
Not everyone who loves to hike and camp has the stamina – or desire – to haul a pack around at 11,000ft above sea level. Around Taos, you don't need to – that's what the llamas are for! Wild Earth Llama Adventures ( 800-758-5262; www.llamaadventures.com) runs day hikes and multiday treks in the sweetest spots in the Sangres. They're experts at getting even young kids out into the backcountry, and their lead guide also happens to be a chef. No, no llama riding, but you might be too busy doing your 'Julie Andrews in an alpine meadow' impersonation to care.
Day trips (adult/child $99/69) run year-round; multiday trips (adult/child from $329/119; prices vary with length) run from March to November and can be customized to your needs.
Doña Luz Inn INN $$
( 575-758-9000; www.stayintaos.com; 114 Kit Carson Rd; r $59-229; ) Funky and fun, this inn is a true Taos experience. Rooms, with adobe fireplaces, patios, kitchenettes and hot tubs, range from the cozy La Luz (at $59, the best deal in town) to the three-level Rainbow Room suite with a hot tub on the rooftop sundeck. All are decorated in colorful Spanish colonial style, a cheerful clutter of Native American and Spanish colonial antiques, artifacts and art – lots of it sacred and all of it beautiful.
Historic Taos Inn HISTORIC HOTEL $$
( 575-758-2233; www.taosinn.com; 125 Paseo del Pueblo Norte; r $75-275; ) Even though it's not the plushest place in town, it's still fabulous, with a cozy lobby, a garden for the restaurant, heavy wooden furniture, a sunken fireplace and lots of live local music at its famed Adobe Bar. Parts of this landmark date to the 1800s – the older rooms are actually the nicest.
American Artists Gallery House B&B B&B $$
( 800-532-2041; www.taosbedandbreakfast.com; 132 Frontier Lane; r/ste from $85-190; ) Art flows here in ever-changing shows drawn from local galleries. George the peacock and lots of cats will be your inn-mates, while Jacuzzi suites will blow your mind. All rooms have wood-burning fireplaces. The creative breakfasts are legendary.
Casa Benavides Bed & Breakfast B&B $$
( 575-758-1772; www.taos-casabenavides.com; 137 Kit Carson Rd; r $105-300; ) This romantic spot spans five buildings, and has lots of fireplaces, patios, balconies and gardens. Furniture is mostly antique and handmade, and shares space with artful treasures. A couple of the rooms are on the small and dark side, but most are big and bright – see a few if you can. Breakfasts are full and made from scratch.
Old Taos Guesthouse B&B $$
( 800-758-5448; www.oldtaos.com; 1028 Witt Rd; r $84-175; ) This atmospheric treasure has spacious, old-world adobe rooms with undulating walls (just try to find a right angle here) and handcarved wood furnishings and doors; the older rooms are nicest. Hidden away in a quiet residential neighborhood, the shady lawn and gardens beckon, with inviting hammocks and 60-mile sunset views. The proprietors are seasoned adventurers and can point you toward great excursions.
Casa Europa B&B $$
( 575-758-9798; www.casaeuropanm.com; 840 Upper Ranchitos Rd; r $115-185; ) Cool breezes provide the air-conditioning at this stunning 18th-century estate. Views of pastures and mountains are sublime. Euro-styleantiques mix artfully with Southwestern-style pieces. Elaborate breakfast and afternoon treats are offered in summer, evening hors d'oeuvres in winter. Comfort, light and air define this welcoming spot.
El Monte Sagrado LUXURY HOTEL $$$
( 800-828-8267; www.elmontesagrado.com; 317 Kit Carson Rd; r $199-499; ) A lush oasis in the high desert, this lavishly decorated ecoresort has bright, luxurious suites whimsically decorated with Native American, Mexican, Moroccan and Egyptiancultures in mind, all arranged around a flourishing courtyard irrigated with a gray-water system. Its Anaconda Bar is exceptionally attractive. There's a full-service on-site spa and plenty of package deals with the ski valley.
Sun God Lodge MOTEL $
( 575-758-3162; www.sungodlodge.com;919 Paseo del Pueblo Sur; r from $55; ) The hospitable folks at this well-run two-story motel can fill you in on local history and point you to a restaurant to match your mood. Rooms are clean – if a bit dark – and decorated with low-key Southwestern flair. The highlight is the lush-green courtyard dappled with twinkling lights, a scenic spot for a picnic or enjoying the sunset. Pets stay for $20. Located 1.5 miles south of the Plaza, the Sun God is a great budget choice.
El Pueblo Lodge HOTEL $
( 800-433-9612; www.elpueblolodge.com; 412 Paseo del Pueblo Norte; r from $89; ) This standard hotel is right downtown, with big, clean rooms, some with kitchenettes and/or fireplaces, a pool, hot tub and fresh pastries in the morning. Deep discounts are offered in low season or when they're not busy.
La Fonda de Taos HISTORIC HOTEL $$
( 800-833-2211; www.lafondataos.com; 108 S Plaza; r $99-259; ) This upscale hotel,formerly owned by notorious playboy Saki Karavas, just can't shake its sexy vibe – even the kiva gas fireplaces in the smallish, sensually angled suites seem like they're illuminating something that's up to no good. Perhaps it's the 'Forbidden Art' collection of DH Lawrence – banned in 1929 Europe and displayed here to consenting adults – depicting, and perhaps inspiring, all sorts of sinful fun. No children under 13.
Indian Hills Inn HOTEL $
( 575-758-4293; www.taosnet.com/indianhillsinn; 233 Paseo del Pueblo Sur; r from $60; ) This budget hotel close to the Plaza isn't half-bad. The swimming pool is great for kids who've maxed out on art galleries. All rooms were recently recarpeted, but the Deluxe King rooms are noticeably nicer than the Double Queen family rooms. For the location and price, it's a good deal.
#### Eating
There are some really good restaurants here. A few are even right near the Plaza.
Trading Post Cafe INTERNATIONAL $$$
( 575-758-5089; www.tradingpostcafe.com; Hwy 68, Ranchos de Taos; lunch mains $8-14, dinner mains $16-32; 11:30am-9:30pm Tue-Sat, 5-9pm Sun) A longtime favorite, the Trading Post is a perfect blend of relaxed and refined. The food, from paella to pork chops, is always great. Portions of some dishes are so big, think about splitting a dish – or, if you want to eat cheap but well, get a small salad and small soup. It'll be plenty!
Love Apple ORGANIC $$
( 575-751-0050; www.theloveapple.net; 803 Paseo del Pueblo Norte; mains $13-18; 5-9pm Tue-Sun) Housed in the 19th-centuryadobe Placitas Chapel, the understated rustic-sacred atmosphere is as much a part of this only-in-New-Mexico restaurant as the food. From the posole with shepherd's lamb sausage to the grilled trout with chipotle cream, every dish is made from organic or free-range regional foods. Make reservations!
Dragonfly Café & Bakery INTERNATIONAL $$
(www.dragonflytaos.com; 402 Paseo del Pueblo Norte; lunch mains $4-14, dinner mains $12-21; 11am-9pm Mon-Sat, 9am-3pm Sun; ) One of the most charming little places in town, the Dragonfly creates a space that achieves a rustic kind of elegance while remaining comfortable and kid-friendly. Food is delicious and internationally inspired, from Moroccan roast chicken to wild salmon tacos. Monday nights, come for the East Indian menu; every day, come for the fantastic baked goods. Most ingredients are local and/or organic.
Michael's Kitchen NEW MEXICAN $
(304c Paseo del Pueblo Norte; mains $7-16; 7am-2:30pm; ) Locals and tourists both converge on this old favorite because the menu is long, the food's reliably good, it's an easy place for kids, and the in-house bakery produces goodies that fly out the door. Plus, it serves the best damn breakfast intown. You just may spot a Hollywood celebrity or two digging into a chile-smothered breakfast burrito.
El Gamal MIDDLE EASTERN $
(www.elgamaltaos.com; 12 Doña Luz St; mains $6-10; 9am-5pm; ) Vegetarians rejoice! At this casual Middle Eastern place, there's no meat anywhere. We're not sure the falafel quite acheives El Gamal's stated vision to 'promote peace...through evolving people's consciousness and taste buds,' but it's good enough to have as much of a chance as anything else. There's a kids playroom in the back with tons of toys, plus a pool table and free wi-fi.
Taos Pizza Out Back PIZZA $
(712 Paseo del Pueblo Norte; slices $4-6, whole pies $13-27; 11am-10pm May-Sep, to 9pm Oct-Apr; ) Pizza dreams come true with every possible ingredient under the sun at Taos' top pizza palace; for example, the recommended Vera Cruz has chicken breast and veggies marinated in a honey-chipotle sauce. Slices are enormous, and crusts are made with organic flour. Out Back will also bake dough balls for kids, and has a great back patio.
Doc Martin's AMERICAN, NEW MEXICAN $$
( 505-758-1977; Historic Taos Inn, 125 Paseo del Pueblo Norte; breakfast & lunch mains $5-15, dinner mains $12-35; 7:30am-2:30pm, 5pm-9:30pm) Hang out where Bert Philips (the Doc's bro-in-law) and Ernest Blumenschein cooked up the idea of the Taos Society of Artists. Sit by the kiva fireplace, pop a cork on one of the award-winning wines, dive into the _chile rellenos_ and you'll be inspired to great things as well. Reservations recommended.
Graham's Grille MODERN AMERICAN $$
( 505-751-1350; www.grahamstaos.com; 106 Paseo del Pueblo Norte; mains $7-19; 7:30-10:30am & 11:30am-2:30pm Mon-Fri, 8am-2:30pm Sat & Sun, 5-9pm daily; ) Since its opening in 2007, Graham's has consistently been voted one of the best restaurants in Taos. It serves honest, creative food in hip retro-mod environs – think lime-green walls, purple lightbulbs and starched white tablecloths. There's a nice patio out back. The menu features lots of sandwiches and salads, plus seafoods, pasta and an apple-chile-brined pork tenderloin. Yum!
Lambert's MODERN AMERICAN $$$
( 505-758-1009; 309 Paseo del Pueblo Sur; mains $20-35; 5-9pm; ) Winner of multiple 'Best of Taos' awards, including best restaurant, Lambert's is a cozy local hangout where patrons sink deeply into sofas and conversation for hours on end. Lace curtains and subtle elegance make this atmospheric eatery a fine experience, whether you're digging into caribou, buffalo or the pepper-crusted lamb loin ($34).
Taos Diner DINER $
(www.taosdiner.com; 908 Paseo del Pueblo Norte; mains $4-12; 7am-2:30pm) Diner grub at its finest, prepared with a Southwestern, organic spin. Mountain men, scruffy jocks, solo diners and happy tourists –everyone's welcome here. The breakfast burritos rock.
Orlando's NEW MEXICAN $$
( 575-751-1450; www.orlandostaos.com; 1114 Don Juan Valdez Lane; mains $8-12; 10:30am-3pm, 5-9pm; ) Hands down the best New Mexican food in Taos, it can get really busy in high season. Just north of town on the main road.
Gorge Bar & Grill AMERICAN $$
(103 E Plaza; mains $9-25; 11am-10:30pm Mon-Thu, to 11:30pm Fri & Sat, to 9pm Sun) Popular with tourists for its hearty American food, margarita menu, and patio overlooking the plaza.
#### Drinking
###### Bars
Adobe Bar BAR
(Historic Taos Inn, 125 Paseo del Pueblo Norte) There's something about this place. There's something about the chairs, the Taos Inn's history, the casualness, the vibe and the tequila. It's true, the packed streetside patio has some of the state's finest margaritas, along with an eclectic lineup of great live music – and there's almost never a cover.
Anaconda Bar BAR
(El Monte Sagrado, 317 Kit Carson Rd) The Anaconda is a work of art, a real feast for the eyes. The bartenders and chefs take care of the other senses, with perfectly made drinks and gourmet pub grub. It is pricey, but it's unique.
Alley Cantina BAR
(121 Terracina Lane) It figures that the oldest building in Taos is a comfy bar, built more than three centuries ago by forward-thinking Native American capitalists as the Taos Pueblo Trading Post. Nowadays you can catch live music ranging from zydeco to rock and jazz almost nightly.
Eske's Brew Pub & Eatery BREWERY
(106 Des Georges Lane) This crowded hangout rotates more than 25 microbrewed ales, from Taos Green Chile to Doobie Rock Heller Bock, to complement hearty bowls of Wanda's green chile stew and sushi on Tuesday. Live local music, from acoustic guitar to jazz, is usually free.
###### Cafes
Mondo Kultur CAFE
(622 Paseo del Pueblo Sur; snacks $2-4; ) Arguably the best coffee in town, with bagels, pastries and other goodies. All ages, from tattooed teens to retirees, gather here. If you've got a laptop, it's hard to beat for getting work done.
Caffe Tazza CAFE
(122 Kit Carson Rd) Not everyone's cup of tea, Tazza caters mostly to the crunchy-hipster-tattooed crowd. Come at night to sample the local literary arts, with open mics, readings and live music.
#### Entertainment
KTAO Solar Center LIVE MUSIC
(www.ktao.com; 9 Ski Valley Rd) Taos's best venue for live music. Local, national and even international acts stop here to rock the house. Even on nights when there are no shows, you can watch the DJs in the booth at the 'world's most powerful solar radio station' while hitting happy hour at the Solar Center's bar ( from 4pm).
Taos Chamber Music Group CLASSICAL MUSIC
(www.taoschambermusicgroup.com) For classical and jazz, this group performs at venues throughout the region. See the website for schedules.
Taos Center for the Arts PERFORMING ARTS
( 575-758-2052; www.tcataos.org; 133 Paseo del Pueblo Norte) In a remodeled 1890s adobe mansion, the TCA stages local and international performances of everything from chamber music to belly dancing to theater.
Storyteller Cinema CINEMA
( 505-758-9715; 110 Old Talpa Cañon Rd; tickets adult/child $9/6) Catch mainstream flicks at Taos' only movie house, right off Paseo del Pueblo Sur.
### GOOD DAY SUNSHINE
Just as the Rio Grande Gorge opens up to engulf US Hwy 68 for the scenic climb into Taos, your radio will start to sputter. Don't put on that tired old CD; flip to KTAO 101.9 FM (www.ktao.com), broadcasting shows like 'Trash and Treasures' (an on-air flea market) and lots of great music.
KTAO has been doing it all with solar power since 1991, when station founder Brad Hockmeyer installed 50,000 watts worth of photovoltaic cells atop Mount Picuris. The station plays whatever the real live DJs feel like playing and features daily horoscope readings (at 10am and 6pm) by local astrologer Josseph the Starwatcher. During 'Licorice Pizza' (10pm weekdays) a whole album – er, CD – is played in its entirety with no commercial interruption. Weekly shows include 'Moccasin Wire' (7:30pm to 10pm Monday), devoted to Native American music, and 'Listen Up' (7pm to 8pm Thursday), a talk show by and for Taos teens.
While this may sound dangerously like small-town schlock, it's anything but. KTAO consistently wins statewide awards for its programming and excellence in journalism.
Attached to the staton is the KTAO Solar Center, the best place in town to see concerts. It's family-friendly, and kids under 12 are free. We only hope that they'll be allowed to stage shows out on the back lawn again, like they used to before certain neighbors complained about it. Now, bands play inside a big tentlike structure.
The radio station is no longer associated with the Taos Solar Music Festival (www.solarmusicfest.com), which is still held at the end of June and still fun! The festival format and location has been fluid for the past couple of years, so check details. You can probably count on there being a 'solar village,' showcasing anything from the Los Alamos National Laboratory's solar-powered supercomputer to homemade solar cookers. Grab a cup of solar-percolated coffee and chat up alternative-energy lovers pitching straw-bale construction, solar cars, passive solar design ('used at Taos Pueblo for a thousand years!') and of course the Taos Earthships.
#### Shopping
Taos has historically been a mecca for artists, and the huge number of galleries and studios in and around town are evidence of this. The John Dunn Shops (www.johndunnshops.com) pedestrian arcade between the Plaza and Bent St. is lined with indie shops and galleries.
Taos Drums MUSIC
(www.taosdrums.com; 3956 Hwy 68, Ranchos de Taos) Just south of town you'll find what's touted as the world's largest selection of Native American drums. All are handmade by masters from Taos Pueblo and covered with real hide. Choose from hand drums, log drums, natural-looking drums or ones painted with wildlife or Pueblo motifs.
El Rincón Trading Post VINTAGE
(114 Kit Carson Rd) This shop dates back to 1909, when German Ralph Meyers, one of the first traders in the area, arrived. Even if you're not looking to buy anything, stop in here to browse through the dusty museum of artifacts, including Indian crafts, jewelry and Old West memorabilia.
Buffalo Dancer JEWELRY
(103a East Plaza) One of the older outlets for Native American jewelry on the Plaza, this store carries Rodney Concha's fine pieces plus other work in silver and semiprecious stones.
#### Information
Holy Cross Hospital ( 575-758-8883; 1397 Weimer Rd)
Police ( 575-758-2216; 107 Civic Plaza Dr)
Post office (Paseo del Pueblo Norte at Brooks St)
Taos Vacation Guide (www.taosvacationguide.com) Good site with sections in French, German and Spanish.
Taos Visitor Center ( 575-758-3873; Paseo del Pueblo Sur at Paseo del Cañon; 9am-5pm; )
Wired? (705 Felicidad Lane; 8am-6pm Mon-Fri, 8:30am-6pm Sat & Sun) Coffee shop with free wi-fi if you've got a laptop; if not you can log on to their computers (per hour $7).
#### Getting There & Around
One mile north of town, Paseo del Pueblo Norte forks: to the northeast it becomes Camino del Pueblo and heads toward Taos Pueblo, and to the northwest it becomes Hwy 64. The 'old blinking light' north of town is a major landmark for directions (though it now functions as a regular traffic light); from it, Hwy 64 heads west to the Rio Grande Gorge Bridge, Hwy 522 heads northwest to Arroyo Hondo and Questa, and Hwy 150 heads northeast to Arroyo Seco and the Taos Ski Valley.
North Central Regional Transit (www.ncrtd.org) provides free shuttle bus service to Española, where you can transfer to Santa Fe and other destinations; pick-up/drop-off is at the Taos County offices off Paseo del Pueblo Sur, about a mile south of the plaza. Taos Express (www.taosexpress.com) has shuttle service to Santa Fe Friday through Sunday ($10). Twin Hearts Express ( 800-654-9456) will get you to Santa Fe ($40) and the Albuquerque airport ($50).
The Chile Line (www.taosgov.com; one-way 50¢; 7am-5:30pm Mon-Fri) runs north–south along NM 68 between the Rancho de Taos post office and Taos Pueblo every 30 minutes. It also serves the ski valley and Arroyo Seco in winter. All buses are wheelchair-accessible.
## AROUND TAOS
The area around Taos has fabulous skiing, cool little towns and some of the best scenery around. Driving the Enchanted Circle makes a fantastic day trip from Taos, while a night in little Arroyo Seco delivers rural New Mexican flavor and crisp high desert air. There's good fly-fishing and cross-countryskiing around Red River, and plenty of wilderness to escape to.
### Taos Pueblo
Whatever you do, don't miss it. Built around 1450 and continuously inhabited ever since, Taos Pueblo ( 505-758-1028; www.taospueblo.com; Taos Pueblo Rd; adult/child $10/5, photography or video permit $5; 8am-4pm) is the largest existing multistoried pueblo structure in the USA and one of the best surviving examples of traditional adobe construction. It's what all that Pueblo Revival architecture in Santa Fe wants to be when it grows up. Note the Pueblo closes for 10 weeks annually, starting in March, for ritual purposes.
Taos Mountain Casino (www.taosmountaincasino.com; Taos Pueblo Rd; 8am-1am Sun-Wed, to 2am Thu-Sat) has less razzle-dazzle than some casinos, but you might appreciate its alcohol-and-smoke-free atmosphere.
Taos Indian Horse Ranch ( 505-758-3212, 800-659-3210; 1hr/2hr easy ride $55/95, 2hr experienced ride $125) offers riding trips through Indian land – experienced riders can go fast. It also does an overnight rafting/riding/camping trip; ring for details.
One of New Mexico's largest and most spectacular Indian celebrations, San Geronimo Day (September 29 and 30) is celebrated with dancing and food. The huge Taos Pueblo Pow-Wow ( 505-758-1028; www.taospueblopowwow.com; Taos Pueblo Rd; admission $5) in the second week of July features Plains and Pueblo Indians gathering for dances and workshops as this centuries-old tradition continues. Of all the Pueblos in northern New Mexico, Taos Pueblo has the most events and celebrations open to the public.
For food, everyone, and we mean everyone, heads to Tewa Kitchen (Taos Pueblo Rd; mains $6-13; 11am-5pm Wed-Mon Sep-May, to 7pm daily Jun-Aug). It's one of the few places in the state where you can sit down to a plate of Native treats like _phien-ty_ (blue-corn fry bread stuffed with buffalo meat), _twa chull_ (grilled buffalo) or a bowl of heirloom green chile grown on Pueblo grounds.
You can also grab tacos and the most delicious chewy Indian fry bread ($3 to $5) at the main pueblo.
Just outside the Pueblo, stop at the Tony Reyna Indian Shop (Taos Pueblo Rd; 8am-noon & 1-6pm), which has a vast collection of arts and crafts from Taos and other tribes.
Several craftspeople sell fine jewelry, micaceous (mica is an aluminum mineral found in local rocks) pottery and other arts and crafts at the main pueblo; you can peruse after touring the place.
### Arroyo Seco
For some unprocessed local flavor, a groovy plaza and a growing art scene, Arroyo Seco is the place to be. It's just 10 minutes north of Taos; there's not much to do, but you'll find plenty of ways to do nothing.
Backpackers will find their version of sleeping paradise at the popular, and extremely affordable, Abominable Snowmansion ( 575-776-8298; www.snowmansion.com; 476 Hwy 150; campsites $15, dm $20, r with shared/private bath $45/59; ). This HI hostel has a cozy lodge, with clean (if a tad threadbare) private rooms, a wonderful campground with an outdoor kitchen, and simple dorm rooms. For something different – especially if you've got the kids – try sleeping in a tipi ($35)!
The Adobe and Stars B&B ( 575-776-2776; www.taosadobe.com; 584 Hwy 150; r incl breakfast $125-190; ) has eight large, amazing rooms with working kiva fireplaces, some with Jacuzzi tubs and peaceful mountain views.
Taos Cow (mains $5-8; 7am-6pm; ) serves sandwiches, breakfast specials, pastries and its much-loved all-natural ice cream in some flavors you'll find nowhere else (like Piñon Caramel).
### Taos Ski Valley
People move to New Mexico just to 'ski bum' at Taos for a couple years. Some end up staying longer than they planned. There's just something about the snow, challenging terrain and laid-back atmosphere that makes this mountain a wintery heaven-on-earth – that is, if heaven has a 3275ft vertical drop.
Most visitors come in winter for the skiingand snowboarding. (Once exclusive to skiers,Taos is now open to boarders). Offering some of the most difficult terrain in the USA, it's a fantastic place to zip down steep tree glades and jump cliffs into untouched powder bowls. Summer visitors to the village, which was once the rough-and-tumble gold-mining town of Twining, find an alpine wilderness with great hiking and cheap lodging.
Seasoned skiers luck out here, with more than half of the 70-plus trails at the Taos Ski Valley (www.skitaos.org; half-/full-day lift ticket $48/71) ranked expert; the valleyhas a peak elevation of 11,819ft and gets an average of more than 300in of all-natural powder annually – but some seasons are much better than others. In addition to opening up to snowboarders, the resort added a skier-cross obstacle course to its popular terrain park. Check the resort website for ski-and-stay deals, including weeklong packages with room, board, lessons and lift tickets. At the beginning of the season there are oftenreduced-rate lift tickets and very good specials on offer.
In summer, several hiking trailheads are located along Hwy 150 to Taos Ski Valley and at the northern end of the Ski Valley parking lot, including one to the top of Wheeler Peak, New Mexico's highest at 13,161ft.
When it comes to lodging, high season is from Thanksgiving to Easter, but there are dips in March and November and peaks during the holidays. From March to October, many lodges are closed, while those that are open offer excellent discounts.
Probably the best all-round option – with the best specials – is the giant Snakedance Condominiums & Spa ( 800-322-9815; www.snakedancecondos.com; 110 Sutton Pl; r $225-575; ), which offers ski-lodge condo-style digs at the bottom of the lifts. It also has a restaurant, a bar, in-room massages and lots of other amenities, including a hot tub, a sauna and in-room kitchens. Prices vary wildly around the year; those listed here are for the bulk of the ski season (much higher than summer rates but lower than Christmas/spring break).
Famous for its flame-roasted red and green chile, Tim's Stray Dog Cantina ( 505-776-2894; 105 Sutton Pl; mains $9-13; 8am-9pm Dec-May; 11am-9pm Jun-Nov) is a ski valleyinstitution. It serves fabulous New Mexican cuisine – the breakfast burritos are perfect fuel-up food – along with fresh margaritas and a big selection of bottled brews. The perfect après-ski or après-hiking hangout.
To reach the valley, take Hwy 64 north out of Taos to the old blinking light (now a regular traffic signal), and veer right on Hwy 150 toward Arroyo Seco. The 20-mile drive winds along a beautiful mountain stream. During the winter, the Chile Line runs several times a day from downtown Taos.
### DH Lawrence Ranch & Memorial
In 1924, Mabel Dodge Luhan gave DH Lawrence's wife, Frieda, this 160-acre ranch ( 575-776-2245; www.unm.edu/~taosconf/Taos/DHlawrence.htm; admission free; sunrise-sunset), now administered by the University of New Mexico, where the Lawrence-obsessed can pay their respects to the famed author of such classics as _Lady Chatterley's Lover_.
Lawrence and Frieda lived here for only a few months in 1924–25 along with artist Dorothy Brett, who accepted Lawrence's invitation to create 'Rananim,' a utopian society. Lawrence spent his time repairing the cabins, chopping wood, hiking the trails and (with the help of Frieda) fighting off the attentions of Dorothy and patron Mabel Dodge Luhan. He also managed to complete the novella _St Maw,_ his biblical drama _David,_ parts of _The Plumed Serpent_ and other works in between. Relax beneath the Lawrence Tree, which brings in the O'Keeffe fans (yep, it looks just like her painting) and contemplate what he called 'the greatest experience I ever had from the outside world.'
Lawrence returned to Europe in 1925 and succumbed to tuberculosis in 1930. After Frieda moved back to Taos in 1934, she ordered his body exhumed and cremated, and had the ashes brought here. Luhan and Brett both showed up uninvited to help scatter said ashes, which, according to legend, prompted Frieda to finally dump the remains into a wheelbarrow full of wet cement, saying, 'Let's see them try to steal this!' According to one story, the cement was used to make the memorial's altar – and his personal symbol, the phoenix, rises therefrom.
Ascend the meandering paved walkway to the memorial, designed by Frieda's third husband, where the lump of concrete has been inscribed with Lawrence's initials and green leaves and yellow flowers. It's heartwarming, with a scandalous giggle, just like Lawrence would have wanted.
At the time of research, the ranch had closed for renovations for an indefinite period. Hopefully it will be open by the time you read this, but this is New Mexico, so no guarantees.
### SCENIC DRIVE: VALLE VIDAL LOOP
In the mood for a longer drive through the highlands? Try the 173-mile Valle Vidal Loop, which departs the Enchanted Circle in Questa, heading north past the Wild Rivers Recreation Area on NM 522 and rejoining the road more traveled in Eagle Nest via US 64.
The bulk of the route is impassable during winter, and the washboard gravel road of FR 1950 is no picnic at the best of times – bring a spare tire. The northern gate to FR 1950 is closed April 1 to early June for elk calving season, while the southern gate closes January through March to let them winter in peace. The estimated 1800 elk are a major attraction the rest of the year and are best seen in the morning and evening.
From the small town of Costilla, just below the Colorado border, take NM 196 east. Before long, the road turns to dirt and heads into a wilderness – where elk, wildcats and bears roam – that's sometimes called 'New Mexico's Yellowstone.'
FR 1950 follows stocked Rio Costilla – a fly-fisher's paradise and a great place to relax – and opens on to national forest with unlimited access to multiday backpacking adventures. The road wends through meadows and forest, with outstanding views of granite peaks. Though it's possible to make this drive in a long day trip from Taos, it's much better to stay overnight, either in one of the four developed campgrounds or in the backcountry.
The route becomes blessedly paved again when you make a left onto US 64 for the drive back to Eagle Nest, where you rejoin the Enchanted Circle.
### Enchanted Circle
Unplug, sit back, unwind and absorb the beauty. You'll understand why they call this 84-mile loop the Enchanted Circle once you start driving – or, to really experience the sublime natural nuances along this stretch of pavement, ride it on your mountain bike. In warm weather, the route is popular with cyclists from around the world for its scenery and challenging altitude and terrain. Comprising NM 522, NM 38 and US 64, the scenic byway is generous with its views – of crystalline lakes, pine forests draped with feldspar, alpine highlands rising to 13,161ft Wheeler Peak, and rolling steppes carpeted with windswept meadows. Welcome to marmot and elk country.
Most towns on the circuit (with the notableexception of Questa) are relatively young, founded in the 1880s gold rush by mostly Anglo settlers looking for the mother lode. It never quite panned out, however, and the abandoned mines and ghost towns are highlights of the trip.
Those settlers who remained turned to tourism, opening ski resorts at Red River and Angel Fire; knickknack shops and adventure tour companies are probably the other two major employers. Just driving through is a pleasant skim of the surface, but take a little time to explore and you may discover one the highlights of your trip. Folks who've moved here compare their rare world to the Bermuda Triangle; find out why.
The site www.enchantedcircle.org has information about events in towns along the route. Taos Vacation Guide (www.taosvacationguide.com) has a quick guide to sights along the way. Fill your gas tank in Taos, where it's cheaper, and allow at least a full day to make the journey.
##### QUESTA
Primarily a mining town (the last vestige being the nearby molybdenum mine – it's the stuff used to help harden steel), Questa is also a growing enclave of artists, subsistence farmers and other organic types who are choosing to move off the grid.
The town's roots go back more than 400 years. It was once the northernmost settlement in the Americas, when Spain held sway. Its name comes from a typo when the town was founded in 1842: it was meant to be called 'Cuesta,' meaning 'cliff, large hill,' which would fit its looks perfectly, but thanks to a misspelling it became Questa! The Artesanos de Questa & Visitor Center (41 Hwy 38; 11am-4pm Mon & Thu-Sat) sells work by local artists, can recommend B&Bs, and will point you toward local artists' studios.
Just northeast of town is the Latir Peak Wilderness. Scenic alpine trails that climb high above treeline include a loop that ascends 12,708ft Latir Peak. It's one of the sweetest spots around, perfect for a rewarding night or two of backpacking, or an intense day hike.
Southwest of Questa, the Wild Rivers Recreation Area offers access to one of the most impressive stretches of the Rio Grande gorge, where it confluences with the Red River. A few trails plunge 800 feet down into the canyon while others meander along the mesa. The trek back up from river to rim is substantial, so be prepared with water and snacks. If you don't feel like a hike, drive the scenic 13-mile Wild Rivers Backcountry Byway loop, which gives some real visual rewards for a minimal amount of effort. La Junta provides the perfect spot for a picnic, overlooking the twin gorges. The visitor center (NM 378; tent sites $5-7, day-use $3; 10am-6pm Jun-Aug, reduced hours Sep-May) has information about camping. There are five semideveloped tent campgrounds with 22 spaces accessible by car. Four hiking trails lead to another 16 primitive riverside campsites at the bottom of the canyon.
Grab a bite at the Questa Café (2422 Hwy 522; mains $4-9; 7am-8:30pm Mon-Sat, to 3pm Sun), an expansive diner beloved for its Frito pie, chile cheese fries (go for red) and homemade deserts.
##### RED RIVER
The cusp of the 19th and 20th centuries saw a pretty wild populace of gold miners and mountain men here, with saloons and brothels lining Red River's muddy thoroughfares. The early years of this century finds mountain men, and women as well, only this time tricked out in Gore-Tex instead of skins, and looking for a whole different kind of extracurricular activity – for the most part. When the hard-drinking miners' hopes were crushed by the difficulty of processing the ore, those who stayed realized that their outdoor paradise might appeal to flatlanders with income. Indeed.
The town appears as a cluster of cheerfully painted shops and chalets, gleaming in the high desert sun. Red River, ski resort for the masses, is decked out in German-peasant style with an Old West theme – you'd think it wouldn't work, but it does.
Six historic buildings and lots of dilapidated mines have been joined by a ski resort, adventure outfitters, ticky-tacky shops galore and, this being New Mexico, art galleries.
The Red River Chamber of Commerce ( 800-348-6444; www.redrivernewmex.com; 100E Main St; 8am-5pm Mon-Fri) publishes a comprehensive visitors guide with great information on events and activities. The town virtually shuts down during the off-season, from mid-March to mid-May.
###### Activities
Enchanted Forest SKIING
( 800-966-9381; www.enchantedforestxc.com; NM38; adult/teen/child $15/12/7; 9am-4:30pm Nov-Mar) Twenty-three miles of groomed cross-country ski trails and another 12 of snowshoe trails wend though aspen and fir forests at New Mexico's premier Nordic ski area. One section is pet-friendly, and a number of trails lead to scenic viewpoints. You can even stay overnight at one of the backcountry yurts ($75). Special events include the illuminatedChristmas Luminaria Tour, Moonlight Ski Tours (the Saturday before a full moon) and Just Desserts Eat & Ski (late February), when you'll ski from stand to stand as area restaurants showcase their sweet stuff.
Red River Ski Area SKIING
( 800-331-7669; www.redriverskiarea.com; full-/half-day lift ticket $64/49) Red River gets most of its tourism in the wintertime, when folks flock to this ski area. The resort caters to families and newbies, with packages that include lessons and equipment or half-price weekends during the early season (beginning of December). Snowboarders and skiers alike should check out the terrain park complete with boxes and rails, specifically designed to lure you east from Angel Fire.
Frye's Old Town Shootout WILD WEST
(Main St; admission free; 4pm Tue, Thu & Sat Jun-Sep; ) In the summer, the kids won't want to miss downtown Frye's Old Town Shootout. It celebrates the Second Amendment in all its ten-gallon-hat, buckskin-jacket glory, as good guys try to stop the bad guys from robbing a bank and end up in a faux showdown right in the center of town.
Take NM 578 to the edge of the Wheeler Peak Wilderness for challenging but oh-so-worth-it hikes. Horseshoe Lake Trail leaves the Ditch Cabin Site for a 12-mile round-trip to the 11,950ft-high lake with good camping and fishing. The trailhead is on FR 58A, off Hwy 578, about 8 miles from Red River.
###### Sleeping
Red River has more than 50 RV parks, lodges, B&Bs and hotels, many of which offer package deals with local outfitters and the ski area. Discounts on summer room rates are steeper than the slopes here. There are lots of USFS campgrounds along the road between Questa and Red River, open from the end of May until sometime in September.
Copper King Lodge LODGE $$
( 800-727-6210; www.copperkinglodge.com; 307 East River St; r $84-200; ) Rough-hewn wood, rustic furnishings and a great backyard make these cabin-style apartments and condos with kitchenettes great value. But it's the hot tub next to the river that seals the deal. Rates vary wildly throughout the year.
Lodge at Red River INN $$
( 575-754-6280; www.lodgeatredriver.com; 400 E Main St; r from $85; ) First built in the 1940s, the Lodge feels historic and quaint but not old. Rooms are small but comfy, and there's an upstairs lounge with couches and books. Downstairs is Texas Red's Steakhouse (mains $10-29), Red River's best beef house, which also serves seafood, lamb, chicken and elk.
###### Eating & Drinking
Shotgun Willie's DINER $
(cnr Main St & Pioneer Rd; mains $6-12; 7am-7pm) Locals love this place serving the ultimate hangover sop-up, artery-clogging breakfast specials of fried eggs, meats and potatoes. The true house specialty is the barbecue, served by the pound. Order the brisket combo.
If you prefer a little line dancing with your barbecue, Red River is a favorite stop on the country and western music circuit. Catch live acts on weekends at venues around town, including the Motherlode Saloon next to the Lodge at Red River.
##### EAGLE NEST
This windswept high-meadow hamlet is a better place to explore the great outdoors if you can't take the tourist overkill of Red River. The tiny chamber of commerce ( 575-377-2420, 800-494-9117; www.eaglenest.org; Therma Dr; 10am-4pm Tue-Sat) has reams of information. The town sits on the edge of Eagle Nest Lake State Park (www.nmparks.com; day-use per vehicle $5; tent/RV sites $8/14), a 2400-acre lake filled with trout and kokaneesalmon. Boat rentals are available at Eagle Nest Marina (www.cti-excursions.com; Hwy 64; half-day rentals $80).
Three miles east of Eagle Nest on US 64, Cimarron Canyon State Park (www.nmparks.com; day-use per vehicle $5; tent/RV sites $8/14) runs alongside a dramatic 8-mile stretch of the scenic Cimarron River, hued in pine greens and volcanic grays. It also encompasses Horseshoe Mine, beaver ponds, lots of wildlife and fishing, and plenty of hikes.
For sleeping, try the Laguna Vista Lodge ( 505-377-6522; www.lagunavistalodge.com; 51 Therma Dr; r $125; ). It has spacious rooms with amenities galore, including kitchenettes in the family suites and full kitchens in the lake-facing cabins. The on-site country-style restaurant serves lunch and dinner.
##### ANGEL FIRE
Some love it, others hate it. But regardless, it remains one of New Mexico's more popular ski resorts. In summer a slew of hippie festivals draw baked refugees from lower elevations. No one can question the beauty of the surrounding mountains and valleys, and famous northern New Mexico light – even if the town looks a bit like time-share condo-land.
As if the 2077ft vertical drop and 450 acres of trails weren't enough, Angel Fire Resort ( 800-633-7463; www.angelfireresort.com; NM 434; half-/full-day lift ticket $48/64; ) allows snowbiking (on bikes with skis) and snowskating (on skateboards without wheels), along with tamer pursuits like snowshoeing. There's a ski park just for kids, making this one serious winter wonderland.
The resort also boasts a Chris Gunnarson-designed, 400ft-long, competition-quality half-pipe with a wicked 26% grade, plus a couple of terrain parks.
In warmer weather golfers can test their skills on one of the highest-altitude 18-hole courses (green fees from $45; dawn-dusk May–mid-Oct) in the USA.
###### Sleeping & Eating
NM 434, or Mountain View Blvd as it is known in town, is the main drag through Angel Fire and has a couple of places to stay not listed here.
Lodge at Angel Fire LODGE $$
( 800-633-7463; www.angelfireresort.com; NM 434; r $100-165; ) Families will really dig the ski resort's lodging option. The resort organizes loads of children's activities, especially in summertime, and also offers family-oriented packages. If you don't have the kids, it's still a nice place, with a ski-chalet style. The concierge can arrange everything from golf to horseback riding, plus it's big enough to not feel like kid central if you're not traveling with children. Three on-site restaurants mean you won't go hungry. Multinight stays are often required.
Elkhorn Lodge LODGE $$
( 575-377-2811; www.elkhornlodgenm.com; 3377 NM 434; r $100-250; ) This place has a central location, decks off all rooms, and suites that sleep six and have kitchenettes. The Equestrian Center gives lessons and trail rides. Rates drop in the off-season.
Willie's Smokehouse & Grill BARBECUE $$
(Pinewood Plaza, 3453 Mountain View Blvd; mains $9-12; 11am-8pm Mon-Sat) Head here for barbecued chicken, beef and pork, but if you want to do like the locals, order the burrito grande ($7); it's huge and delicious.
Roasted Clove MODERN AMERICAN $$$
( 575-377-0636; www.roastedclove.com; 48 N Angel Fire Rd; mains $17-35; 5-9pm Wed-Mon) This long-established restaurant is everyone's favorite for fine dining: from grilled elk tenderloin to the unique Volcano Ahi Stack, and a list of fine wines.
###### Getting There & Around
Angel Fire is strung out along the northern terminus of NM 434, just south of the intersection with US 64. Continue on US 64 through the Carson National Forest back to Taos.
## MORA VALLEY & NORTHEASTERN NEW MEXICO
East of Santa Fe, the lush Sangre de Cristo Mountains give way to high and vast rolling plains. Dusty grasslands stretch to infinity and further – to Texas. Cattle and dinosaur prints dot a landscape punctuated by volcanic cones. Ranching is an economic mainstay, and on many stretches of road you'll see more cattle than cars. You'll probably see herds of bison.
The Santa Fe Trail, along which pioneer settlers rolled in wagon trains, ran from New Mexico to Missouri. You can still see the wagon ruts in some places off I-25 between Santa Fe and Raton. For a bit of the Old West without a patina of consumer hype, this is the place.
### SCENIC DRIVE: CAPULIN VOLCANO & FOLSOM MAN TERRITORY
A 50-mile loop through the high mountain plains above Raton, the Capulin Volcano and Folsom Man Territory Scenic Drive isn't just another stretch of pavement – it's also a history lesson (with volcanoes, which alone should be enticement enough to excite the kids).
America's most important archaeological discovery was made near the tiny town of Folsom, about 40 miles east of Raton. In 1908, George McJunkin, a local cowboy, noticed some strange bones in Wild Horse Arroyo. Cowboy that he was, he knew that these were no ordinary cattle bones. And so he kept them, suspecting correctly that they were bones from an extinct species of bison. McJunkin spoke of his find to various people, but it wasn't until 1926–28 that the site was properly excavated, first by fossil bone expert Jesse Figgins and then by others.
Until that time, scientists thought that humans had inhabited North America for, at most, 4000 years. With this single find, the facts about the continent's ancient inhabitants had to be completely revised. Subsequent excavations found stone arrowheads in association with extinct bison bones dating from 8000 BC, thus proving that people had lived here for at least that long. These Paleo-Indians became known as Folsom Man.
Recent dating techniques suggest that these artifacts are 10,800 years old, among the oldest discovered on the continent, although it is clear that people have lived in the Americas for even longer.
The area is also known for its volcanoes. Rising 1300ft above the surrounding plains, Capulin Volcano National Monument is the easiest to visit. From the visitor center (www.nps.gov/cavo; per vehicle $5; 8am-4pm), a 2-mile road winds precariously up the mountain to the crater rim (which is at 8182ft). There, a quarter-mile trail drops into the crater and a mile-long trail follows the rim. The entrance is 3 miles north of Capulin, which is 30 miles east of Raton on Hwy 87.
### Raton & Around
Though Raton isn't a big tourist destination, the well-preserved town will hold your attention for a short stroll. It was founded with the arrival of the railroad in 1879 and quickly grew into an important railway stop and mining and ranching center. The small historic district along 1st, 2nd and 3rd Sts (between Clark and Rio Grande Aves) harbors over two dozen buildings, including the Shuler Theater (131 N 2nd St), with an elaborate European rococo interior. Its foyer is graced with eight murals painted during the New Deal (1930s) by Manville Chapman, depicting the region's history from 1845 to 1895.
The International Bank (200 S 2nd St) was originally built in 1929 as the Swastika Hotel. Note the reversed swastika signs (a Native American symbol of good luck) on top. During WWII they were covered with tarp and the hotel changed its name in 1943. For more on local history, visit the Raton Museum (www.ratonmuseum.org; 108 S 2nd St; admission free; 10am-4pm Wed-Sat Sep-Apr, 9am-5pm Tue-Sat May-Aug).
Locals rave about the Oasis Restaurant (1445 S 2nd St; mains $5-15; 6am-8pm, to 8:30 in summer) for breakfast, burgers and burritos. For the best coffee and wi-fi, find Enchanted Grounds (111 Park Ave; 7:30am-4:30pm Tue-Sat; to 2pm Mon; ). There are a string of mom-and-pop motels on 2nd St, while the national chain hotels gather on Hwy 64. But the best place to stay is Sugarite Canyon State Park (www.nmparks.com; NM 526; tent/RV sites $8/14), 10 miles northeast of town in the pretty meadows and forests of the Rocky Mountain foothills. In winter, the 7800ft elevation is perfect for cross-country skiing. In summer, 15 miles of hiking trails begin from a half-mile nature trail. To reach it, take Hwy 72 east out of Raton, then turn north onto Hwy 526; it's signposted about 7 miles north of here.
Forty miles west of Raton is the splendidly sprawling Vermejo Park Ranch ( 575-445-3097; www.vermejoparkranch.com; Hwy 555; r per person incl meals $550; ), 920 sq miles of forests and meadows and mesas maintained by Ted Turner as a premier fishing and hunting lodge. If you're not into killing things, guests can also take wildlife-watching and photography tours, or ride a horse through classic Western terrain.
#### Information
The visitor center (www.raton.info; Clayton Rd; 8am-5pm Mon-Fri) has statewide information.
#### Getting There & Away
Raton is right on I-25, 8 miles south of the Colorado border. It is best reached by private vehicle. Note that during winter snowstorms, Raton Pass (just north of town) can be shut down, which means you may well be stranded in Raton for a night if you're trying to get to Colorado.
### Clayton & Around
Ranches and prairie grasses surround Clayton, a quiet town with a sleepy Western feel on the Texas border. Near the Bravo Dome CO₂ Field (the world's largest natural deposit of carbon dioxide gas), Clayton is where infamous train robber Black Jack Ketchum was caught and hanged in 1901. The Herzstein Memorial Museum ( 575-374-2977; Methodist Episcopal Church, 2nd St at Walnut St; admission free; 10am-5pm Tue-Sun) tells the story.
If you're moseying about these parts, you'll find over 500 dinosaur footprints of eight different species at Clayton Lake State Park (www.nmparks.com; Hwy 370; day-use per vehicle $5, tent/RV sites $8/14), 12 miles northwest of Clayton. The pretty lake is also a good spot for swimming and camping.
Sometimes when you're in the mood for a detour to nowhere, there's nowhere to go. Not true here. Southwest of Clayton, in the most sparsely populated county in New Mexico, the Kiowa National Grasslands consist of high-plains ranchland – endless, vast and lonely. Farmed throughout the early 20th century, the soil suffered from poor agricultural techniques and it became useless, essentially blowing away during the dust-bowl years of the 1930s. The most visited section (though visitors are scarce) is Mills Canyon, north of Roy (with only a gas station and grocery store). About 10 miles northwest of Roy on Hwy 39, a signposted dirt road heads west another 10 miles to the Mills Camping Area, with free primitive camping but no drinking water. The Canadian River forms a small gorge here and the area is quite scenic.
For a meal, a drink, or a good night's sleep you can't do better in these parts than the 1890 Hotel Eklund ( 575-374-2551; www.hoteleklund.com; 15 Main St; r from $75; ). The new owners, Clayton locals, recently made much needed renovations while staying faithful to the original feel of the inn, including the elegant dining room and the Old West saloon with its beautifully carved bar. Call or check online for rates.
### Cimarron
Cimarron has a wild past. It once served as a stop on the Santa Fe Trail, and a hangout for gunslingers, train robbers, desperadoes, lawmen and other Wild West figures like Kit Carson, Buffalo Bill Cody, Annie Oakley, Wyatt Earp, Jesse James and Doc Holliday. The old St James Hotel alone saw the deaths of 26 men within its walls.
Today, Cimarron is a peaceful and serene village with few street signs. Poke around to find what you need, or ask the friendly locals. The town is on Hwy 64, 41 miles southwest of Raton and 54 winding miles east of Taos. The chamber of commerce (www.cimarronnm.com; 104 Lincoln St) has an up-to-date website.
Most historic buildings lie south of the Cimarron River on Hwy 21, including the old town plaza, Dold Trading Post, the Santa Fe Trail Inn (which dates to 1854), Schwenk's Gambling Hall, a Wells Fargo Station and the old jail (1872).
Also here is the St James Hotel ( 888-376-2664; www.exstjames.com; 617 Collison St; r $70-120; ). A saloon since 1873, this well-known place was converted into a hotel in 1880 and renovated 100 years later. It's said to be so haunted that one of the rooms is never rented out. The 10 modern rooms are nice, but it's the authentic period rooms that make this one of the most historic-feeling hotels in New Mexico. Within the hotel, you'll find a decent midrange restaurant and a bar with a pool table.
Get away from it all by booking some time at the Casa del Gavilan ( 575-376-2246, 800-428-4526; www.casadelgavilan.com; Hwy 21; r incl breakfast $94-154; ). Set on 225 acres, it's a magnificent Pueblo Revival–style house built around 1908. The four double rooms are decorated with Southwestern antiques and art and come complete with high ceilings, vigas and thick adobe walls; the house is a treat. A two-room guesthouse sleeps up to four people.
Between Cimarron and Casa del Gavilan, Hwy 21 passes through the Philmont Scout Ranch (www.philmontscoutranch.org). The largest Boy Scout camp in the country, it spreads out over 137,000 acres along the breathtaking eastern slope of the Sangre de Cristos. While you need to be a Scout to trek the trails, anyone can drop into the Philmont Museum (admission free; 8am-5pm Mon-Sat) or tour Villa Philmonte ( 575-376-1136; suggested donation $5; 10:30am & 2:30pm Mon-Fri Apr-Oct), the Spanish Mediterranean mansion built in 1927 by Waite Phillips, the oil baron who was Philmont's original benefactor. Pick up outdoor gear and all sorts of Philmont-related souvenirs, some of which are actually pretty cool, at Tooth of Time Traders ( 7:30am-6:30pm Jun-Aug, 8am-5pm Sep-May).
### MORA VALLEY
This scenic agricultural valley is known throughout northern New Mexico as an enclave where traditional Hispanic ways still remain strong. It was the real-life model for the setting of Frank Waters' novel, _People of the Valley;_ it's also one of the poorest nooks in the state, where over 25% of families live below the poverty line. The town of Mora is the hub of the valley, with small communities strung out to the east and west along Hwy 518.
Kids love visiting the Victory Ranch ( 575-387-2254; www.victoryranch.com; Hwy 434; adult/child $5/3; 10am-4pm, closed Jan-Mar 15; ), 1 mile north of Mora, where you can hand-feed the cute and fluffy herds of alpacas, shop for alpaca wool gifts and even watch a shearing if you time it right (early June).
On Mora's main drag, stop into Tapetes de Lana Weaving Center (www.tapetesdelana.com; Hwy 518, at Hwy 434; 9am-4pm, closed Sat in winter), where you can see handlooms in action, browse for handmade rugs and buy yarns that are spun and dyed on site. In back is one of the few active wool mills in the U.S.; tours (per person $5; 9am-3pm Mon-Fri) are possible.
Three miles west of Mora on Hwy 518 is the Cleveland Roller Mill Historical Museum (www.clevelandrollermillmuseum.com; adult/child $2/1; 10am-3pm, Sat & Sun summer only), housed in a functional 19th-century flour mill – a beautiful old adobe and stone structure with gears and cogs and pulleys inside.
Six miles east of Mora, the Salman Ranch at La Cueva ( 866-281-1515; Hwy 518, at Hwy 442; 10am-4pm Tue-Sun in season; ) is famous for its acres of pesticide-free raspberry fields, where you can pick your own for $5 a pound. Picking season usually runs from mid-August to mid-October (subject to weather). If you're passing by in off-season, you can still stop by the ranch store and take a look at La Cueva Mill ( 9am-4pm Thu-Mon Jan-May, to 5pm daily Jun-Dec), a National Historic Site and one of the best-preserved examples of 19th-century industrial adobe buildings.
Getting hungry? Hit Little Alaska (Hwy 518; mains $5-7; 11am-6pm Sun-Thu) in Mora, specializing in barbeque, enchiladas and ice cream. For some of the best tamales ever (plus burgers, burritos and more), served in a friendly local joint, head 6 miles west of Mora to the village of Holman, where you'll find Casa de Teresa's Tamales (Hwy 518; mains $5-7; 8am-5pm Mon-Sat, Sun in summer).
Heading to or from Las Vegas, consider taking Hwy 94, a ridiculously scenic stretch of road, which passes old adobe farmhouses and Morphy Lake State Park (www.nmparks.com; per vehicle $5, tent/RV sites $8/10), with picnic tables, trout fishing and camping, but no drinking water.
### Las Vegas & Around
Long before they were discovering carnal pleasures in Las Vegas, NV they were dishing it out in the bordellos of America's original sin city, Las Vegas, NM. Home to the Comanche people for some 10,000 years, the city was established by the Mexican government in 1835, just in time to serve as a stop along the Santa Fe Trail and later the Santa Fe Railroad. It quickly grew into one of the biggest, baddest boomtowns in the West, and in 1846 the USA took possession of it. Nineteenth-century Las Vegas was a true-blue outlaw town, a place where Billy the Kid held court with his pal Vicente Silva (leader of the Society of Bandits – the roughest, toughestgang in New Mexico) and Doc Holliday owned a saloon (although ultimately his business failed because he kept shooting at the customers).
A century and a half later, there's still the occasional shoot-out, but Las Vegas has grown into a place of faded charm with a lively social swirl (most of it radiating from its two small universities) that feels much more like a small town than New Mexico's third-largest city. More than 900 historic buildings grace its quaint downtown that's served as a Western backdrop for many a Hollywood picture; _Wyatt Earp_ , _The Ballad of Gregorio Cortez_ and Oscar-winner _No Country for Old Men_ are just a few of the movies filmed here. Las Vegas also serves as gateway to the southeastern corner of the Pecos Wilderness (Click here) and to Las Vegas National Wildlife Refuge.
#### Sights & Activities
Hwy 85, or Grand Ave, which runs north–south, parallels the interstate and is the main thoroughfare. The center of the historic district is the Old Town Plaza.
##### LAS VEGAS
The chamber of commerce publishes walking tours of various historic districts and beautiful neighborhoods surrounding the plaza and Bridge St. Around the historic center, note the lovely Plaza Hotel; it was built in 1880 and is still in use.
City of Las Vegas Museum &
Rough Rider Memorial Collection MUSEUM
(727 Grand Ave; 10am-4pm Tue-Sat) This small but informative museum chronicles the fabled cavalry unit led by future US president Theodore Roosevelt in the 1898 fight for Cuba. More than one-third of the volunteer force came from New Mexico, and in this museum you'll see their furniture, clothes and military regalia. You can even download stories about the Rough Riders on to your MP3 player.
Santa Fe Trail Interpretive Center MUSEUM
(116 Bridge St; 10am-3pm Mon-Sat) At this interpretive center, the local historical society displays an impressive collection of old photos and artifacts from Las Vegas' heyday as a rough-and-tumble trading post on the Santa Fe Trail. Guided tours are available.
##### AROUND LAS VEGAS
Montezuma HOT SPRING
Five miles northwest of Las Vegas on Hwy 65, this little area is dominated by Montezuma Castle, built in 1886 as a luxury hotel. It's now the United World College of the West. Along the road there, you can soak in a series of natural hot spring pools. Bring a swimsuit and test the water – some are scalding hot! Don't miss the Dwan Light Sanctuary (admission free; 6am-10pm) on the school campus, a meditation chamber where prisms in the walls cast rainbows inside during daylight hours.
Santa Fe National Forest OUTDOORS
(www.fs.fed.us/r3/sfe) Continue past Montezuma, and Hwy 65 will take you to the eastern edge of the forest, where trails lead into the Pecos Wilderness. The most popular day hike in the area starts at El Porvenir campground (tent/RV sites $8, no hookups) and follows trail 223 to the 10,160ft summit of Hermit Peak . It's a 10-mile round-trip; sections of the trail switchback steeply and might be a little unnerving if you're prone to vertigo. The peak itself is flat, with amazing views. For more info on hiking, stop into the ranger station, which has topo maps and free trail guides.
Las Vegas National
Wildlife Refuge WILDLIFE RESERVE
(Rte 1; dawn-dusk) Five miles southeast of Las Vegas on Hwys 104 and 67, this 14-sq-mile refuge has marshes, woodlands and grasslands to which upwards of 250 bird species have found their way. Visitors can follow a 7-mile drive and walking trails.
Villanueva State Park OUTDOORS
(www.nmparks.com; day-use per vehicle $5, tent/RV sites $8/14) This pretty state park, about 35 miles south of Las Vegas, lies in a red rock canyon on the Rio Pecos valley. A small visitor center and self-guided trails explain the area's history: it was once a main travel route for Native Americans and, in the 1500s, for the Spanish conquistadors. Head south on I-25 for 22 miles, then take Hwy 3 south for 12 miles. A campground is open April to October.
Villanueva & San Miguel HISTORIC SITE
Along Hwy 3 are the Spanish colonial villages of Villanueva and San Miguel (the latter with a fine church built in 1805), surrounded by vineyards belonging to the Madison Winery (www.madisonvineyards.com;Hwy 3; noon-6pm Wed-Sun), which has a tasting room. While here, don't miss La Risa (www.thelarisacafe.com; Hwy 3; mains $8-13; 11am-8pm Thu-Sat, 8am-6pm Sun; ), a gourmet anomaly in the middle of nowhere, with homemade desserts, breads and pastries.
#### Festivals & Events
The four-day party surrounding the Fourth of July is a colorful mix of festivities that includes Mexican folk music, dancing and mariachi bands. Other events include the San Miguel County Fair on the third weekend in August and a Harvest Festival, on the third Saturday of September, with music and food.
#### Sleeping
Plaza Hotel HOTEL $
( 505-425-3591, 800-328-1882; www.plazahotel-nm.com; 230 Old Town Plaza; r incl breakfast from $79; ) This is Las Vegas' most celebratedand historic lodging, and it's also a decent value. It was opened in 1882 and carefully remodeled a century later; architectural details abound. Recently expanded, it now offers 72 comfortable rooms. Choose between Victorian-style, antique-filled rooms in the original building or bright, monochromatic, kind of sterile rooms in the new adjoining wing.
Sunshine Motel MOTEL $
( 505-425-3506; 1201 N Grand Ave; r from $35; ) One of the better budget choices on Grand Ave, rooms at this simple motel recently got a fresh coat of paint. It's no-frills but clean, and the owners are friendly.
#### Eating
Estella's Café NEW MEXICAN $
(148 Bridge St; mains $6-12; 11am-3pm Mon-Wed, 11am-8pm Thu-Fri, 10am-3pm Sat) Talk about stepping back in time – this is a classic localdiner. Devoted patrons come for the homemade red chile, _menudo_ (tripe soup) and scrumptious enchiladas. Owned by the Gonzalez family since 1950, this crowded gem is the best place in town for simple and tasty New Mexican food.
Charlie's Spic & Span Bakery & Café DINER $
(715 Douglas Ave; mains $7-11; 6:30am-5:30pm Mon-Fri, 7am-5pm Sat, 7am-3pm Sun; ) This Las Vegas institution has listened to the town's gossip for half a century now, and it remains the place for locals to hang out and catch up over a cup of coffee (or vanilla latte) and New Mexican diner fare. Think bean-and-cheese-stuffed _sopaipillas_ (fried dough), pancake sandwiches and good old-fashioned hamburgers. Save room for dessert.
World Treasures Traveler's Café CAFE $
(1814 Plaza St; snacks $3-6; 7am-6:30pm Mon, Tue & Sat, 7am-9pm Wed-Fri, 9am-3pm Sun; ) This coffee-and-sandwich shop housed in a weaving gallery is oriented towards international travelers and locals alike, with wi-fi, a book exchange, board games and couches.
Landmark Grill AMERICAN $$
(Plaza Hotel; 230 Plaza; mains $7-24; 7am-2pm & 5-9pm) Inside the Plaza Hotel, this is the most upscale restaurant in town, yet it remains down to earth. There's something for almost everyone on the diverse menu, though vegetarians may be limited to salads.
#### Drinking & Entertainment
Cafes and coffee shops on Bridge St may have poetry readings or folk music.
Byron T Saloon BAR
(Plaza Hotel; 230 Old Town Plaza) Within the Plaza Hotel, this bar hosts live jazz, blues and country music on weekends.
Fort Union Drive-In CINEMA
( 505-425-9934; 3300 7th St; per car $12; Fri-Sun May-Sep) One of New Mexico's few remaining drive-in movie theaters lies just north of town and has great views of the surrounding high desert. Call for showtimes.
#### Information
Visitor Center ( 800-832-5947; www.lasvegasnewmexico.com; 500 Railroad Ave; 10am-5pm Mon-Fri, 11am-4pm Sat & Sun mid-Oct–Apr, extended hours May–mid-Oct)
Alta Vista Regional Hospital ( 505-426-3500; 104 Legion Dr; 24hr emergency)
Police ( 505-425-7504; 318 Moreno)
Santa Fe National Forest Ranger Station ( 505-425-3534; 1926 7th St; 8am-5pm Mon-Fri)
#### Getting There & Around
Las Vegas is located on I-25, 65 miles east of Santa Fe. Autobuses Americanos ( 505-425-8387; www.autobusesamericanos.us; 1901 W Grand) stop at Pino's Truck Stop several times a day on their way to Raton and Albuquerque.
Amtrak ( 800-872-7245; www.amtrak.com) operates the _Southwest Chief_ , which runs between Chicago and Los Angeles. It stops in Las Vegas daily at 12:40pm westbound, 3:58pm eastbound.
## CHACO CANYON & NORTHWESTERN NEW MEXICO
New Mexico's wild northwest is home to wide-open, empty spaces. It is still dubbed 'Indian Country,' and for good reason: huge swaths of land fall under the aegis of the Navajo, Zuni, Acoma, Apache and Laguna tribes. This portion of New Mexico showcases remarkable ancient Indian sites alongside modern, solitary Native American settlements. And when you've had your fill of culture, you can ride a historic narrow-gauge railroad through the mountains, hike around some trippy badlands, or cast for huge trout.
### Chama
Eight miles south of the Colorado border, little Chama is tucked into a lush valley that's carved into Rocky Mountain foothills. Native Americans lived and hunted here for centuries, and Spanish farmers settled the Chama River Valley in the mid-1700s, but it was the arrival of the Denver & Rio Grande Railroad in 1880 that really put Chama on the map. Although the railroad closed, the prettiest part still operates as one of the most scenic train trips in the American West.
#### Sights & Activities
Cumbres & Toltec Scenic Railway TRAIN RIDE
( 575-756-2151; www.cumbresandtoltec.com; adult/child $91/50; late May–mid-Oct) This railway is both the longest (64 miles) and highest (over the 10,015ft-high Cumbres Pass) authentic narrow-gauge steam railroad in the USA. The train runs between Chama and Antonito and is a beautiful trip, through mountains, canyons and high desert. It's at its finest in September and October, when the aspens are ashimmer with golden leaves. Some carriages are fully enclosed, but none are heated, so dress warmly. Whatever you do, make reservations two weeks in advance. There is a snack bar and rest room on board, and the train makes a lunch stop in Osier.
Chama Ski Service SKIING
( 575-756-2492; www.cvn.com/~porters) This place can outfit you with skis and provide information on ski touring. It also provides backcountry touring equipment, including snowshoe rentals.
Cumbres Nordic Adventures SKIING
( 575-756-2746; www.yurtsogood.com) Offers backcountry ski tours in the snowy San Juan Mountains and deluxe backcountry yurt rentals for $109 to $140 per night.
#### Festivals & Events
Chama has a few events worth dropping in for, including the Chama Chile Classic Cross-Country Ski Race (www.chamaski.com; early or mid-February), which attracts hundreds of competitors to 3.1-mile and 6.2-mile races; the Chama Valley Music Festival (every Friday and Saturdayin July), which features national and international acts; and Chama Days (early August), which features a rodeo, firefighters' water fight and chile cook-off.
#### Sleeping & Eating
Elkhorn Lodge & Café CABIN $$
( 575-756-2105; www.elkhornlodge.net; Hwy 84; r from $80, cabins from $90; ) On the banks of the Rio Chama, Elkhorn offers blue-ribbon fly-fishing spots, chuckwagon barbecue dinners and old-time cowboy dances. Choose a simple but spacious motel room in the main log cabin or a freestanding cabin with a kitchenette (especially great for families).
Chama Trails Inn MOTEL $
( 575-756-2156; www.chamatrailsinn.com; 2362 Hwy 17; r from $75; ) This is more than another roadside motel, with 16 character-packed rooms with an abundance of handmade Southwestern furniture, local artwork and hand-painted tiles. A few rooms are further warmed with a gas fireplace. A communal hot tub and sauna come in handy after hiking.
Foster Hotel HISTORIC HOTEL $
( 575-756-2296; www.fosters1881.com; 393 S Terrace Ave; s/d $55/65) If you're looking for local culture, look no further. Built in 1881 as a bordello, the hotel is the only building in Chama that wasn't wiped out by a massive fire in the 1920s. A few of the rooms are said to be so haunted that the doors are locked shut. The others are a bit rough around the edges, so stay for the experience, not for luxury.
High Country Restaurant & Saloon STEAKHOUSE $$
(2289 S Hwy 17; mains $5-23; 11am-10pm Mon-Sat, 8am-10pm Sun) This Wild West saloon dishes up burgers, New Mexican food, steak and seafood. It's probably the best all-round eating bet in town.
### SCENIC DRIVE: CHAMA TO TAOS
This nearly 100-mile route makes a fabulous, scenic way to get between Chama and Taos from late May through the first snows in mid-October. The best time for the drive is late September or early October, when the leaves are turning.
From Chama, take Hwy 84/64 about 11 miles south to see the spectacular cliffs in scenic Brazos Canyon. Just south of Los Brazos in Los Ojos, don't miss a visit to the famous Tierra Wools ( 575-588-7231, 888-709-0979; www.handweavers.com; 91 Main St; r $65-85), a 100-year-old weaving cooperative in a rustic, century-old building. On weekends, village artisans carry on the Hispanic weaving tradition, with hand-spinning, dyeing and weaving. In addition to a two-bedroom guesthouse, Tierra Wools also offers weaving classes (April to October).
From tiny TA (as Tierra Amarilla is locally know), head east on scenic Hwy 64 over a 10,000ft pass in the Tusas Mountains to Taos, 80 miles away.
#### Getting There & Away
Downtown is 1.5 miles north of the so-called Y-junction of Hwy 84/64 and Hwy 17. Hwy 17 heads north toward Antonito, CO. Hwy 84/64 heads west toward Farmington and Pagosa Springs, CO.
### Jicarilla Apache Indian Reservation
The Apache were relatively late arrivals in the Southwest, migrating from the north in the 14th century. This hawkish group was known to use warlike ways to get what they wanted from the more peaceful Pueblo peoples already living here. Indeed, the Zuni Indian word for 'enemy,' _apachu,_ led to the Apache's present name. Jicarilla (pronounced hic-a- _ree_ -ya) means 'little basket,' reflecting their great skill in basket weaving and other crafts. Apache crafts generally draw visitors to the 1360-sq-mile reservation (www.jicarillaonline.com), home to about 3200 people.
Tiny Dulce, on Hwy 64 in the northern part of the reservation, is the tribal capital. Unlike at most reservations, alcohol is available. No permits or fees are needed to drive through the reservation, and photography is permitted. The Little Beaver Celebration, which includes a rodeo, pow-wow and Spam-carving contest, is held the third weekend of July.
### Navajo Dam
Trout are jumpin' and visitors are floating. Navajo Lake, which stretches over 30 miles northeast and across into Colorado, was created by damming the San Juan River. At the base of the dam, there's world-class trout fishing. You can fish year-round, but a series of designated zones, each with different regulations, protect the stocks.
The tiny community of Navajo Dam has several outfitters providing equipment, information and guided trips. Talk to the folks at Born-n-Raised on the San Juan River, Inc ( 505-632-2194; www.sanjuanriver.com; Hwy 173; half-day/full day from $235/315), based at Abe's Motel & Fly Shop; the guy who started these personalized trips – he now has guides working for him – has been fishing the San Juan since he was a child. The more people in your group, the cheaper the trip.
River floating is also popular around here. Rent boats at the Navajo Lake Marina ( 505-632-3245; www.navajomarina.com) or the Sims Mesa Marina ( 505-320-0885; www.simsmarina.com) and put in at the Texas Hole parking lot at milepost 12 on Hwy 511. Then lazily float 2.5 miles to Crusher Hole. Ahhh.
The Enchanted Hideaway Lodge ( 505-632-2634; www.enchantedhideawaylodge.com; Hwy 173; ste from $65; ) rents a couple of drift boats ($125 per day). You can also stay the night. It's a friendly and low-key place with several highly recommended and pleasant suites as well as a private house and condos with kitchens and gas grills. The spacious Stone House, with a heavenly outdoor hot tub set in a grove of trees, is particularly nice; fisherfolk on a budget can stay in the cost-effective Fly Room.
Anglers can also try the Soaring Eagle Lodge ( 800-866-2719; www.soaringeaglelodge.net; Hwy 173; r incl breakfast from $140; ), which offers multinight guided fishing tours and half- and full-board options (perfect for those wanting to devote all their waking hours to fishing). Nestled under the cliffs against the river, this beautiful and peaceful place has simple suites with kitchenettes. Try to get one of the units right on the river.
Visit El Pescador (Hwy 173; mains $5-12; 11am-8pm) for standard, but decent, Mexican and American fare.
There are a few campgrounds (www.nmparks.com; tent/RV sites $8/14) along the river. The biggest one is Pine River, just past the dam on Hwy 511, with a visitor center and marina. About 10 miles south of the lake, Cottonwood Campground (Hwy 511) occupies a lovely spot under the cottonwoods on the river. It has drinking water and toilets but no showers.
### Aztec
Although Aztec is primarily on the traveler's map because of the reconstructed Great Kiva at Aztec Ruins, the old downtown has several interesting turn-of-the-19th-century buildings, many on the National Register of Historic Places. The quaint downtown area is along Main St.
An alternative to the bigger and more visited sites like Chaco Culture National Historical Park and Mesa Verde National Park, the 27-acre Aztec Ruins National Monument (www.nps.gov/azru; admission $5; 8am-5pm Sep-May, to 6pm Jun-Aug) features the largest reconstructed kiva in the country, with an internal diameter of almost 50ft, originally built around AD 1100. Let your imagination wander as you sit inside the Great Kiva. Rangers give early-afternoon talks about ancient architecture, trade routes and astronomy during the summer months.
The small but excellent Aztec Museum & Pioneer Village (www.aztecmuseum.org; 125 N Main Ave; admission free; 10am-4pm Tue-Sat) features an eclectic collection of historical objects, including telephones, barbershop chairs and a great display of late-19th-century regional photographs. Outside, a small 'pioneer village' has original and replica early buildings, such as a church, jail and bank.
The annual Aztec Fiesta Days (first weekend in June) has arts and crafts, food booths and a bonfire during which 'Old Man Gloom' is burned to celebrate the beginning of summer.
If you're into river sports, check out the seconds at Jack's Plastic Welding (www.jpwinc.com; 115 S Main Ave) for good deals on slightly imperfect dry bags and Paco Pads (camping mattresses).
Calling itself Wonderful House (115 W Aztec Blvd; mains $8-15; 11am-9pm Tue-Sun) may be overstating things, but this Chinese restaurant sure is popular. Next door is the best place to stay in Aztec, the Step Back Inn ( 505-334-1200; www.stepbackinn.com; 123 W Aztec Blvd; r from $72; ), with Victorian-style rooms.
If you need more info, try the helpful visitor center ( 888-838-9551; www.aztecnm.com; 110 N Ash St; 8am-5pm Mon-Fri).
Hwy 516 from Farmington becomes Aztec Blvd in town and continues as Hwy 550, to Durango, Colorado. Turn on to Hwy 173 for Navajo Dam State Park.
### Farmington & Around
Well sited for an overnight stay, the region's largest town serves as an OK base for excursions to nearby sites. Farmington itself has nice some parkland on the San Juan River, a quaint downtown and some good trading posts, but most visitors hang around because they're passing through on their way to Monument Valley (on the Arizona–Utah border) or visiting the remote and beautiful Chaco Culture National Historical Park, located about two hours' drive south of Farmington.
#### Sights & Activities
Shiprock MOUNTAIN
The coolest sight around these parts by far is outside of Farmington proper. Shiprock, a 1700ft-high volcanic plug and a lofty landmark for Anglo pioneers, is also a sacred site to the Navajo. It rises eerily over the landscape west of Farmington. It's certainly visible from Hwy 64, but there are better views from Hwy 491. (Formerly Hwy 666, this stretch of road had a starring role in Oliver Stone's _Natural Born Killers_ ). Indian Hwy 13, which almost skirts its base, is another good photo-op area.
Salmon Ruin & Heritage Park RUIN
(adult/child $3/1; 8am-5pm Mon-Fri, 9am-5pm Sat & Sun) Off of Hwy 64 between Bloomfield and Farmington, the ancient Pueblo that's now a heritage park features a large village built by the Chaco people in the early 1100s. Abandoned, resettled by people from Mesa Verde and again abandoned before 1300, the site also includes the remains of a homestead, petroglyphs, a Navajo hogan and a wickiup (a rough brushwood shelter). Take Hwy 64 east 11 miles toward Bloomfield.
Farmington Museum at Gateway Park MUSEUM
(www.farmingtonmuseum.org; 3041 E Main St; suggested donation $2; 8am-5pm Mon-Sat) Farmington itself won't hold your attention for long, but if you need something to do, then this museum is the most worthy pause. It mounts national and juried regional art shows, and houses a permanent exhibit on the cultures and history of Farmington.
Bisti Badlands HIKING
One of the weirdest microenvironments in New Mexico is 38 miles south of Farmington, off Hwy 371. The Bisti Badlands, part of the Bisti/De-Na-Zin Wilderness Area, is an undeveloped realm of multicolored hoodoos, sculpted cliffs and balancing rocks. From the parking area, you have to follow the beaten (but unmaintained) path for at least a mile before getting into the heart of the formations, then just wander as you will, taking care not to damage the fragile geology. The hours just after sunrise and before sunset are most spectacular. Overnight camping is allowed, but you have to haul in all your water. The Farmington BLM office ( 505-599-8900; www.nm.blm.gov; 1235 La Plata Hwy; 8am-4:30pm Mon-Fri) has information.
### FINDING NAVAJO RUGS
Sure, Navajo rugs are sold at galleries in a number of New Mexican cities and towns, but why not have a little adventure and look for some near where the best weavers live? About 35 miles south of Shiprock, tucked into the eastern flank of the Chuska Mountains, the villages of Two Grey Hills and Toadlena are renowned as the sources of the finest rugs anywhere in Navajo country. Weavers from this area have largely rejected commercially produced wool and synthetic dyes, preferring the wool of their own sheep in its natural hues. They card white, brown, grey and black hairs together, blending the colors to the desired effect, then they spin and weave the wool – tight – into mesmerizing geometric patterns. The Toadlena Trading Post ( 888-420-0005; www.toadlenatradingpost.com), just off Hwy 491 in the town of Newcomb, is the local market where many of these world-class artisans sell their work. Prices range from about $125 to $7000 or more.
Another off-the-beaten-path spot to check out Indian textiles is at the monthly Crownpoint Navajo Rug Auction (www.crownpointrugauction.com; Crownpoint), where you can talk to and buy from the weavers directly. Check the website for dates and driving directions.
#### Festivals & Events
Farmington likes to celebrate.
Invitational Balloon Festival & Riverfest BALLOON
Late May, with music, arts & crafts and food.
Totah Festival CULTURAL
Labor Day weekend, with juried Native American arts and crafts and a Navajo rug auction.
Northern Navajo Reservation Fair CULTURAL
Held in Shiprock in early October, featuring a rodeo, powwow and traditional dancing. This fair is perhaps the most traditional of the large Native American gatherings and begins with the Night Way, a complex Navajo healing ceremony, and the Yei Bei Chei chant, which lasts for several days.
#### Sleeping
There's every chain hotel imaginable around the crossroads of Broadway and Scott Ave.
Kokopelli's Cave QUIRKY $$$
( 505-860-3812; www.bbonline.com/nm/kokopelli; r from $260) For something truly unique, sleep 70ft below the ground in this incredible 1650-sq-ft cave carved from La Plata River sandstone. Equipped with a kitchen stocked for breakfast and lunch, a DVD player with DVDs and a hot tub, this spacious cave dwelling offers magnificent views over the desert and river. The isolation is magnificent. A 3-mile drive on dirt roads and a short hike is required to reach it.
Silver River Adobe Inn B&B B&B $$
( 575-325-8219, 800-382-9251; www.silveradobe.com; 3151 W Main St; r $115-175; ) Three miles from downtown, this lovely two-room place offers a peaceful respite among the trees on the San Juan River. Fall asleep to the sound of the river, wake to organicblueberry juice and enjoy a morning walk to the prairie-dog village. The additional guesthouse is attractively rustic and is made of adobe and timbers. Advance reservations are required.
#### Eating & Drinking
Three Rivers Eatery & Brewhouse AMERICAN $$
(101 E Main St; mains $8-26; 11am-10pm; ) Managing to be both trendy _and_ kid-friendly, this almost hip spot has good food and its own microbrews. Try the homemade potato skins or artichoke and spinach dip, but keep in mind that the steaks are substantial. Plenty of spiffy sandwiches (like a Thai turkey wrap) and soups (broccoli cheddar) are served at lunchtime.
#### Information
Bureau of Land Management ( 505-599-8900; 1235 La Plata Hwy; 7:45am-4pm Mon-Fri) Take Hwy 64 west across La Plata River and head north on La Plata Hwy.
San Juan Regional Medical Center Hospital ( 505-325-5011; 801 W Maple St)
Visitors Bureau ( 505-326-7602; www.farmingtonnm.org; Farmington Museum at Gateway Park, 3041 E Main St; 8am-5pm Mon-Fri)
#### Getting There & Away
Greyhound ( 505-325-1009; www.greyhound.com; 126 E Main St) has one or two daily buses to Albuquerque ($53, 3½ hours) and Durango, Colorado ($19, 1½ hours).
### CHACO CULTURE NATIONAL HISTORICAL PARK & CUBA
Chaco, the center of a culture that extended far beyond the immediate area, was once a carefully engineered network of 30ft-wide roads. Very little of the road system is easily seen today, but about 450 miles have been identified from aerial photos and ground surveys. Clearly, this was a highly organized and integrated culture.
The park (per vehicle/bike $8/4; 7am-sunset) contains massive and spectacular Puebloan buildings, evidence of 5000 years of human occupation, set in a remote high desert environment. The largest building, Pueblo Bonito, towers four stories tall and may have had 600 to 800 rooms and kivas. None of Chaco's sites have been reconstructed or restored. If you like isolation and using your imagination, few places compare.
All park routes involve rough and unpaved dirt roads, which can become impassable after heavy rains or snow. Park rangers prefer that visitors enter via Hwy 44/550 on the north side. About 3 miles south of the Nageezi Trading Post on Hwy 44/550 and about 50 miles west of Cuba, turn south at mile marker 112.5 on CR 7900, which is paved for 5 miles. Continue on the marked unpaved county road for 16 miles to the park entrance.
Park facilities are minimal – there's no food, gas or supplies. The nearest provisions are along Hwy 44, 21 miles from the visitor center ( 505-786-7014; www.nps.gov/chcu; 8am-5pm), where free backcountry hiking permits (no camping) are available. Inquire here about nighttime astronomy programs (April to October).
Ask at the visitor center (where you can also pick up water – it's the only place where water is available) about directions to the Gallo Campground (campsites $10), which operates on a first-come, first-served basis. There are no hookups, but toilets, grills and picnic tables are available. Bring your own wood or charcoal.
Mountainous Cuba, about 50 miles from the Chaco turnoff, is your closest hotel bet, with a number of motels catering to Chaco visitors on the town's main street.
For something different try the friendly Circle A Ranch Hostel ( 575-289-3350; www.circlearanchhostelry.com; off Hwy 550; dm/r from $25/50; May–mid-Oct). A real gem, this place is set on 360 beautiful acres in the Nacimiento Mountains. The lovely old adobe lodge, which has exposed beams, grassy grounds, hiking trails and a classic kitchen, is a peaceful and relaxing place to hang out. Choose between private bedrooms (some with quilts and iron bedsteads) and shared bunk rooms. Look for the ranch 5 miles north of Cuba at the end of Los Pinos Rd.
### Gallup
The mother town on New Mexico's Mother Road seems stuck in time. Settled in 1881, when the railroad came to town, Gallup had her heyday during the road-tripping 1950s, and many of the dilapidated old hotels, pawn shops and billboards, mixed in with today's galleries and Native American handicraft stores, haven't changed much since the Eisenhower administration.
Just outside the Navajo Reservation, modern-day Gallup is an interesting mix of Anglos and Native Americans; it's not unusual to hear people speaking Navajo on their cell phones while buying groceries at the local Walmart. Gallup's tourism is limited mostly to Route 66 road-trippers and those in search of Native American history. Even with visitors, it's not exactly crowded, and at night it turns downright quiet.
The 'main street of America' (Route 66) runs straight through downtown Gallup's historic district and is lined with pretty, renovated light-red sandstone buildings housing dozens of kitschy souvenir shops and arts and crafts galleries selling Native American wares. Gallup is starting to capitalize on its outdoor attractions, and a growing number of rock climbers and mountain bikers come to challenge their bodies on surrounding sandstone buttes and red mesa tops.
#### Sights
All roads in downtown Gallup dead-end at Route 66, which runs uninterrupted through town – take Exit 20 or 22 from Hwy 40 to access the best of Route 66 downtown.
Historic District NEIGHBORHOOD
Gallup's historic district is lined with about 20 structures of historic and architectural interest, built between 1895 and 1938. Most are located along 1st, 2nd and 3rd Sts between Hwy 66 and Hill Ave and are detailed in a brochure found at the visitor center. Among these is the small Gallup Historical Museum ( 505-863-1363; 300 W Rte 66; admission by donation; 8:30am-3:30pm Mon-Fri), in the renovated,turn-of-the-19th-century Rex Hotel.
El Morro Theatre THEATER
(www.elmorrotheatre.com; 207 W Coal Ave; hours vary). Downtown Gallup's centerpiece is this beautifully restored Spanish Colonial–style theater. Built in 1926 as the town's showcase theatrical house, its renovated interior is comfortably modern. It hosts Saturday movies and children's programs, as well as live theatre, music and dance.
Gallup Cultural Center CULTURAL BUILDING
(www.southwestindian.com; 218 E Rte 66; 8am-5pm) This cultural center houses a small but well-done museum with Indian art, including excellent collections of both contemporary and old kachina dolls, pottery, sand painting and weaving. A 10ft-tall bronze sculpture of a Navajo code-talker honors the sacrifices made by many men of the Navajo Reservation in WWII. A tiny theatre screens films about Chaco Canyon and the Four Corners region. In summer, traditional dances are held nightly at 7pm.
#### Activities
Red Rock Park OUTDOORS
( 8am-4:30pm Mon-Fri, trading post 6:30am-5:30pm) Gallup's gaining a reputation as the kind of outdoors town where you can still get lost on the bike trails should you wish. Read: fewer crowds. Hikers should head 6 miles east of town to beautiful Red Rock State Park. It has a little museum with modern and traditional Indian crafts, a campground and hiking trails. Try the 3-mile round-trip Pyramid Rock trail past amazing rock formations. From the 7487ft summit you can see as far as 50 miles on a clear day.
High Desert Trail System MOUNTAIN BIKING
Mountain bikers can test their skills on the High Desert Trail System, which offers a variety of terrain for different skill levels, including plenty of sick, slick rock – try the loops off the main trail for the most challenging rides. The trail system is 3 miles north of Gallup on Hwy 491 off the Chico/Gamerco Rd. Pick up maps at the tourist office.
Mentmore Rock Climbing Area ROCK CLIMBING
This climbing area lets you challenge yourself with 50 different bolted toprope climbs and some free-climbing areas. Difficulty levelsrange from 5.0 to 5.13 – grab maps and info at the visitor center. You'll need your own gear and to know what you are doing. Reach the park via Exit 16 off I-40; head north on County Rd 1.
### STRETCH YOUR LEGS: GALLUP MURAL WALK
Home to numerous outdoor murals depicting town life throughout the centuries, Gallup is further proof that New Mexico lives and breathes art. Painted over the last 80 years, the murals grace numerous downtown buildings, including the City Hall. Old and new, they showcase Gallup's tricultural and distinctly Southwestern soul.
Gallup's original murals date back to the 1930s and were created during the Depression as part of President Franklin D Roosevelt's WPA program – an initiative to give out-of-work men jobs building and beautifying towns and parks on railway lines across the country. Some of the original murals can still be seen around town – check out the McKinley County Courthouse (213 Coal Ave).
The city takes pride in promoting the outdoor arts, and recently commissioned 12 local artists to paint new murals in central downtown. Nine have been completed and can be viewed on a short mural walk (about 10 blocks total). The murals range from abstract to realist and depict stories of peace and turmoil throughout Gallup's 126-year-old history. Although the murals are large, they don't detract from Gallup's historic aesthetic; rather, they lend a different look to another small, struggling Western town, and take the concept of a public gallery to an entirely different level.
Start your walk at the corner of W Aztec Ave and S 2nd St. The first mural, Great Gallup __ by Paul Newman and Steve Heil, is on the west-facing wall of the City Hall building and uses a variety of media to create a graphic narrative of life in Gallup in panels. Look for locals on horseback in one, and a blue pick-up truck, so laboriously detailed it resembles an old photograph, in another. The Gallup Inter-Tribal Indian Ceremonial Mural by Irving Bahl is our other favorite mural. The last mural on the walk is found on the Ceremonial Building between 2nd and 3rd Sts on Coal Ave. It depicts Native American traditions and sacred Navajo symbols.
#### Festivals & Events
Book accommodations as far ahead as possible during these annual events.
Gallup Inter-Tribal Indian Ceremonial CULTURAL
(www.theceremonial.com) Thousands of Native Americans and non-Indian tourists throng the streets of Gallup and the huge amphitheater at Red Rock State Park in early August for the Inter-Tribal Indian Ceremonial Gallup. The 90-year-old tradition includes a professional all-Indian rodeo, beautifully bedecked ceremonial dancers from many tribes and a powwow with competitive dancing.
Navajo Nation Fair CULTURAL
(first weekend in September) While this huge fair is actually just across the Arizona border in nearby Window Rock (Click here), it feels like it spills over into Gallup – which is a better place to stay.
Lions Club Rodeo CULTURAL
In the third week in June, this is the most professional and prestigious of several area rodeos.
Balloon Rally BALLOON
Almost 200 colorful hot-air balloons take part in demonstrations and competitions at the Balloon Rally at Red Rock State Park in the first weekend in December.
Local Native Americans perform social Indian dances at 7pm nightly from late June to early September at the McKinley County Courthouse.
#### Sleeping
Gallup has a number of chain and independent motels just off I-40 – including a Best Western and Holiday Inn. Follow the billboards or Route 66 outside of downtown for a few miles. A number of the motor lodges from the 1950s have gone out of business, but some are still open, a lot of which are pretty dodgy. Rooms cost between $45 and $125, except during Ceremonial week and other big events, when prices can double.
El Rancho HISTORIC HOTEL $$
( 505-863-9311; www.elranchohotel.com; 1000 E Hwy 66; r from $75; ) Hollywood goes Native American–futuristic at Gallup's best, and only, full-service historic lodging option. This town-center hotel with a neon facade was opened in 1937 and quickly became known as the 'home of the movie stars.' Many of the great actors of the '40s and '50s stayed here, including Humphrey Bogart, Katharine Hepburn and John Wayne, when he was filming Westerns in the area. El Rancho features a superb two-story open lobby decorated in rustic old National Park lodge–style. Rooms are big, bright and decorated with eclectic Old West fashions. The hotel has a restaurant and bar, which sometimes hosts bands. If El Rancho is full, the modern motel next door is under the same ownership. It has less interesting rooms that are a bit cheaper.
Red Rock Park Campground CAMPING $
( 505-722-3839; Churchrock, off Hwy 66; tent/RV sites $15/18; ) Pop your tent up in this beautiful setting with easy access to tons of hiking trails. Six miles east of town, it has showers, flush toilets, drinking water and a grocery store.
#### Eating & Drinking
Gallup is a good town to fill up your stomach –there are a number of restaurants and watering holes. Many restaurants in Gallup do not serve liquor, so choose carefully if having beer with dinner is important.
Coffee House CAFE $
(203 W Coal Ave; mains $4-10; 7am-3pm Mon-Fri, 8am-3pm Sat) With local art on the walls and casual simplicity infusing the space, this is Gallup's quintessential coffee shop. Soups, sandwiches and pastries are all good.
El Rancho Restaurant AMERICAN $$
(1000 E Hwy 66; breakfast & lunch mains $6-12, dinner mains $8-22; 6:30am-10pm; ) The menu here seems to have been created way before the women's rights movement: most of the 'leading lady' dishes at the movie-themed restaurant are of the fruit with sorbet or cottage cheese variety. Boys, you can sink your teeth into a hunk of beef – there are lots of steak and burger choices. Photos of old-time movie stars plaster the walls; heavy furniture dots the landscape. It's straight out of a movie set. The hotel's 49ers Lounge offers drinks in an Old West setting and live music once a month. Stop by for the schedule.
Genaro's Café NEW MEXICAN $
(600 W Hill Ave; mains $6-12; 10:30am-7:30pm Tue-Sat) This small, out-of-the-way place serves large portions of New Mexican food, but no alcohol. If you like your chile hot, you'll feel right at home here, just like the rest of Gallup – this place can get crowded.
Earl's Family Restaurant DINER $$
(1400 E Hwy 66; mains $8-15; 6am-9pm Mon-Sat, 7am-9pm Sun; ) The name says it all – Earl's is a great place to bring the kids. It has also been serving great green chile and fried chicken (but no alcohol) since the late 1940s. And the locals know it; the fast-food, diner-like place is packed on weekends. Perhaps you'll even get some shopping done here: Navajo vendors sell goods at the eatery to tourists passing through.
#### Shopping
Gallup serves as the Navajo and Zuni peoples' major trading center, and is arguably the best place in New Mexico for top-quality goods at fair prices. Many trading posts are found downtown in the historic district on Hwy 66.
Just outside of town on the road to Zuni, seek out Ellis Tanner Trading Company (www.etanner.com; 1980 Hwy 602; 8am-7pm Mon-Sat), run by a fourth-generation local trader, where you can buy everything from rugs and jewelry to hardware and groceries. Be sure to check out the pawn shop.
#### Information
Gallup Visitor Information Center ( 505-727-4440; www.gallupnm.org; 201 E Rt 66; 8am-5pm Mon-Fri) Grab a copy of the full-color, helpful – it has a good map – Gallup visitors guide, produced annually.
Rehoboth McKinley Christian Hospital ( 505-863-7000; 1901 Red Rock Dr; 24hr emergency)
Police ( 505-722-2231; 451 State Rd 564)
Post office (950 W Aztec Ave)
#### Getting There & Around
The Greyhound bus station ( 505-863-3761), at the Amtrak building next to the cultural center, has three daily buses to Flagstaff, AZ ($53, 3½ hours), Albuquerque ($34.50, 2½ hours) and beyond.
Amtrak ( 800-872-7245; www.amtrak.com; 201 E Hwy 66), which has an 'Indian Country Guide' providing informative narration between Gallup and Albuquerque, runs an afternoon train to Albuquerque ($17, 3½ hours) and a daily evening train to Flagstaff, AZ ($4, 2½ hours).
### Zuni Pueblo
This pueblo, 35 miles south of Gallup, is well known for its jewelry, and you can buy beautiful pieces at little shops throughout the town along Hwy 53. If shopping doesn't interest you, it's still worth driving through for the sublime sandstone scenery.
In town, past stone houses and beehive-shaped mud-brick ovens is the massive Our Lady of Guadalupe Mission, featuring impressive locally painted murals of about 30 life-size kachinas (ancestral spirits). The church dates from 1629, although it has been rebuilt twice since then.
The Ashiwi Awan Museum & Heritage Center (Ojo Caliente Rd; admission by donation; 9am-5pm Mon-Fri) displays early photos and other tribal artifacts. The center will also cook traditional meals for groups of 10 or more ($10 per person) with advance reservations. Next door, Pueblo of Zuni Arts & Crafts (www.puebloofzuniartsandcrafts.com) sells locally made jewelry, baskets and other crafts.
The most famous ceremony at Zuni is the all-night Shalak'o ceremonial dance, held on the last weekend in December. The Zuni Tribal Fair (late August) features a powwow, local food, and arts-and-crafts stalls. To participate in any ceremony hosted by the Zuni community, you must attend an orientation; call the tourist office for more information.
The friendly Inn at Halona ( 505-782-4547, 800-752-3278; www.halona.com; Halona Plaza;r from $79), decorated with local Zuni arts and crafts, is the only place to stay on the Pueblo. Since each of the eight pleasant rooms is very different, check out as many as you can to see which fits your fancy. Full breakfasts are served in the flagstone courtyard in the summer. The inn is located behind HalonaPlaza, south from Hwy 53 at the only four-way stop in town.
Information is available from the extremely helpful Zuni Tourism Office ( 505-782-7238; www.zunitourism.com; 8am-5:30pm Mon-Fri, 10am-4pm Sat, noon-4pm Sun), which sells photography permits. The office also offers daily tours.
### Scenic Route 53
A great alternative way to reach Grants from Gallup is via Scenic Route 53. To get onto Route 53 from I-40 in Gallup, cut south on Hwy 602. Running parallel to I-40, it is home to some of the coolest natural wonders and ancient history in the region. To really experience the out-of-this-world landscape of lava tubes and red arches, traditional old New Mexican towns, volcanic craters and ice caves, you'll need to devote a full day to driving the route and exploring the attractions just off it.
Start your day a half-hour south of Gallup on Hwy 602. Turn east on Hwy 53 to begin. First up is El Morro National Monument (www.nps.gov/elmo; adult/child $3/free; 9am-6pm Jun-Aug, 9am-5pm Sep-Oct, 9am-4pm Nov-May), 52 miles southeast of Gallup. Throughout history travelers have left their mark on Inscription Rock, which is something like a sandstone guestbook. Well worth a stop, this 200ft outcrop is covered with thousands of carvings, from Pueblo petroglyphs at the top (c 1250) to inscriptions by Spaniard conquistadors and Anglo pioneers. Of the two trails that leave the visitor center, the paved, half-mile loop to Inscription Rock is wheelchair accessible. The unpaved, 2-mile Mesa Top loop trail requires a steep climb to the pueblos. Trail access ends one hour before closing.
To camp, visit El Morro RV Park & Cabins ( 505-783-4612; www.elmorro-nm.com; Hwy 53; tent/RV sites $10/25, cabins $79-94; ) a mile east of the visitor center with 26 sites and six cabins. Call ahead in the winter since it may be closed from October through April. The on-site Ancient Way Café (mains $6-10; 9am-5pm Sun-Thu, 9am-8pm Fri & Sat; ) serves home-cooked American, New Mexican and veggie specialties in a rustic dining room. You can wake up in the morning with an espresso and eggs.
Before you reach El Morro, you'll pass through the small town of Ramah. Some of Ramah's Navajo population still practice sheep raising, weaving and other land-based traditions. Most non-Indians are descendents of Mormon settlers. The Stage Coach Café (3370 Bond St/Hwy 53; mains $5-15; 7am-9pm Mon-Sat) is a worthy place to eat. It offers great steaks, Mexican food and a giant selection of pies. Service is friendly.
Animal-lovers won't want to miss the Wild Spirit Wolf Sanctuary ( 505-775-3304; www.wildspiritwolfsanctuary.org; 378 Candy Kitchen Rd; tours adult/child $7/4; 10am-4:30pm Tue-Sun; ), a 20-mile detour off Hwy 53, southeast of Ramah. Home to rescued captive-born wolves and wolf-dog mixes, the sanctuary offers four interactive walking tours per day, where you walk with the wolves – and get closer than you imagined – that roam the sanctuary's large natural-habitat enclosures. On the quarter-mile walk you'll learn everything you ever wanted to know about wolves –from behavior to what they like to eat to why they make terrible watchdogs. If you want to stay here overnight, primitive camping is available for $10 per night, with all the wolf howling you ever wanted to hear included. At the time of research, a newly built guest cabin with two bedrooms, a big loft and full kitchen was about to open; call for rates.
For a few more comforts, head back to Hwy 53 and drive a bit more until you hit Cimarron Rose ( 505-783-4770; www.cimarronrose.com; 689 Oso Ridge Rd; ste $110-185) an ecofriendly B&B between Miles 56 and 57. There are three Southwestern-style suites, with tiles, pine walls and hardwood floors (two have kitchens), plus a charming common room. Two goats and a horse organically fertilize Cimarron's perennial gardens, which provide food and shelter for more than 80 species of birds.
Before long, Hwy 53 curves through otherworldly volcanic badlands. Bandera Ice Cave (www.icecaves.com; adult/child $10/5; 8am-4:30pm), known to PuebloIndians as Winter Lake, is 25 miles southwest of Grants on Hwy 53. Inside part of a collapsed lava tube, this is a large chunk of ice (tinted green by Arcticalgae) that stays frozen year-round – the ice on the cave floor is 20ft thick and temperatures never rise above 31°F (0°C)! Unfortunately, it sounds more interesting than it actually is.
Next up is El Malpais National Monument (www.nps.gov/elma). Pronounced el mahl-pie- _ees,_ which means 'bad land' in Spanish, the monument consists of almost 200 sq miles of lava flows abutting adjacent sandstone. Five major flows have been identified; the most recent one is pegged at 2000 to 3000 years old. Prehistoric Native Americans may have witnessed the final eruptions since local Indian legends refer to 'rivers of fire.' Scenic Hwy 117 leads modern-day explorers past cinder cones and spatter cones, smooth pahoehoe lava and jagged aa lava, ice caves and a 17-mile-long lava tube system. At the time of research, all lava tube caves were temporarily closed.
El Malpais is a hodgepodge of NationalPark Service (NPS) land, private land, conservation areas and wilderness areas administered by the Bureau of Land Management (BLM). Each area has different rules and regulations, which change from year to year. The BLM Ranger Station ( 505-528-2918; Hwy 117; 8:30am-4:30pm), 9 miles south of I-40, has permits and information for the Cibola National Forest. The El Malpais Information Center ( 505-783-4774; www.nps.gov/elma; Hwy 53; 8:30am-4:30pm), 22 miles southwest of Grants, has permits and information for the lava flows and NPS land. Backcountry camping is allowed, but a free permit is required.
Though the terrain can be difficult, there are several opportunities for hiking through the monument. An interesting but rough hike (wear sturdy footwear) is the 7.5-mile (one way) Zuni-Acoma Trail, which leaves from Hwy 117 about 4 miles south of the ranger station. The trail crosses several lava flows and ends at Hwy 53 on the west side of the monument. Just beyond La Ventana Natural Arch, visible from Hwy 117 and 17 miles south of I-40, is the Narrows Trail, about 4 miles (one-way). Thirty miles south of I-40 is Lava Falls, a 1-mile loop.
County Rd 42 leaves Hwy 117 about 34 miles south of I-40 and meanders for 40 miles through the BLM country on the west side of El Malpais. It passes several craters, caves and lava tubes (reached by signed trails) and emerges at Hwy 53 near Bandera Crater. Since the road is unpaved, you'll want a high-clearance 4WD. Be prepared for poor signage at multiple forks in the road, so drive it during daylight, when you can (hopefully) intuit which turns to make. If you go spelunking, the park service requires each person to carry two sources of light and to wear a hard hat. Take a companion – this is an isolated area.
### Grants
Once a booming railway town, and then a booming mining town, today Grants relies on jobs at state prison facilities located nearby. The town seems to be a perpetually shrinking strip on Route 66. There aren't a whole lot of reasons to pull off the interstate, but if you do, check out the New Mexico Mining Museum ( 505-287-4802; adult/7-18yr $3/2; 9am-4pm Mon-Sat; ), which bills itself as the only uranium-mining museum in the world. Hands-on exhibits are made for kids, who will dig descending into the 'Section 26' mine shaft in a metal cage, then exploring the underground mine station.
About 16 miles northeast of Grants looms 11,301ft Mt Taylor. Follow Hwy 547 to USFS (US Forestry Service) Rd 239, then USFS Rd 453, to La Mosca Lookout at 11,000ft, for views. There are a couple of USFS campgrounds along the way. Otherwise, your best lodging options are the chain hotels around Exit 85 off I-40. For food, go to El Cafecito (820 E Santa Fe Ave; mains $3-9; 7am-9pm Mon-Fri, to 8pm Sat), easily the most popular place in town.
#### Information
Cibola National Forest Mount Taylor Ranger Station ( 505-287-8833; 1800 Lobo Canyon Rd; 8am-noon & 1-5pm Mon-Fri)
#### Getting There & Away
Greyhound ( 505-285-6268; www.greyhound.com) stops at 1700 W Santa Fe Ave and operates two daily buses to Albuquerque ($25, 1½ hours), Flagstaff, AZ ($58, five hours) and beyond. Pay the driver in cash or book online.
### Acoma Pueblo
Journeying to the top of 'Sky City' is like journeying into another world. There are few more dramatic mesa-top locations – the village sits 7000ft above sea level and 367ft above the surrounding plateau. It's one of the oldest continuously inhabited settlements in North America; people have lived at Acoma since the 11th century. In addition to a singular history and a dramatic location, it's also justly famous for its pottery, which is sold by individual artists on the mesa. There is a distinction between 'traditional' pottery (made with clay dug on the reservation) and 'ceramic' pottery (made elsewhere with inferior clay and simply painted by the artist), so ask the vendor.
Visitors can only go to Sky City on guided tours, which leave from the visitor center ( 800-747-0181; http://sccc.acomaskycity.org; tours adult/child $20/12; hourly 10am-3pm Fri-Sun mid-Oct–mid-Apr, 9am-3:30pm daily mid-Apr–mid-Oct) at the bottom of the mesa. Note that between July 10 and July 13 and either the first or second weekend in October, the Pueblo is closed to visitors. Though you must ride the shuttle to the top of the mesa, you can choose to walk down the rock path to the visitor center on your own. It's definitely worth doing this.
Festivals and events include a Governor's Feast (February), a harvest dance on San Esteban Day (September 2) and festivities at the San Esteban Mission from December 25 to 28. Photography permits are included in the ticket price.
The Sky City visitor center is about 13 miles south of I-40 exit 96 (15 miles east of Grants) or I-40 exit 108 (50 miles west of Albuquerque).
Sky City Hotel ( 888-759-2489; www.skycity.com; I-40, exit 102; r from $62; ), the Pueblo's modern casino, has 132 motel-style rooms and suites dressed up in Southwestern decor. Amenities include live entertainment, dining options, room service and a pool.
### Laguna Pueblo
From Albuquerque you can zoom along I-40 for 150 miles to the Arizona border in a little over two hours. But don't. Stop at the Native American reservation of Laguna, about 40 miles west of Albuquerque or 30 miles east of Grants. Founded in 1699, it's the youngest of New Mexico's Pueblos and consists of six small villages. Since its founders were escaping from the Spaniards and came from many different Pueblos, the Laguna people have diverse ethnic backgrounds.
The imposing stone and adobe San José Mission ( 9am-3pm Mon-Fri), visible from I-40, was completed in 1705 and houses fine examples of early Spanish-influenced religious art. It will beckon you off the interstate.
Main feast days include San José (March 19 and September 19), San Juan (June 24) and San Lorenzo (August 10 and Christmas Eve). Contact Laguna Pueblo ( 505-552-6654; www.lagunapueblo.org) for more information.
### EL CAMINO REAL
_El Camino Real de Tierra Adentro_ – the Royal Road of the Interior Lands – was the Spanish colonial version of an interstate highway, linking Mexico City to the original capital of New Mexico at Ohkay Owingeh Pueblo. Later, the trail was extended to Taos. Merchants, soldiers, missionaries and immigrants followed the route up the Rio Grande Valley, usually covering about 20 miles a day, stopping at night in _parajes_ (inns or campsites) along the way. By 1600, two decades before the Mayflower hit Plymouth Rock, it was already heavily traveled by Europeans. Along this route, the first horses, sheep, chickens and cows were brought into what would become the western US. For over 200 years the Camino Real wasn't just the sole economic and cultural artery connecting it to Colonial Spain – it was the only road into New Mexico until the Santa Fe Trail reached the area in 1821. This explains why, unlike many other states with large Latino populations, most Hispanics in New Mexico are and always have been American citizens. Some families were here before the signing of the Declaration of Independence, and many were here before New Mexico became part of the US.
Thirty miles south of Socorro at Exit 115 on I-25, El Camino Real International Heritage Center (www.caminorealheritage.org; adult/child $5/free; 8:30am-5pm Wed-Sun) explores the history of the Royal Road with artifacts, bilingual visual displays and special events. You can drive El Camino Real de Tierra Adentro National Historic Trail through the desolate Jornada del Muerto – the notoriously dry 90-mile stretch that earned its name by claiming more than a few lives. Coming from the south, start at Exit 32 along I-25; from the north, begin at Exit 139 or 124; see the Heritage Center website for more details.
## SILVER CITY & SOUTHWESTERN NEW MEXICO
The Rio Grande Valley unfurls from Albuquerque down to the bubbling hot springs of funky Truth or Consequences and beyond. Before the river hits the Texas line, it feeds one of New Mexico's agricultural treasures: Hatch, the so-called 'chile capital of the world.' East of the river, the desert is so dry it's been known since Spanish times as the Jornada del Muerto – the Journey of Death. Pretty appropriate that this was the area chosen for the Trinity Site, where the first atomic bomb was detonated.
With the exception of Las Cruces, the state's second-largest city, residents in these parts are few and far between. To the west, the rugged Gila National Forest is wild with backcountry adventure, while the Mimbres Valley is rich with archaeological treasures.
Be open to surprises: one of the state's most unique museums is in little Deming, and there are plenty more unexpected finds if you look around.
### Socorro
A quiet and amiable layover, Socorro has a downtown with a good mix of buildings dating from the 1800s to the late 20th century. Its standout is a 17th-century mission. Most visitors are birders drawn to the nearby Bosque del Apache refuge.
Socorro means 'help' in Spanish. The town's name supposedly dates to 1598, when Juan de Onate's expedition received help from Pilabo Pueblo (now defunct). The Spaniards built a small church nearby, expanding it into the San Miguel Mission in the 1620s. With the introduction of the railroad in 1880 and the discovery of gold and silver, Socorro became a major mining center and New Mexico's biggest town by the late 1880s. The mining boom went bust in 1893. The New Mexico Institute of Mining and Technology (locally called Tech) offers postgraduate education and advanced research facilities here, and runs a mineral museum.
#### Sights & Activities
Bosque Del Apache
National Wildlife Refuge WILDLIFE RESERVE
(www.fws.gov/southwest/refuges/newmex/bosque; per vehicle $5; dawn-dusk) Most travelers flock to Socorro because of its proximity to this refuge. About 8 miles south of town, the refuge protects almost 90 sq miles of fields and marshes, which serve as a majorwintering ground for many migratory birds – most notably the very rare and endangered whooping cranes, of which about a dozen winter here. Tens of thousands of snow geese, sandhill cranes and various other waterfowl also roost here, as do bald eagles. The wintering season lasts from late October to early April, but December and January are the peak viewing months and offer the best chance of seeing bald eagles. Upwards of 325 bird species and 135 mammal, reptile and amphibian species have been sighted here. From the visitor center ( 575-835-1828; 7:30am-4pm Mon-Fri, 8am-4:30pm Sat & Sun), a 15-mile loop circles the refuge; hiking trails and viewing platforms are easily accessible. To get here leave I-25 at San Antonio (10 miles south of Socorro) and drive 8 miles south on Hwy 1.
San Miguel Mission CHURCH
(403 San Miguel Rd) Most of the historic downtown dates to the late 19th century. Pick up the chamber of commerce's walking tour, the highlight of which is the San Miguel Mission, three blocks north of the plaza. Although restored and expanded several times, the mission still retains its colonial feel, and parts of the walls date back to the original building.
#### Festivals & Events
Socorro's Balloon Rally in late November is not to be missed; balloonists line up on the street and inflate their balloons prior to a mass ascension. At the 49ers Festival (third weekend of November), the entire town gets involved in a parade, dancing and gambling, while the Festival of the Cranes on the same weekend features special tours of Bosque del Apache, wildlife workshops and arts and crafts.
#### Sleeping & Eating
There are budget motels and a few national chains on California St.
Socorro Old Town B&B B&B $$
( 575-838-2619; www.socorrobandb.com; 114 WBaca St; r $125; ) In the Old Town neighborhood, this B&B has a casual attitude – and entering through the unkempt, screened-in porch, you may wonder if this is just a private home. Inside, that's what it feels like, with easygoing hosts and clean, comfortable rooms. By the time you read this, they should have wi-fi.
Socorro Springs Brewing Co ITALIAN $$
(www.socorrosprings.com; 1012 N California St; mains $6-24; 11am-9pm) In the mood for a relatively sophisticated experience? Come to this renovated adobe joint for a really good clay-oven pizza, big calzones, decent pasta dishes, lots of salads and homemade soups. At times, the selection of brews can be limited, but whatever they're serving at the moment is smooth and tasty.
Owl Bar Café BURGERS $
(77 Hwy 380; mains $6-15; 8am-8:30pm Mon-Sat) If you can't make it to Hatch (Click here) it's worth getting off I-25 at Exit 139 near San Antonio for the Owl Bar Café's green chile cheeseburgers. The sandwich is a potent mix of greasy beef, soft bun, sticky cheese, tangy chile, lettuce and tomato. It drips onto the plate in perfect burger fashion.
### ONLY IN NEW MEXICO: SCENIC ROUTE 60
Highway 60 runs west from Socorro to the Arizona border, cutting past the surreal Sawtooth Mountains, across the vast Plains of San Agustin, and through endless juniper hills. Along the way there are a few spots that are well worth a detour if you've got the time.
About 40 miles west of Socorro, 27 huge antenna dishes (each weighing 230 tons) together comprise a single superpowered telescope – the Very Large Array Radio Telescope (VLA; www.nrao.edu; off Hwy 52; admission free; 8:30am-sunset), run by the National Radio Astronomy Observatory. Four miles south of US 60, they move along railroad tracks, reconfiguring the layout as needed to study the outer limits of the known universe. To match the resolving power of the VLA, a regular telescope would have to be 22 miles wide!
The VLA has increased our understanding of black holes, space gases and radio emissions, among other celestial phenomena. And it's had starring and cameo roles in Hollywood films, including _Contact_ , _Armegeddon_ and _Independence Day_. If none of that's enough to interest you, well, they are just unbelievably cool. There's a small museum at the visitor center, where you can take a free, self-guided tour with a window peak into the control building.
Further west on Hwy 60, you'll pass through Pie Town. Yes, seriously, a town named after pie. And for good reason. They say you can find the best pies in the universe here (which makes you wonder what they've _really_ been doing at the VLA). The Pie-O-Neer Café (Hwy 60; 575-772-2711; www.pie-o-neer.com; slices $4.50; Thu-Mon 11am-4pm summer, Thu-Sun 11am-4pm winter) just might prove their case. The pies are dee-lish, the soups and stews they serve are homemade, and you'll be hard pressed to find another host as welcoming as Kathy Knapp – who advises you to call in advance to make sure they won't run out of pie before you get there! On the 2nd Saturday of September, Pie Town holds its annual Pie Festival (www.pietownfestival.com), with baking and eating contests, the crowning of the Pie Queen, wild west gunfight reenactiments and horned toad races.
Heading on toward the Arizona border, out in the high desert plains around Quemado, gleams the Lightning Field ( 505-898-3336; Quemado; www.diacenter.org/sites/main/lightningfield; adult/child $250/100 Jul-Aug, $150/100 May, Jun, Sep & Oct), an art installation created by Walter de Maria in 1977. Four hundred polished steel poles stand in a giant grid, with each stainless rod about 20ft high – but the actual lengths vary so the tips are all level with each other. During summer monsoons, the poles seem to draw lightning out of hovering thunderheads. The effect is truly electrifying! You can only visit if you stay overnight in the simple on-site cabin, with only six visitors allowed per night. Advance reservations are required. Check out the website for more details.
Hwy 60 can also be reached by heading south along back roads from Zuni Pueblo, Scenic Route 53 and El Malpais.
#### Information
The chamber of commerce ( 575-835-0424; www.socorro-nm.com; 101 Plaza; 8am-5pm Mon-Fri, 10am-noon Sat) is helpful.
#### Getting There & Around
Socorro is on I-25, about 75 miles (a one-hour drive) south of Albuquerque. It is best reached via private vehicle. The historic downtown is small and easily walkable and there is usually plenty of parking.
### Truth or Consequences & Around
Home to a growing number of New Age hippies, off-the-grid artists and sustainable-living ecowarriors, kooky Truth or Consequences (T or C) vies for the title of quirkiest little town in New Mexico.
Situated on the banks of the Rio Grande, this high-desert oasis is hot property these days. And we're not just talking about the mineral-rich springs on which it was built and named (T or C was known as Hot Springs until 1950, when the town officially changed its name to match a popular radio game show in an effort to increase tourism). T or C's latest publicity stunt? It's about to become the world's first commercial launch pad to outer space. Yup, you heard us, Richard Branson's Virgin Galactic is set to start blasting tourists off the planet from the nearbyspaceport sometime in the near future.
Space travel aside, T or C has also gained a reputation as the place for arty-holistic types to move, drop out and start a different journey – the geothermal energy here is supposedly comparable to Sedona's. The shabby-chic main drag is filled with crystal shops, herbalist offices, yoga studios and a dozen eclectic art galleries and off-the-wall boutiques, the brainchildren of the spiritual seekers, healers, writers and painters who came to find their vision.
#### Sights & Activities
It won't take you more than an hour, but get your bearings in tiny T or C by strolling down Main St. Each day it seems another art gallery or new herbal-remedy shop opens, and it's fun to just walk and window-shop.
Geronimo Springs Museum MUSEUM
(211 Main St; adult/student $6/3; 9am-5pm Mon-Sat, noon-5pm Sun) An engaging mishmash of exhibits, this museum features minerals, local art and plenty of historical artifacts ranging from prehistoric Mimbres pots to beautifully worked cowboy saddles.
Hot Springs HOT SPRINGS
For centuries people from these parts, including Geronimo, have bathed in the area's mineral-laden hot springs. Long said to have therapeutic properties, the waters range in temperature from 98°F to 115°F (36°C to 46°C) and have a pH of 7 (neutral).
Most of T or C's hotels and motels double as spas. As there are dozens of places to choose from, have a look at a couple of different spas to find your ideal relaxing spot. Massages and other treatments are usually available. Guests soak free. The swankiest place to take a hot dip by far is Sierra Grande Lodge & Spa ( 575-984-6975; www.sierragrandelodge.com; 501 McAdoo St), with mineral baths and a holistic spa offering everything from massage to aromatherapy. The resort charges nonguests $25 for the first person, then $5 for each additional person in the party, to use its mineral springs. For a more casual experience, try Riverbend Hot Springs, which offers outdoor tubs by the river. It costs between $10 and $25 per person to soak.
Elephant Butte Lake State Park LAKE
(www.nmparks.com; I-25; vehicle per day $5, tent/RV sites $8/14). Just 5 miles north of T or C, the state's largest artificial lake (60 sq miles) is an angler's paradise. It's popular with day-trippers from T or C who come for waterskiing, windsurfing and, of course, trophy bass fishing. The nearby marina ( 575-744-5567; www.marinadelsur.info) rents tackle and boats (for fishing, pontoon and skiing). Spring and fall are best for fishing; guides will help you get the most out of your time for about $225 to $350 per day (for one to four anglers). Contact professional angler Frank Vilorio, who operates Fishing Adventures ( 800-580-8992; www.stripersnewmexico.com) to make sure you take home your fill of striped bass.
#### Festivals & Events
The T or C Fiesta, held the first weekend in May, celebrates the town's 1950 name change with a rodeo, barbecue, parade and other events. The Sierra County Fair (late August) has livestock and agricultural displays, and the Old Time Fiddlers State Championship (third weekend in October) features country and western, bluegrass and mariachi music.
### SPACEPORT AMERICA: THE ULTIMATE SIDE TRIP
White Sands earned its nickname 'Birthplace of the Race to Space' in 1947, when humanity, courtesy of NASA's Werner von Braun, successfully hurled its first missile out past the stratosphere from among those rolling, pure white dunes. Today, thanks to Virgin Galactic CEO Sir Richard Branson, former Governor Bill Richardson and lots of other pie-in-the-sky visionaries (not to mention state taxpayers who may foot most of the projected $225 million bill), the world's first private spaceport has opened right next door.
Space tourism may well involve a simple 62-mile (straight up) add-on to your New Mexico vacation package. For just $200,000, you can book your flight on _VSS Enterprise_ online for a 90-minute ride in a plush cruiser with reclining seats, big windows and a pressurized cabin so you won't need space suits. The vessel is designed by legendary aerospace engineer Bob Rutan, whose _SpaceShipOne_ was the first privately funded (by Microsoft cofounder Paul Allen) manned vehicle to reach outer space twice in a row, winning him the $10 million 2004 Ansari X-Prize.
It's not all about tourism, however. Spaceport America has been used by UP Aerospace to launch cheap cargo carriers into low Earth orbit since 2006 and has banked over a million dollars in deposits for future scientific research trips. It's also the new home of the X-Prize competition (the race for private development of reusable spacecraft), as well as other aerospace-themed expositions to be held throughout the year.
Studies estimate that Spaceport America will pump hundreds of millions of dollars annually into the state, particularly in the neighboring towns of Alamogordo and Truth or Consequences. Officials also hope to raise international awareness of New Mexico as a serious high-tech center.
'We might even be able to allow those aliens who landed at Roswell 50 years ago in a UFO a chance to go home,' adds Richard Branson.
#### Sleeping & Eating
When it comes to places to get away, T or C is definitely taking off, but it's still not exactly happening by city standards – it's more of a make-your-own-fun type of place. Don't expect much in the way of nightlife or even lots of eating options. Still, the ones that exist are great. Think about booking ahead in summer.
Blackstone Hotsprings BOUTIQUE HOTEL $
( 575-894-0894; www.blackstonehotsprings.com; 410 Austin St; r $75-125; ) New on the scene, Blackstone embraces the T or C spirit with an upscale wink, decorating each of its seven rooms in the style of a classic TV show, from the to the _Golden Girls_ to _I Love Lucy_. Best part? Each room comes with its own hot spring tub or waterfall. Worst part? If you like sleeping in darkness, a subtantial amount of courtyard light seeps into some rooms at night.
Riverbend Hot Springs BOUTIQUE HOTEL $
( 575-894-7625; www.riverbendhotsprings.com; 100 Austin St; r from $70; ) Former hostel Riverbend Hot Springs now offers more traditional motel-style accommodations –no more tipis – from its fantastic perch beside the Rio Grande. Rooms exude a bright, quirky charm, and several units work well for groups. Private hot-spring tubs are available by the hour (guest/nonguest $10/15 for the first hour, then $5/10 per additional hour), as is a public hot spring pool (free for guests; nonguests $10 for the first hour then $5 per hour or $25 per day).
Happy Belly Deli DELI $
(313 N Broadway; mains $2-8; 7am-3pm Mon-Fri, 8am-3pm Sat, 8am-noon Sun) Draws the morning crowd with fresh breakfast burritos.
Café BellaLuca ITALIAN $$
(www.cafebellaluca.com; 303 Jones St; lunch mains $6-15, dinner mains $10-34; 11am-9pm Sun-Thu, to 10pm Fri & Sat) Earns raves for its Italian specialties; pizzas are amazing and the spacious dining room is a pitch-perfect blend of classy and funky.
#### Information
The visitor center ( 575-894-1968; www.truthorconsequenceschamberofcommerce.org; 211 Main St; 9am-4:30pm Mon-Fri, 9am-5pm Sat, noon-5pm Sun) and Gila National Forest Ranger Station ( 575-894-6677; 1804 N Date St; 8am-4:30pm Mon-Fri) have detailed information.
### CHLORIDE
In the foothills of the Black Range, tiny Chloride (population 8) was abustle with enough silver miners to support eight saloons at the end of the 19th century. By the end of the 20th century, the town was on the verge of disintegration. Fortunately, the historic buildings are being restored by Don and Dona Edmund, who began renovating the old Pioneer Store ( 575-743-2736; www.pioneerstoremuseum.com; 10am-4pm) in 1994. Today, this general store from 1880 is a museum with a rich collection of miscellany from Chloride's heyday, including wooden dynamite detonators, farm implements, children's coffins, saddles and explosion-proof telephones used in mines. You can see the Hanging Tree to which rowdy drunks were tied until they sobered up; the Monte Cristo Saloon (now an artist co-op/gift shop); and a few other buildings in various stages of rehabilitation.
You can stay overnight in the two-bedroom Harry Pye Cabin ($100) – Chloride's first building – which has been renovated and modernized. There's even a microwave, since, as Dona puts it, 'I didn't want the women to have to spend their time cooking instead of enjoying the place.' They've got plans to open a cafe during summer.
To get to Chloride from T or C, take I-25 north to exit 83, then take Hwy 52 west.
### Scenic Route 152
South of T or C, Hwy 152 west leads into mining country and twists over the Black Range to Silver City.
The first community you'll drive through is charming Hillsboro, which was revived by local agriculture after mining went bust. Today it's known for its Apple Festival on Labor Day, when fresh-baked apple pies, delicious apple cider, street musicians and arts-and-crafts stalls attract visitors. Grab a bite at the Hillsboro General Store Café (100 Main St; mains $8-15; 8am-3pm Sun-Fri, 11am-7pm Sat), the historic building that was once the town's dry-goods shop, or at Lynn Nusom's Kitchen (602 Main St; mains $5-7; 11am-6pm Wed-Sun), run out of a house by an award-winning Southwestern cookbook author. Note that it's cash only. You can stay at the homey Enchanted Villa B&B ( 575-895-5686; r from $65; ).
Continuing west on Hwy 152, you'll pass the town of Kingston, which once had 7000 residents during the silver rush of the 1880s, but today is home to just a handful of folks. The road will soon start to snake around a series of hairpin curves –it's slow going up to 8228ft Emory Pass, where a lookout gives expansive views of the Rio Grande basin to the east. Heading down the other side, you'll pass a number of USFS campgrounds.
At San Lorenzo, you could turn north onHwy 35 and head up the Mimbres Valley toward the Gila Cliff Dwellings, or continue west toward Silver City, passing the impossible-to-miss Santa Rita Chino Open Pit Copper Mine, which has an observation point on Hwy 152 about 6 miles before it hits Hwy 180. Worked by Indians and Spanish and Anglo settlers, it's the oldest active mine in the Southwest. A staggering 1.5 miles wide, the gaping hole is 1800ft deep and produces 300 million pounds of copper annually.
### Silver City & Around
Silver City's streets are dressed with a lovely mishmash of old brick and cast-iron Victorians and thick-walled red adobe buildings, and the place still emits a Wild West air. Billy the Kid spent some of his childhood here, and a few of his haunts can still be found mixed in with the new gourmet coffee shops, quirky galleries and Italian ice-cream parlors gracing its pretty downtown.
Once a rough-and-ready silver hub (and still a copper-mining town), Silver City is now attracting a growing number of adventure addicts who come to work and play in its surrounding great outdoors. With some 15 mountain ranges, four rivers, the cartoonish rock formations in City of Rocks State Parks and the action-packed Gila National Forest all in the vicinity, it's easy to understand the burgeoning love affair between visitors and this classic, Southwestern small town. Plus, as the home to Western New Mexico University, Silver City is infused with a healthy dose of youthful energy.
#### Sights & Activities
The heart of this gallery-packed Victorian town is encompassed by Bullard, Texas and Arizona Sts between Broadway and 6th St. The former Main St, one block east of Bullard, washed out during a series of massive floods in 1895. Caused by runoff from logged and overgrazed areas north of town, the floods eventually cut 55ft down below the original height of the street. In a stroke of marketing genius, it's now called Big Ditch Park.
Western New Mexico University Museum MUSEUM
(www.wnmu.edu/univ/museum.shtml; 1000 W College Ave; admission free; 9am-4:30pm Mon-Fri, 10am-4pm Sat & Sun) This university museum boasts the world's largest collection of Mimbres pottery, along with exhibits detailing local history, culture and natural history. The gift shop specializes in Mimbres motifs.
Pinos Altos HISTORIC SITE
Seven miles north of Silver City along Hwy 15 lies Pinos Altos, established in 1859 as a gold-mining town. These days, it's almost a ghost town; its few residents strive to retain the 19th-century flavor of the place. Cruise Main St to see the log-cabin schoolhouse built in 1866, an opera house, a reconstructed fort and an 1870s courthouse. The Buckhorn Saloon is a great place to come for dinner or a beer.
Silver City Museum MUSEUM
(www.silvercitymuseum.org; 312 W Broadway; suggested donation $3; 9am-4:30pm Tue-Fri, 10am-4pm Sat & Sun) This museum, ensconced in an elegant 1881 Victorian house, displays Mimbres pottery, as well as mining and household artifacts from Silver City's Victorian heyday. Its shop has a good selection of Southwestern books and gifts.
City of Rocks State Park OUTDOORS
(www.nmparks.com; Hwy 61; day-use $5, tent/RV sites $8/10) Rounded volcanic towers create a cartoonish beauty in nearby City of Rocks State Park. You can camp among the towers in secluded sites with tables and fire pits. A nature trail, drinking water and showers are available. The park is 33 miles southeast of Silver City; take Hwy 180 east to Hwy 61 south.
Gila Hike and Bike MOUNTAIN BIKING
( 575-388-3222; www.gilahikeandbike.com; 103 E College Ave; 9am-5:30pm Mon-Fri, 9am-5pm Sat, 10am-4pm Sun) Come here for the scoop on regional single-track routes. Make sure to ask about the gorgeous trail on Signal Peak, a mountain just above the town, with tracks through oaks and ponderosas and views all the way to Mexico. The shop also rents bicycles, snowshoes and camping equipment for exploring the region's outdoor attractions.
#### Sleeping
Palace Hotel HISTORIC HOTEL $
( 575-388-1811; www.silvercitypalacehotel.com; 106 W Broadway; r from $51; ) This venerable old hotel is the spot to slumber in Silver City. A restored 1882 hostelry, it exudes a low-key, turn-of-the-19th-century charm. The rooms vary from small (with a double bed) to two-room suites (with king- or queen-size beds) outfitted with refrigerators, microwaves, phones and TVs. All have old-fashioned Territorial-style decor.
Gila House Hotel B&B $$
( 575-313-7015; www.gilahouse.com; 400 N Arizona St; r from $85; ) Housed in an adobe that's over 100 years old, this B&B has preserved its character while upgrading to 21st-century comforts. The common area doubles as one of downtown Silver City's well-regarded art galleries.
KOA CAMPGROUND $
( 575-388-3351; www.koa.com; 11824 E Hwy 180; tent/RV sites $24/34, cabins from $47; ) Five miles east of town, this campground franchise is a clean, child-friendly option with a playground and coin laundry. The 'kamping kabins' are compact but cute and good value, with all the necessities packed into the square wooden rooms. The place fills up in summer, so reserve ahead.
#### Eating & Drinking
Buckhorn Saloon STEAKHOUSE, BAR $$
( 575-538-9911; Main St, Pinos Altos; mains $10-35; 4-10pm Mon-Sat) About 7 miles north of Silver City, this restored adobe eatery offers serious steaks (a house specialty) and seafood amid 1860s Wild West decor – try the buffalo burgers, they're fresh and tasty. Live country music livens up the joint most nights. The crowd ranges from Silver City gallery-owners to hard-core mountain men.
Shevek & Co INTERNATIONAL $$$
( 575-534-9168; www.silver-eats.com; 602 N Bullard St; mains $20-30; 5-8:30pm Sun-Tue & Thu, to 9pm Fri & Sat) This delightful eatery is at turns formal, bistro-like and patio-casual –it depends on which room you choose. Sunday brunch is decidedly New York, à la Upper West Side; dinners range from Moroccan to Spanish to Italian, and everything can be ordered tapas-size. Enjoy the excellent selection of beer and wine.
Javalina CAFE $
(201 N Bullard St; pastries from $2; 6am-9pm Mon-Thu, to 10pm Fri & Sat, to 7pm Sun; ) This is a great coffee shop, with seating of all sizes and styles, from couches to love seats to wooden chairs. There are board games and reading material and a few computer terminals if you don't have your laptop with you.
Diane's Restaurant & Bakery AMERICAN $$
( 575-538-8722; 510 N Bullard St; mains $8-25; 11am-2pm & 5-9pm Tue-Fri, 9am-2pm Sat & Sun) Diane's is the local restaurant of choice, especially for weekend breakfasts. If you visit then, order the Hatch Benedict eggs; the house version of the original is doused with the region's beloved chile pepper. Diane's does a busy lunch trade during the week. The romantic appeal is upped at dinner, when there is dim lighting and white linen.
Peace Meal Cooperative VEGETARIAN $
(601 N Bullard St; mains $5-8; 9am-3pm Mon-Sat; ) This vegetarian smoothie, sandwich and salad shop is the antidote to the meat overload you might be experiencing by this time on your trip. Try the tofu curry.
#### Information
Gila National Forest Ranger Station ( 575-388-8201; www.fs.fed.us/r3/gila; 3005 E Camino Del Bosque; 8am-4:30pm Mon-Fri)
Gila Regional Medical Center ( 575-538-4000; 1313 E 32nd)
Post office (500 N Hudson St)
Visitor center ( 575-538-3785; www.silvercity.org; 201 N Hudson St; 9am-5pm Mon-Fri, 10am-2pm Sat & Sun) Publishes a map with the city's galleries.
#### Getting There & Around
Silver City sits just south of the junction of Hwy 180 and Rte 90 and is best reached by private transportation. It's 115 miles from Las Cruces, the closest sizeable junction town. To get here from Las Cruces, head west on US 10 then follow Hwy 180 all the way north to Silver City.
Downtown Silver City is small and walkable and street parking is plentiful. The town also serves as the gateway to the Gila National Forest, just north of town.
### Gila National Forest
If you're looking for isolated and undiscovered and a real sense of wildness, 'The Gila' has it in spades. Its 3.3 million acres cover eight mountain ranges, including the Mogollon, Tularosa, Blue and Black. It's here that legendary conservationist Aldo Leopold spearheaded a movement to establish the world's first designated wilderness area, resulting in the creation of the Gila Wilderness in 1924; in 1980, the adjacent terrain to the east was also designated as wilderness and named after Leopold.
This is some rugged country, just right for black bears, mountain lions and the reintroduced Mexican grey wolves. Trickling creeks are home to four species of endangered fish, including the Gila trout. In other words, it's ideal for remote and primitive hiking and backpacking. Silver City is the main base for accessing the Gila Wilderness and the interior of the forest, while T or C or Hillsboro are more convenient for reaching the eastern slope of the Black Range.
If you're only up for a day trip, the Gila has a few gems. On the western side of the forest, 65 miles northwest of Silver City off Hwy 180, the Catwalk trail follows a suspended metal walkway through narrow Whitewater Canyon. You can see the creek rushing beneath your feet. The catwalk is wheelchair-accessible and great for kids. While some will find it disappointingly short, it offers a painless way to experience a bit of the Gila – and from the end of it you can continue forever into the mountains on dirt trails, if you like. To get here, turn east onto Hwy 174 at Glenwood, where the forest service maintains Bighorn campground (admission free; year-round) with no drinking water or fee.
Just north of Glenwood off of Hwy 180, Hwy 159 twists its way for 9 vertiginous miles on the slowgoing route to Mogollon, a semi–ghost town (inaccessible during the winter). Once an important mining town, it's now rather deserted and empty, inhabited by only a few antique and knickknack shops and, as is typical for middle-of-nowhere New Mexico, one proud little restaurant. This one is called the Purple Onion (Main St; mains $5-10; 9am-5pm Fri-Sun May-Oct), and it's as good as you'd hope after making the trip.
If you've got a high-clearance 4WD vehicle and a little extra time, you can take one of New Mexico's most scenic roads from the Silver City area right through the heart of the Gila. From Hwy 35 north of Mimbres, Forest Rd 150 wends through the forest for 60 miles before emerging onto the sweeping Plains of San Agustin. Another option off of Hwy 35 is to drive the rough Forest Rd 151 to the Aldo Leopold Wilderness boundary, then hike a few miles up to the top of McKnight Mountain, the highest summit in the Black Range.
For serenely comfortable forest slumber, rent one of the five stunningly situated Casitas de Gila Guesthouse ( 877-923-4827; www.casitasdegila.com; off Hwy 180, near Cliff; casitas $160-210; ), adobe-style casitas set on 90 beautiful acres. Each unit has a fully stocked kitchen, plenty of privacy and one or two bedrooms. Stay a while and the rates drop. There are telescopes, an outdoor hot tub and grills to keep you occupied.
In addition to the Gila National Forest offices in Silver City and T or C, Mimbres' wilderness ranger station ( 575-536-2250; Hwy 35; 8am-4:30pm Mon-Fri) is particularly useful.
##### GILA CLIFF DWELLINGS
Mysterious, relatively isolated and easily accessible, it's easy to imagine how these remarkable cliff dwellings might have looked at the turn of the first century. Here, the influence of the Ancestral Puebloans (Click here) on the Mogollon culture is writ large. Take the 1-mile round-trip self-guided trail that climbs 180ft to the dwellings, overlooking a lovely forested canyon. Parts of the trail are steep and involve ladders. The trail begins at the end of Hwy 15, 2 miles beyond the visitor center (www.nps.gov/gicl; admission $3; 8:30am-5pm Jun-Aug, 9am-4pm Sep-May). Between the visitor center and trailhead are two small campgrounds with drinking water, picnic areas and toilets. They're free on a first-come, first-served basis and often fill on summer weekends. A short trail behind the Lower Scorpion Campground leads to pictographs.
##### GILA HOT SPRINGS
Used by local tribes since ancient times, these springs are 39 miles north of Silver City, within the Gila Hotsprings Vacation Center ( 575-536-9551; www.gilahotspringsranch.com; Hwy 15; tent/RV sites $15/20, r from $76; ). The pet-friendly resort (dogs can stay for an extra $5 per night) has simple rooms with kitchenettes in a giantred barn-like structure, along with camping sites and an RV park with a spa and showers fed by hot springs. Primitive camping is adjacent to the hot pools (hot pools $3, camping & hot pools $4). You can arrange horseback rides, guided fishing and wilderness pack trips and other outfitting services in advance through the center.
### Deming & Around
In the least populous of the state's four corners, Deming (founded in 1881 as a railway junction) is popular with retirees. It's surrounded by cotton fields on the northern edge of the Chihuahuan Desert. But if this is a desert, where does all the water come from for the family farms and ranches? It's tapped from the invisible Mimbres River, which disappears underground about 20 miles north of town and emerges in Mexico.
Run by the Luna County Historical Society, the Deming Luna Mimbres Museum ( 505-546-2382; 301 S Silver Ave; admission free; 9am-4pm Mon-Sat, 1:30-4pm Sun, closed major holidays) is one of the best regional museums in New Mexico. The display of Mimbres pottery is superb, as is the doll collection – including one rescued from the rubble of Hiroshima. One room is devoted to snapshots of local families, dating back as late as the 1800s. You can see an actual iron lung, and, get this, a braille edition of _Playboy_ (maybe someone _was_ reading it for the articles).
Fourteen miles southeast of Deming via Hwys 11 and 141, Rock Hound State Park (www.nmparks.com; per car $5; tent/RV sites $8/14) is known for the semiprecious or just plain pretty rocks that can be collected here, including jasper, geodes and thunder eggs. Don't know what you're looking for? Stop at the Geolapidary Museum & Rock Shop ( 505-546-4021; admission $1; 9am-5pm Thu-Tue), 2 miles before the park entrance. The Spring Canyon ( 8am-4pm Wed-Sun) section of the park has shaded picnic tables and the half-mile Lovers Leap trail.
### SHAKESPEARE'S GHOSTS
As far as we know, the dusty southwestern corner of New Mexico isn't haunted by any spirits speaking in iambic pentameter, but it is where you'll find Shakespeare (www.shakespeareghosttown.com; Hwy 494; 1hr tours adult/child $4/3), 2½ miles south of Lordsburg. One of the best-preserved of any Old West ghost towns (despite having lost its general store in a 1997 fire), it was first established as a stop on the Southern Pacific Mail Line, then grew into a silver mining boom town. Plenty of the West's famous outlaws roosted here at one time or another: 'Curly' Bill Brocius, the killer and rustler, called this home; a young Billy the Kid was a dishwasher at the still-standing Stratford Hotel; Black Jack Ketchum's gang used to come into town to buy supplies.
Shakespeare is open to visitors one weekend a month between July and December, with occasional historical reenactments. Check the website for exact dates.
Kids will like Lucy's Pasture Donkey Sanctuary (www.lucyspasture.com; 4745 Franklin Rd; admission free; 10am-5pm), 1.8 miles south of Hwy 549, 17 miles east of Deming on the noninterstate route to Las Cruces. Over 30 donkeys and horses are sheltered here, many after being abused or neglected by their former owners. All are cute and some are talented, like the donkey that can slam dunk a ball through a net. Also on Hwy 549, 3 miles east of Deming, is the tasting room for St Clair Winery (www.stclairwinery.com; 9am-6pm Mon-Sat, noon-6pm Sun), New Mexico's largest vintner.
Although it has a good museum and nearby state parks, Deming's big draw is the Great American Duck Races, held on the fourth weekend in August. Attracting tens of thousands of visitors, the late summer race is perhaps the most whimsical and popular festival in the state. The main event is the duck races themselves, which offer thousands of dollars in prize money. Anyone can enter for a $10 fee ($5 for kids), which includes 'duck rental.' Other wacky events include the Tortilla Toss (winners toss tortillas over 170ft), Outhouse Races and a Duckling Contest. As if that weren't enough, entertainment ranges from cowboy poets to local musicians, and there's a parade, hot-air balloons and food.
Room rates rise during duck races and the state fair (late September), when you need to make reservations. Probably the best bet in town, the Grand Motor Inn ( 575-546-2632; www.grandmotorinndeming.com; 1721 E Pine St; r from $47; ) offers discounts when it's slow. It's a decent spot to sleep, with a grassy inner courtyard and restaurant.
Deming has a handful of good and simple Mexican-American restaurants, along with the brand new Mimbres Valley Brewery (www.demingbrew.com; 200 S Gold Ave; mains $6-9; 11am-10pm Sun-Thu, to 11pm Fri & Sat), which does pub food right in a casual local atmosphere.
If you just finished your book, trade it in at Readers' Cove (200 S Copper St; 10am-5pm), a fantastic used-book store in a 19th-century adobe house with shelves full of everything from literature to history to pulp.
The visitor center (www.demingchamber.com; 800 Pine St; 9am-5pm Mon-Fri, to 3pm Sat; ) has tons of local info and wi-fi.
Greyhound ( 800-231-2222; www.greyhound.com; 300 E Spruce St) runs daily buses to El Paso, TX ($36, 2 hours), Phoenix, AZ ($75, 6 hours), and Las Cruces ($20, 1 hour), along the I-10 corridor.
### Las Cruces & Around
At the crossroads of two major highways, I-10 and I-25, Las Cruces makes a great pit stop, once you get past the shock that this rural outpost is actually New Mexico's second-biggest city! Las Cruces and her sister city, Mesilla, sit at the edge of a broad basin beneath the fluted Organ Mountains. There is something special about the combination of bright white sunlight, glassy blue skies, flowering cacti, rippling red mountains and desert lowland landscape found here. The city itself, however, is less than a dream town: sprawling, and beastly hot for a good part of the year.
Las Cruces is an eclectic mix of old and young. The city is home to New Mexico State University (NMSU), whose 15,000-strong student body infuses it with a healthy dose of youthful liveliness, while at the same time its 350 days of sunshine and numerous golf courses are turning it into a popular retirement destination.
Mesilla is the perfect place to lose track of time. Let the centuries slide back as you wander its beautiful historic plaza surrounded by lovely 19th-century buildings adorned with colorful _ristras_ (strings of chiles) and shops selling souvenirs ranging from cheap and kitschy to expensive.
#### Sights
Mesilla NEIGHBORHOOD
(www.oldmesilla.org). Four miles south of Las Cruces is her sister city, Mesilla. Dating back 150 years (and looking pretty much the way it did back then), Mesilla is a charming old adobe town rich in culture and texture. Despite the souvenir shops and tourist-oriented restaurants, the Mesilla Plaza and surrounding blocks remain a step back in time. Wander a few blocks beyond the Plaza to garner the essence of a mid-19th-century Southwestern border town. One highlight of a walk through town is visiting the San Albino Church on the plaza. The church, originally built of adobe in 1855, still offers Masses today, both in English and Spanish. Outside the church is a memorial to parishioners who died in combat.
New Mexico Farm
& Ranch Heritage Museum MUSEUM
(www.nmfarmandranchmuseum.org; 4100 DrippingSprings Rd; adult/child $5/2; 9am-5pm Mon-Sat, noon-5pm Sun; ) This terrific museum has more than just engaging displays about the agricultural history of the state – it's got livestock! There are daily milking demonstrations and an occasional 'parade of breeds' of cattle, along with stalls of horses, donkeys, sheep and goats. Other demonstrations include blacksmithing (Friday to Sunday), spinning and weaving (Wednesday), and heritage cooking (call for the schedule). You'll understand much more about New Mexican life and culture after a visit here.
Chile Pepper Institute GARDENS
( 575-646-3028; www.chilepepperinstitute.org; cnr E College Ave & Knox St, Gerald Thomas Hall, room 265; admission by donation; 8am-noon & 1-5pm Mon-Fri) Part of NMSU, the Chile Pepper Institute works with the university's Chile Breeding and Genetics program to promote education and research into New Mexico's flagship food. The institute's office has informative displays (and a chile-themed gift shop), but the real reason to visit is to see the demonstration gardens, filled with a boggling variety of growing chile peppers. The best time to come is just before harvest – July or early August; call in advance to set up a garden tour.
White Sands Missile Test
Center Museum MUSEUM
(www.wsmr-history.org; Bldg 200, Headquarters Ave; 8am-4pm Mon-Fri, 10am-3pm Sat) Explore New Mexico's military technology history with a visit to this museum, 25 miles east of Las Cruces along Hwy 70. It represents the heart of the White Sands Missile Range, a major military testing site since 1945. There's a missile garden, a real V-2 rocket and a museum with lots of defense-related artifacts. Park outside the Test Center gate and check in at the office before walking to the museum.
Both Mesilla and Las Cruces are home to a burgeoning fine arts and performing arts community, with more than 40 galleries and a number of theatrical and musical production companies scattered around the valley. What's neat about gallery-hopping here is that many of the places double as the artists' studios and most are happy to chat with visitors about their passion. Find out more about arts, theaterand dance at the Branigan Cultural Center (501 N Main St Mall, Las Cruces; admission free; 9am-4:30pm Mon-Sat). The center also houses the Museum of Fine Art & Culture and the Las Cruces Historical Museum, with small collections of local art, sculpture, quilts and historic artifacts.
#### Festivals & Events
Whole Enchilada Fiesta FOOD
(www.enchiladafiesta.com) In late September, the fiesta is the city's best-known event. It features live music, food booths, arts and crafts, sporting events, a chile cook-off, carnival rides and a parade. It culminates in the cooking of the world's biggest enchilada on Sunday morning.
Southern New Mexico
State Fair & Rodeo CULTURAL
(www.snmstatefair.com) From late September to early October. Features a livestock show, auction, lively rodeo and country-music performances.
International Mariachi Conference MUSIC
(www.lascrucesmariachi.org) Celebrates this folkloric dance with educational workshops and big-time performances in mid-November.
Fiesta of Our Lady of Guadalupe RELIGIOUS
This fiesta, held in the nearby Indian village of Tortugas from December 10 to 12, is different. Late into the first night, drummers and masked dancers accompany a statue of Mary in a procession from the church. On the following day, participants climb several miles to Tortugas Mountain for Mass; dancing and ceremonies continue into the night in the village.
#### Sleeping
Las Cruces has a dearth of hotel and motelchains. At the cheapest places you can score a room for as little as $45 (plus taxes); the average for a Best Western– or HamptonInn–style motor lodge with an on-site restaurant and pool is around $80.
Lundeen Inn of the Arts B&B $$
( 505-526-3326; www.innofthearts.com; 618 S Alameda Blvd, Las Cruces; r incl breakfast $80-125, ste $99-155; ) This large, turn-of-the-19th-century Mexican Territorial–style inn is one of the nicest in its genre. The 20 thoughtfully decorated guest rooms are each unique and named for – and decorated in the style of – New Mexico artists. Check out the soaring pressed-tin ceilings in the great room decked out with old-world Jacobean-style furniture and dark wood floors. Owners Linda and Jerry offer the kind of genteel hospitality you don't find much anymore.
Mesón de Mesilla INN $
( 575-525-9212; www.mesondemesilla.com; 1803 Ave de Mesilla, Mesilla; r $79-129; ) This stylish and graceful adobe house has 15 guest rooms with antiques, Southwestern furnishings and modern amenities. A short walk from Mesilla Plaza, the 'boutique-style' house also has a lovely courtyard; attractive gardens surround the house.
Hotel Encanto de Las Cruces HOTEL $$
( 505-522-4300; www.hotelencanto.com; 705 S Telshor Blvd, Las Cruces; r from $99; ) This former Hilton is the city's best big hotel. It's got 200 spacious rooms done up in warm Southwestern style. Also on-site is an exercise room, restaurant and lounge.
Royal Host Motel MOTEL $
( 575-524-8536; 2146 W Picacho Ave, Las Cruces; r $45-65; ) Pets are welcome (extra $10) at this downtown spot with 26 spacious rooms. It's a basic budget motel, but clean and friendly. An on-site restaurant and swimming pool win points.
#### Eating
There are two main eating areas: Las Cruces and Mesilla. Located in the heart of the chile capital of the world, this area is home to some of the spiciest Mexican food in the state. Yum.
##### LAS CRUCES
Nellie's Café NEW MEXICAN $
(1226 W Hadley Ave; mains $5-8; 8am-2pm Tue-Sun) Without a doubt the favored local Mexican restaurant, Nellie's has been serving homemade burritos, _chile rellenos_ and tamales for decades now and has garnered a dedicated following. The slogan here is 'Chile with an Attitude' and the food is deliciously spicy. It's small and humble in decor, but big in taste.
Spirit Winds Coffee Bar CAFE $
(2260 S Locust; mains $5-15; 7am-7pm Mon-Fri, 7:30am-7pm Sat, 8am-6pm Sun; ) Join the university crowd for excellent cappuccino and gourmet tea, as well as good sandwiches, salads, soups and pastries, and some more substantial dishes come dinner. An eclectic gift and card shop and occasional live entertainment keeps the students, artsy types and business folks coming back.
Cattle Baron STEAKHOUSE $$
(www.cattlebaron.com; 790 S Telshor Blvd; mains $9-25; 11am-9:30pm Sun-Thu, to 10pm Fri & Sat; ) This small regional chain restaurant serves the best fine steaks in town, cooked to order. If you're not into red meat, don't fear: the Baron offers a wide range of chicken, pasta and seafood options as well as a salad bar and kids' menu. A good spot to bring the tots.
##### MESILLA
La Posta NEW MEXICAN $$
(www.laposta-de-mesilla.com; 2410 Calle de San Albino; mains $8-15; 11am-9:30pm) The area's most famous Mexican eatery is housed in an early-19th-century adobe house that predates the founding of Mesilla. A Butterfield stagecoach stop in the 1850s, today's restaurant claims to have the largest collection of tequila in the Southwest (with close to 100 varieties). Order enchiladas or fajitas.
Double Eagle Restaurant STEAKHOUSE $$$
( 575-523-6700; www.double-eagle-mesilla.com; 308 Calle de Guadalupe; mains $27-65; 11am-10pm Mon-Sat, noon-9pm Sun) Central courtyards, chandeliers and a 30ft bar are all fabulous assets to this upscale eatery, which serves delicious Continental and Southwestern cuisine in an elegant 19th-century Victorian-and Territorial-style setting. The steak is the thing. The restaurant is on the National Register of Historic Places; make sure to walk off lunch with a stroll around the property.
Chope's Bar & Café NEW MEXICAN $
(Hwy 28; mains $5-10; 11:30am-8:30pm Tue-Sat) About 15 miles south of town and worth every second of the drive, Chope's is a southern New Mexican institution. It isn't anything to look at, but the hot chile will turn you into an addict within minutes. From _chile_ _rellenos_ to burritos, you've seen the menu before; you just haven't had it this good. The adjacent bar is loads of fun.
#### Drinking & Entertainment
The _Bulletin,_ is a free weekly published on Thursday, that has up-to-the-minute entertainment information.
El Patio BAR
(Mesilla Plaza) In an old adobe building, this historic place has been rocking Mesilla since the 1930s. It serves cocktails along with live rock and jazz.
Graham Central Station THEME BAR
(www.grahamcentralstationlascruces.com; 505 S Main St, Las Cruces; cover $2-20) Join the university students for a night of revelry at this four-in-one club buffet. Listen to big-name country artists, enter a shot-taking contest or dance like you're in Miami at a South Beach–themed lounge under the same roof. It's a bit of a meat market – college kids come here to hook up.
Fountain Theater CINEMA
(www.mesillavalleyfilm.org; 2469 Calle de Guadalupe, Mesilla; adult/student $7/6) Home of the nonprofit Mesilla Valley Film Society, this theater screens foreign and art films. Check out the website to see what's playing when you're in town.
The American Southwest Theater Company presents plays at the Hershel Zohn Theater (http://panam.nmsu.edu/hershelzohntheatre.html; Pan Am Center) on the NMSU campus, while the Las Cruces Symphony (www.lascrucessymphony.com) performs at the NMSU Music Center Recital Hall.
### HATCH
The town of Hatch, 40 miles north of Las Cruces up I-25, is known as the 'Chile Capital of the World,' sitting at the heart of New Mexico's chile-growing country. New Mexican chiles didn't originate here – most local varieties have centuries-old roots in the northern farming villages around Chimayo and Española – but the earth and irrigation in these parts proved perfect for mass production. Recent harvests have declined sharply, as imported chile is starting to take over the market, but the town still clings to its title. Even if you miss the annual Labor Day Weekend Chile Festival (www.hatchchilefest.com; per vehicle $10), just pull off the interstate at Exit 41 and pop into Sparky's Burgers (www.sparkysburgers.com; 115 Franklin St; mains $4-10; 10:30am-7pm Thu-Mon, to 7:30 Fri & Sat) for what might be the best green chile cheeseburger in the state ( _New Mexico Magazine_ thinks so), served with casual pride. Lots of the locals actually order the barbecue – after you smell it, you might too!
#### Information
Las Cruces Convention & Visitors Bureau ( 800-343-7827; www.lascrucescvb.org; 211 N Water) Loads of tourist info.
Memorial Medical Center ( 575-522-8641; 2450 S Telshor Blvd, Las Cruces; 24hr emergency)
Mesilla Visitor Center ( 575-647-9698; www.oldmesilla.org; 2231 Ave de Mesilla; 9:30am-4:30pm Mon-Sat, 11am-3pm Sun)
Police ( 505-526-0795; 217 E Picacho Ave, Las Cruces)
Post office (201 E Las Cruces Ave, Las Cruces)
#### Getting There & Away
Greyhound ( 575-524-8518; www.greyhound.com; 490 N Valley Dr) has buses traversing the two interstate corridors (I-10 and I-25), as well as buses to Roswell and beyond. Las Cruces Shuttle Service ( 800-288-1784; www.lascrucesshuttle.com) runs 12 vans daily to the El Paso International Airport ($45 one-way, $15 to $25 for each additional person) and vans to Deming, Silver City and other destinations on request.
## CARLSBAD CAVERNS & SOUTHEASTERN NEW MEXICO
Two of New Mexico's greatest natural wonders are tucked down here in the arid southeast: mesmerizing White Sands National Monument and magnificent Carlsbad Caverns National Park. This region also swirls with some of the state's most enduring legends: aliens in Roswell, Billy the Kid in Lincoln, and Smokey Bear in Capitan. Most of the lowlands are covered by hot, rugged Chihuahuan Desert –which once used to be under the ocean – but you can always escape to the cooler climes around the popular forested resort towns of Cloudcroft or Ruidoso.
### White Sands National Monument
Undulating through the Tularosa Basin like something straight out of a dream, these ethereal dunes are a highlight of any trip to New Mexico and a must on every landscape photographer's itinerary. Try to time a visit to White Sands (www.nps.gov/whsa; adult/under 16yr $3/free; 7am-9pm Jun-Aug, 7am-sunset Sep-May) with sunrise or sunset (or both), when it's at its most magical. From the visitor center drive the 16-mile scenic loop into the heart of the dazzlingly white sea of sand that is the world's largest gypsum dune field, covering 275 sq miles. Along the way, get out of the car and romp around a bit. Hike the Alkali Flat, a 4.5-mile (round-trip) backcountry trail through the heart of the dunes, or the simple 1-mile loop nature trail. Don't forget your sunglasses – the sand is as bright as snow!
Spring for a $15 plastic saucer at the visitor center gift shop then sled one of the back dunes. It's fun, and you can sell the disc back for $5 at day's end (no rentals to avoid liability). Check the park calendar for sunset strolls and occasional moonlight bicycle rides (adult/child $5/2.50), the latter best reserved in advance.
Backcountry campsites, with no water or toilet facilities, are a mile from the scenic drive. Pick up one of the limited permits ($3, issued first-come, first-served) in person at the visitor center at least one hour before sunset.
### Alamogordo & Around
Despite a dearth of amenities, Alamogordo (Spanish for 'fat cottonwood tree') is the center of one of the most historically important space and atomic research programs. Most of the sights in town are kid-oriented, but adults who are young at heart will enjoy them too. You can also check out the tiny art outpost of La Luz or the fine vineyard in equally small Tularosa, both nearby towns.
White Sands Blvd (WSB; also called Hwy 54, 70 or 82) is the main drag through town and runs north–south. Addresses on North White Sands Blvd correspond to numbered cross streets (thus 1310 N WSB is just north of 13th); addresses on South WSB are one block south of 1st.
#### Sights & Activities
New Mexico Museum of Space History MUSEUM
(www.nmspacemuseum.org; Hwy 2001; adult/child$6/4; 9am-5pm; ). The most important museum is the four-story New Mexico Museum of Space History. Nicknamed 'the golden cube,' it looms over the town and has excellent exhibits on space research and flight. Its Tombaugh IMAX Theater & Planetarium (adult/child $6/4.50; ) shows outstanding films on everything from the Grand Canyon to the dark side of the moon, as well as laser shows and multimedia presentations on a huge wraparound screen. If your child has ever been interested in space travel, the museum runs a summer Space Academy (per day/week $150/$475; ) for kids aged 5 through 17. The education-based science program includes some pretty cool features, including flight training in a cockpit simulator, field trips and other hands-on experiments. The week-long sleepover camp is great if you have the time, but even if you're just in town for a few days, it's worth checking out the day camp. So far they plan to keep this running, despite the end of the manned space program...
### THREE RIVERS PETROGLYPH NATIONAL RECREATION AREA
The uncrowded Three Rivers Petroglyph NRA ( 575-525-4300; County Rd B30, off Hwy 54; per car $2, tent/RV sites $2/10; 8am-7pm Apr-Oct, to 5pm Nov-Mar) showcases over 21,000 petroglyphs inscribed 1000 years ago by the Jornada Mogollon people. The 1-mile hike through mesquite and cacti offers good views of the Sacramento Mountains to the east and White Sands Monument on the horizon. Nearby is a pit house in a partially excavated village. There are six camping shelters with barbecue grills (free), restrooms, water and two hookups for RVs. The BLM ( 575-525-4300; Marquess St, off Valley Dr) in Las Cruces has details. Pets are allowed in the campground but are banned from the trails.
The site is 27 miles north of Alamogordo on Hwy 54, and then 5 miles east on a signed road. If you want to rough it for the night, a dirt road continues beyond the petroglyphs for about 10 miles to the Lincoln National Forest, where you'll find Three Rivers Campground.
Toy Train Depot MUSEUM
(www.toytraindepot.homestead.com; 1991 N White Sands Blvd; admission $4; noon-4:30pm Wed-Sun; ) Railroad buffs and kids flock to the Toy Train Depot, an 1898 railway depot with five rooms of train memorabilia and toy trains, and a 2.5-mile narrow-gauge minitrain you can ride through Alameda Park.
Alameda Park & Zoo ZOO
(1021 N White Sands Blvd; adult/3-11yr $2.50/1.50; 9am-5pm; ) Established in 1898 as a diversion for railway travelers, this is the oldest zoo west of the Mississippi. Small but well run, it features exotics from around the world, among them the endangered Mexican gray wolf.
Alamogordo Museum of History MUSEUM
(www.alamogordohistorymuseum.com; 1301 N White Sands Blvd; 10am-4pm Mon-Fri, 10am-3pm Sat, 1-4pm Sun) This small and thoroughly local museum focuses on Mescalero Indians and the mining, railroad and logging industries. The museum's most cherished holding is a 47-star US flag, one of only a handful that exist because Arizona joined the USA just six weeks after New Mexico did.
La Luz & Tularosa NEIGHBORHOODS
Alamogordo's most attractive attractions lie outside the city limits. Head 4 miles north on Hwy 54 to the tiny art enclave of La Luz. Home to a motley crew of painters, writers and craftspeople who share a passion for creating artwork and living off the land, this wild outpost remains untouched by commercial tourism and is well worth a browse.
Continue north another 10 miles to the attractive village of Tularosa. It's dominated by the 1869 St Francis de Paula Church, built in a simple New Mexican style. Tularosa Vineyards ( 575-585-2260; www.tularosavineyards.com; Hwy 54; 9am-5pm Mon-Sat, noon-5pm Sun) is a friendly and picturesque winery about 2 miles north of Tularosa. It offers daily tastings and tours by appointment
#### Sleeping & Eating
This town doesn't have much in the way of creativity; besides the places listed here, there are many other chains scattered along White Sands Blvd. There's free dispersed camping off of Hwy 82, east of Alamogordo on the way to Cloudcroft.
Oliver Lee State Park CAMPGROUND $
(www.nmparks.com; 409 Dog Canyon Rd; tent/RV sites $8/14) Twelve miles south of Alamogordo, this park is set in a spring-fed canyon where you might see ferns and flowers growing in the desert. From the campground, Dog Canyon National Recreational Trail climbs some 2000 feet over 5.5 miles, featuring terrific views of the Tularosa Basin.
### THE BLAST HEARD 'ROUND THE WORLD
On just two days a year (the first Saturday in April and October), the public is permitted to tour the Trinity Site (per car $25), 35 miles west of Carrizozo, where the first atomic bomb was detonated on July 16, 1945. The eerie tour includes the base camp, the McDonald Ranch house where the plutonium core for the bomb was assembled, and ground zero itself. The test was carried out above ground and resulted in a quarter-mile-wide crater and an 8-mile-high cloud mushrooming above the desert. The radiation level of the site is 'only' 10 times greater than the region's background level; a one-hour visit to ground zero will result in an exposure of one-half to one milliroentgen (mrem) – two to four times the estimated exposure of a typical adult on an average day in the USA. Trinitite, a green, glassy substance resulting from the blast, is still radioactive, still scattered around and still must not be touched. Resist the urge to add it to your road-trip rock collection. This desolate area is fittingly called Jornada del Muerto (Journey of Death) and is overshadowed by 8638ft Oscura Peak (Darkness Peak on state maps). Travel to Trinity is permitted only as part of an official convoy. Call the Alamogordo Chamber of Commerce ( 505-437-6120; www.alamogordo.com) in advance for information.
Best Western Desert Aire Motor Inn HOTEL $$
( 575-437-2110; www.bestwestern.com; 1021 SWhite Sands Blvd; r from $78; ) Recently remodeled, this chain hotel has standard-issue rooms and suites (some with kitchenettes), along with a sauna and whirlpool. In summer, the swimming pool is a cool sanctuary.
Satellite Inn MOTEL $
( 575-437-8454; www.satelliteinn.com; 2224 N White Sands Blvd; r $44; ) An old-school Alamogordo independent with simple and clean double rooms that have microwave and refrigerator. Rooms are basic, but it's a bit more personal-feeling than your typical roadside motel.
Pizza Patio & Pub ITALIAN $$
(2203 E 1st St, mains $7-15; 11am-8pm Mon-Thu & Sat; til 9pm Fri; ) This is the best something-for-everyone place in Alamogordo, with an outdoor patio and casual indoor dining room. Pizzas and pastas are good, salads are big, and pitchers or pints of beer are on tap.
Margo's NEW MEXICAN $
(504 E 1st St; mains $6-15; 10:30am-9pm Mon-Sat, 11am-8:30pm Sun) There's not much to look at inside, but the New Mexican cuisine is solid and the prices are fair. Family-owned since the early 1980s, Margo's has a robust and tasty combo plate.
Stella Vita AMERICAN $$$
(www.stellavitarestaurant.com; 902 New York St; lunch mains $9-11, dinner mains $20-32; 11am-2pm Mon-Fri, 5-9pm Tue-Sat) This is Alamogordo's most upscale eatery, where you can dine from a meaty menu in an atmosphere of faux elegance under the gaze of a large cow skull. The staff is very friendly, but the light jazz background music is pretty irritating – maybe they'll turn it down for you...
#### Information
Hospital ( 575-439-6100; 2669 N Scenic Dr; 24hr emergency)
Lincoln USFS National Forest Ranger Station ( 575-434-7200; 1101 New York Ave; 7:30am-4:30pm Mon-Fri)
Police ( 575-439-4300; 700 Virginia Ave)
Post office (30 E 12th St)
Visitor center ( 575-437-6120; www.alamogordo.com; 1301 N White Sands Blvd; 8am-5pm Mon-Fri, 9am-5pm Sat & Sun; )
#### Getting There & Around
Greyhound ( 800-231-2222; www.greyhound.com; 601 N White Sands Blvd) has daily buses to Albuquerque ($65, 4½ hours), Roswell ($43, 2½ hours), Carlsbad ($77, 4½ hours) and El Paso, TX ($34, 2½ hours). The Alamo El Paso Shuttle ( 575-437-1472; Best Western Desert Aire Motor Inn) has four buses daily to the El Paso, TX International Airport ($48, 1½ hours).
### Cloudcroft & Around
Nestled high in the mountains, Cloudcroft is pleasant year-round. In winter there's snow tubing and snowmobiling across powder-soaked meadows. In summer, at nearly 2 miles high, Cloudcroft offers refreshing respite from the surrounding desert heat, plus awesome hiking and biking. The town itself is a quaint place to wander, with some early-19th-century buildings, a low-key mountain vibe and one of the top historic resorts in the Southwest. But where Cloudcroft really shines is the great outdoors, and most people visit to play in the surrounding peaks and forests.
#### Sights
Hwy 82 is the main drag through town; most places are on Hwy 82 or within a few blocks of it.
Sacramento Peak Observatory OBSERVATORY
( 575-434-7000; visitor center 9am-5pm, closed Feb) One of the world's largest solar observatories is near Sunspot, 20 miles south of Cloudcroft. Though it's primarily for scientists, tourists can take self-guided tours ( dawn-dusk, year-round) or guided tours (adult/child $3/free; 2pm, summer only). The drive to Sunspot, along the Sunspot Scenic Byway, is a high and beautiful one, with the mountains to the east and White Sands National Monument to the west. From Cloudcroft, take Hwy 130 to Hwy 6563. Fill your tank in Cloudcroft before making the drive.
#### Activities
###### Hiking
Hiking is popular here from April to November; outings range from short hikes close to town to overnight backpacking trips. Although trails are often fairly flat, the 9000ft elevation can make for some strenuous hiking if you are not acclimatized. The most popular day hike is the 2.6-mile Osha Loop Trail, which leaves Hwy 82 from a small parking area 1 mile west of Cloudcroft. The Willie White/Wills Canyon Trails loop through open meadows, with a good chance of seeing elk. The ranger station has tons of info, free trail maps and detailed topo maps for sale.
###### Golf
The Lodge Resort has a beautiful 18-hole golf course ( 575-682-2098; 9/18 holes from $26/46) that is one of the highest and oldest in the USA. In the winter, the course is groomed for cross-country skiing. The Lodge also provides guided snowmobile and horse-drawn sleigh rides.
###### Mountain Biking
Trails in the Sacramento Mountains offergreat mountain biking. High Altitude ( 575-682-1229; 310 Burro St; 10am-5:30pm Mon-Thu, to 6pm Fri & Sat; to 5pm Sun) rents bikes and points you in the right direction.
###### Skiing
In winter, grab the lift up and ski, snowboard or race an inner tube (weekends only) down the hill at Ski Cloudcroft (www.skicloudcroft.com; 1920 Hwy 82; all-day ski/tube $35/20; 9am-4pm Nov-Mar). The hill is family oriented, and you can say you've skied the southernmost run in the U.S.
#### Festivals & Events
Autumn is celebrated with Oktoberfest (first weekend of October) and summer is celebrated with an annual Cherry Festival on the third Sunday in June. The nearby hills between Cloudcroft and Alamogordo are rife with cherry orchards.
#### Sleeping & Eating
Cloudcroft is blessed with some heavenly choices. There are several USFS campgrounds in the area, open only in summer.
Lodge Resort & Spa LODGE $$
( 575-682-2566; www.thelodgeresort.com; 1 Corona Pl; r from $79; ) One of the best historic hotels in the Southwest, this place is reason enough to visit Cloudcroft. A grand old Lodge built in 1899 as a vacation getaway for railroad employees, today it is a full-scale resort, with a pampering spa with sauna –where treatments are tailored to the customer – a wonderful restaurant, a golf course and beautifully maintained grounds. Try to get a room in the main Bavarian-style hotel; these are furnished with period and Victorian pieces. Pavilion rooms are a few blocks away in a separate, less attractive building.
Cloudcroft Mountain Park Hostel HOSTEL $
( 575-682-0555; www.cloudcrofthostel.com; 1049 Hwy 82; dm $17, r with shared bath $30-50; ) Six miles west of Cloudcroft, this hostel is the best lodging deal around. Situated on 28 wooded acres, you can follow deer tracks to views of White Sands and the Tularosa Basin, or just enjoy the forest. Entire families can fit in the large rooms, which are simple but tidy. Shared bathrooms are clean, there's a fully equipped kitchen, and coffee and tea are provided. The common area is a great place to swap stories with other travelers.
Rebecca's AMERICAN $$
( 575-682-3131; Lodge Resort & Spa, 1 Corona Pl; mains $8-36; 7-10am, 11:30am-2pm & 5:30-9pm) Stop by Rebecca's, at the Lodge, for the long-standing favorite Sunday brunch. It's equally good for other meals – this is by far the best food in Cloudcroft. Kick back on the outside deck, have a beer and check out the spectacular views, then head inside for an elegant meal from a menu that includes everything from steak tenderloin to cheese enchiladas. Hours vary slightly according to season.
Weed Cafe DINER $
( 575-687-3611; 21 Weed Rd, Weed; mains $6-9; 8am-3pm Mon-Thu, 8am-7pm Fri & Sat, 10am-2pm Sun; ) For what might be the most out-of-the-way wi-fi hot spot in New Mexico, mosey on out to the town of Weed, 23 miles southeast of Cloudcroft in the Sacramento Mountains. Aside from internet access, you'll find a friendly local scene, hearty plates of diner food, and live music jam sessions on Friday and Saturday nights.
#### Information
Stop at the chamber of commerce ( 575-682-2733; www.cloudcroft.net; Hwy 82; 10am-5pm Mon-Sat) or Sacramento Ranger Station ( 575-682-2551; Chipmunk Ave; 7:30am-4:30pm Mon-Fri) for local info.
#### Getting There & Away
Cloudcroft is about 20 miles east of Alamogordo on Hwy 82 and is best reached via private vehicle.
### Ruidoso & Around
You want lively in these parts? You want Ruidoso. Downright bustling in the summer and big with punters at the racetrack, resortlike Ruidoso has an utterly pleasant climate thanks to its lofty and forested perch near the Sierra Blanca (11,981ft). Neighboring Texans and local New Mexicans escaping the summer heat of Alamogordo (46 miles to the southwest) and Roswell (71 miles to the east) are happy campers here (or more precisely, happy cabiners). The lovely Rio Ruidoso, a small creek with good fishing, runs through town. Summertime hiking and wintertime skiing at Ski Apache keep folks busy, as does a smattering of galleries.
#### Sights
Hwy 48 from the north is the main drag through town. This is called Mechem Dr until the small downtown area, where it becomes Sudderth Dr, heading east to the Y-intersection with Hwy 70. Six miles north on Mechem Dr is the community of Alto, with more accommodations.
Hubbard Museum of the American West MUSEUM
(www.hubbardmuseum.org; 841 Hwy 70 W; adult/child $6/2; 9am-5pm; ) This fine museum displays more than 10,000 Western-related items including Old West stagecoaches and American Indian pottery, and works by Frederic Remington and Charles M Russell. An impressive collection of horse-related displays, including a collection of saddles and the Racehorse Hall of Fame, lures horse-lovers.
Ruidoso Downs Racetrack HORSE RACING
(www.raceruidoso.com; Hwy 70; grandstand seats free; Fri-Mon late May-early Sep) The Ruidoso Downs is one of the major racetracks in the Southwest. The big event is Labor Day's All American Futurity. The world's richest quarter-horse race has a purse of $2.4 million. A track casino ( 10am-midnight Sun-Thu, to 1am Fri & Sat) features an all-you-can eat buffet ($7 to $15).
Mescalero Apache Indian Reservation INDIAN RESERVATION
About 4000 Apaches live on this 720-sq-mile reservation (www.mescaleroapache.com), which lies in attractive country 17 miles southwest of Ruidoso on Hwy 70. The nomadic Apache arrived in this area 800 years ago and soon became enemies with local Pueblo Indians. In the 19th century, under pressure from European settlement and with their mobility greatly increased by the introduction of the horse, the Apache became some of the most feared raiders of the West. Despite the name of the reservation, the Apache here are of three tribes: the Mescalero, the Chiricahua and the Lipan. The Cultural Center ( 575-464-4494; Chiricahua Plaza, off Hwy 70, Mescalero; hours vary) has an interesting exhibition about the Apache peoples and customs. Of course there's also the Inn of the Mountain Gods, a casino hotel with a champion golf course ( 800-545-9011; guest/nonguest from $60/75) and guided wild-game hunting if you feel like shooting something.
#### Activities
The best skiing area south of Albuquerque is Ski Apache (snow conditions 575-257-9001; www.skiapache.com; lift ticket adult/child $39/25), 18 miles northwest of Ruidoso on the slopes of beautiful Sierra Blanca Peak. It's not exactly world-class riding, but when it comes to affordability and fun, it's a good choice. Plus, Ski Apache is home to New Mexico's only gondola.
Hiking is popular in warmer months. If you're out for a day, try the 4.6-mile hike from the Ski Apache area to Sierra Blanca Peak, an ascent of 2000ft. Take Trail 15 from the small parking area just before the main lot and follow signs west and south along Trails 25 and 78 to Lookout Mountain (11,580ft). From there an obvious trail continues due south for 1.25 miles to Sierra Blanca Peak. For multiday trips, head into the White Mountains Wilderness, where 50 miles of trails criss-cross 48,000 scenic acres. The ranger station in Ruidoso has maps and information.
Rio Ruidoso and several national forest lakes offer good fishing. Flies Etc ( 505-257-4968; 2501 Sudderth Dr) has tackle and fishing licenses and runs fly-fishing excursions.
#### Festivals & Events
Ruidoso has a lot going on. Some of the highlights:
Apache Maidens' Puberty Ceremony CULTURAL
Takes place for about four days in early July and features a powwow, rodeo and arts-and-crafts demonstrations.
Ruidoso Art Festival ART
Attracts thousands of browsing and buying visitors from all over the Southwest on the last weekend of July.
Golden Aspen Motorcycle MOTORCYCLE RALLY
Draws 30,000 motorcycle-riders the third weekend of September.
Aspenfest STREET
Held on the first weekend in October, Aspenfest features a chile cook-off and a street festival.
Lincoln County Cowboy Symposium CULTURAL
The second weekend in October; features cowboy poetry, chuckwagon cooking and horsebreaking.
Oktoberfest CULTURAL
Bavarian-themed, with German food and beer, along with professional polka dancing and oompah bands. Held the third weekend in October.
#### Sleeping
There are lots of area cabin rentals, but some of the ones in town are cramped. Most of the newer cabins are located in the Upper Canyon. Generally, cabins have kitchens and grills, and often fireplaces and decks. The agency 4 Seasons Real Estate ( 800-822-7654; www.casasderuidoso.com; 712 Mechem Dr; 8am-5pm) arranges condominium, cabin and lodge rentals. There's plenty of free primitive camping along the forest roads on the way to the ski area.
Shadow Mountain Lodge LODGE $$
( 575-257-4886; www.smlruidoso.com; 107 Main St; r & cabins from $149; ) Geared toward couples, these immaculate rooms feature fireplaces and offer romantic allure. A wooden wraparound balcony overlooks the professionally landscaped grounds; the hot tub is tucked away in a gazebo. Individual cabins have Jacuzzi tubs and giant flat-screen TVs. Major discounts are often offered, so check.
Upper Canyon Inn LODGE $$
( 575-257-3005; www.uppercanyoninn.com; 215 Main Rd; r/cabins from $79/119; ) The wide variety of rooms and cabins here range from simple good values to rustic-chic luxury. Bigger doesn't necessarily mean more expensive here, so take a look at a few options. The pricier cabins have some fine interior woodwork and Jacuzzi tubs.
Sitzmark Chalet HOTEL $
( 800-658-9694; www.sitzmark-chalet.com; 627 Sudderth Dr; r from $60; ) This ski-themed chalet offers 17 simple but nice rooms. Picnic tables, grills and an eight-person hot tub are welcome perks.
Inn of the Mountain Gods CASINO HOTEL $$
( 800-545-9011; www.innofthemountaingods.com; 287 Carrizo Canyon Rd; r $129-299; ) This luxury resort hotel on the Mescalero Apache Reservation has surprisingly low rates – online promotions can be even lower. Gamblers can feed slots at the casino, and guided fishing, paddleboat rentals and horseback riding are all just a concierge call away. Several restaurants, a nightclub, a sports bar and a championship golf course are also on-site. It's fun for a night or two.
High Country Lodge LODGE $$
( 575-336-4321; www.highcountrylodge.net; Hwy 48; r from $89; ) Just south of the turnoff to Ski Apache, this funky older place welcomes you with three friendly (wooden) bears. It offers a comfortable selection of rustic and basic two-bedroom cabins, each with kitchen, fireplace and porch. Other facilities include a sauna, hot tub and tennis courts.
Bonito Hollow Campground CAMPGROUND $
( 575-336-4325; tent/RV sites $19/36, r/cabin $45/75; May–mid-Oct) Lots of options on the Bonita River.
Best Western Swiss Chalet HOTEL $
( 575-258-3333; 1451 Mechem Dr; r $69-109; ) Convenient to the ski slopes and forest; ask about ski-and-bike packages.
#### Eating
Rickshaw ASIAN $$
( 575-257-2828; www.rickshawnewmexico.com; 601Mechmem Dr; lunch mains $7-9, dinner mains $11-22; 11am-9pm Thu-Tue) This is the best Asian food south of Albuquerque, with selections inspired by but not slavish to the cuisine of Thailand, China and India. Order from the menu or be adventurous and sit at the Tanoshimu Table, where you'll dine family-style with strangers on whatever dishes the chef sends out of the kitchen; you pay by the hour and can stay as long as you like. Definitely finish with the ginger-pear crumble over homemade cinnamon ice cream.
Cornerstone Bakery BREAKFAST $
(359 Sudderth Dr; mains under $10; 7:30am-2pm Mon-Sat, to 1pm Sun; ) Stay around long enough and the Cornerstone may become your morning touchstone. Everything on the menu, from omelets to croissant sandwiches, is worthy. Locals are addicted.
Casa Blanca NEW MEXICAN $$
( 575-257-2495; 501 Mechem Dr; mains $9-18; 7am-8:30pm) Dine on Southwestern cuisine in a renovated Spanish-style house or on the pleasant patio in the summer. It's hard to go wrong with the New Mexican plates, but they've also got big burgers and chicken-fried steak. Breakfast gets raves.
Café Rio PIZZA $
(2547 Sudderth Dr; mains $5-25; 11am-9pm; ) Thick-crust pizza, with your choice of toppings, is deservedly popular here, but the stuffed calzones and Greek offerings are also decent for a small-town restaurant. Wash it down with a big selection of international and seasonal beer.
Texas Club STEAKHOUSE $$$
( 575-258-3325; 212 Metz Dr; mains $15-35; 5-9pm Wed-Sun, to 10pm Fri & Sat) One of the busiest and best restaurants in town, and decorated with all the bigness you'd expect in a place that takes its name from Texas (think longhorns and cowboy hats), this place serves big tasty steaks and seafood. There is dancing and live entertainment on the weekends. Call for reservations (it's often packed).
#### Drinking & Entertainment
Quarters BAR
(2535 Sudderth Dr) Dance the night away to live blues and rock on the big dance floor, or listen from a barstool or at one of the comfortable tables.
Spencer Theater for the
Performing Arts PERFORMING ARTS
(www.spencertheater.com; 108 Spencer Rd, Alto) In a stunning mountain venue, it hosts theatrical, musical and dance performances. Check the website for what's playing. Take Hwy 220 to Alto.
Flying J Ranch DINNER SHOW
( 505-336-4330; www.flyingjranch.com; Hwy 48;adult/child $24/14; from 5:30 Mon-Sat late May–early Sep; ) Families with little ones will love this place, as it delivers a full night of entertainment, not just dinner. Located 1.5 miles north of Alto, this 'Western village' stages gunfights and offers pony rides with their cowboy-style chuckwagon. Western music tops off the evening.
#### Information
Both the chamber of commerce ( 575-257-7395; www.ruidoso.net; 720 Sudderth Dr; 8am-4:30pm Mon-Fri, 9am-3pm Sat) and the Smokey Bear Ranger Station ( 575-257-4095; 901 Mechem Dr; 7:30am-4:30pm Mon-Fri year-round, plus Sat in summer) are helpful. The chamber's website has Spanish, Italian, German and French translations.
#### Getting There & Around
Greyhound ( 575-257-2660; www.greyhound.com; 138 Service Rd) operates daily service to Alamogordo ($20, one hour), Roswell ($30, 1½ hours), and El Paso, TX ($34, 3½ hours).
### SMOKEY BEAR'S STOMPING GROUNDS
You've seen his likeness in state and national forests everywhere around the region. But did you know that Smokey Bear was also a real black bear? Once upon a time (back in 1950), a little cub was found clinging to a tree, paws charred from a 17,000-acre forest fire in the Capitan Mountains. What better name to give him than that of the famous cartoon bear that had been the symbol of fire prevention since 1944? Nursed back to health, Smokey spent the rest of his days in the National Zoo in Washington, DC, and became a living mascot. At the 3-acre Smokey Bear Historical State Park ( 575-354-2748; per day $1), in the village of Capitan, 12 miles west of Lincoln, you can see the bear's grave and learn tons about forest fires. Every Fourth of July, a Smokey the Bear Stampede features a parade, a rodeo, cookouts and other festivities. Smokey the Bear Days, celebrated the first weekend in May, includes a street dance, wood carving contest, and craft and antique-car shows.
If you're lucky enough to be around on a weekend, make it a point to eat at Chango's ( 575-354-1234; 103 Lincoln Ave; mains $10-18; 4-8pm Fri & Sat, 11am-3pm Sun), a seven-table boutique restaurant where the menu changes weekly. The building, over 100 years old, has an interesting history (it's been a fish house, a mink farm and a hotel), and now doubles as an art gallery with fantastical sculptures and avant-garde quilts.
### Carrizozo
Carrizozo is a little town sitting where the Sacramento Mountains hit the Tularosa Basin. Art galleries and antiques shops line historic 12th St, downtown's main axis. Take a look into Gallery 408 (408 12th St; www.gallery408.com; 10am-5pm Mon, Fri & Sat, noon-5pm Sun). In addition to the work of a number of regional artists, you can see what remains of the herd of Painted Burros – a Carrizozo concept similar to the Cow Parades of Chicago and New York, but on a slightly smaller scale. Some have pun-tasticnames, like The Asstronomer, its body decorated with the night sky. Proceeds from donkey sales benefit the local animal shelter, Miracles Paws for Pets.
For a good breakfast, lunch or caffeine fix, look for La Brewja Café (113 Central Ave; mains under $10; 7am-2pm Mon-Fri; ), a funky coffee shop/art space with old-school Formica tables and matching vinyl chairs.
Four miles west of Carrizozo, explore the rocky blackness of a 125-sq-mile lava flow that's 160ft deep in the middle. A 0.6-mile nature trail at Valley of Fires Recreation Area (Hwy 380; vehicles $3, tent/RV sites $7/12) is well paved, easy for kids and marked with informative signs describing the geology and biology of the volcanic remains. You're also allowed to hike off-trail, simply cutting cross-country over the flow as you like. There are campsites and shaded picnic tables near the visitor center.
### Lincoln
Fans of Western history won't want to miss little Lincoln. Twelve miles east of Capitan along the Billy the Kid National Scenic Byway (www.billybyway.com), this is where the gun battle that turned Billy the Kid into a legend took place.
It's hard to believe that in Billy the Kid's era Lincoln had a bustling population of nearly 900. Today it is essentially a ghost town, with only about 50 people living here. Those who do, however, are dedicated to preserving the town's 1880s buildings. Modern influences, such as souvenir stands, are not allowed in town, and the main street has been designated the Lincoln State Monument. It's a pretty cool place to get away from this century for a night.
Start at the Anderson Freeman Visitor Center & Museum (Hwy 380; adult/child $5/free; 8:30am-4:30pm), where exhibits on the Buffalo soldiers, Apaches and the Lincoln County War explain the town's history. The admission price includes entry to the Tunstall Store (with a remarkable display of late-19th-century merchandise), the courthouse where the Kid famously shot his way to freedom, and Dr Wood's house, an intact turn-of-the-century doctor's home and office.
### LEGEND OF BILLY THE KID
So much speculation swirls. Even the most basic information about Billy the Kid tends to cast a shadow larger than the outlaw himself. Here's what we know, or don't. Most historians agree that he was born sometime in 1859, most likely in New York City (or Indiana or Missouri). He _may_ be buried in Old Fort Sumner, where his skull _may_ have been stolen and _possibly_ recovered) – that is, unless he colluded with his presumed assassin, Sheriff Pat Garrett, and lived to a ripe, old age...somewhere.
The Kid didn't start out as a murderer. His first known childhood crimes included stealing laundry and fencing butter. In the mid-1870s, about the time the teenage Billy arrived in New Mexico, the 400 residents of Lincoln shopped at 'Murphy's,' the only general store in the region. In 1877, though, Englishman John Tunstall arrived and built a competing general store.
Within a year, Tunstall was dead, allegedly shot by Murphy and his boys. The entire region erupted in what became known as the Lincoln County War. Tunstall's most famous follower was a wild teenager named Henry McCarty, alias William Bonney, aka Billy the Kid. Over the next several months the Kid and his gang gunned down any members of the Murphy faction they could find. The Kid was captured or cornered a number of times but managed brazen and lucky escapes before finally being shot by Sheriff Pat Garrett near Fort Sumner in 1881, where he lies in a grave in a barren yard. Maybe.
Enough controversy still dangles over whether he conspired with Sheriff Garrett to fake his death that there is a long-running movement to exhume the body and do a little DNA testing. Brushy Bill Roberts of Hico, Texas, now deceased, claimed that he was actually the elusive outlaw. A man in his 70s claims that Sheriff Garrett's widow told him at the tender age of nine that the conspiracy was, in fact, the truth.
Near the end of his term as governor in 2010, Bill Richardson considered granting the Kid a posthumous pardon, based on historical evidence that he'd been promised one by territorial governor Lew Wallace if he'd give testimony about the murder of Lincoln County Sherriff William Brady in 1878. The Kid testified but, rather than being pardoned, was sentenced to death. After much deliberation, and partly due to protests raised by descendents of Pat Garrett and Lew Wallace, Richardson declined to pardon the Kid.
During the Old Lincoln Days (held the first full weekend in August), now in its sixth decade, musicians and mountain men, doctors and desperadoes wander the streets in period costume, and there are demonstrations of spinning, blacksmithing and other common frontier skills. In the evening there is the folk pageant, 'The Last Escape of Billy the Kid.'
The 19th-century adobe Ellis Store Country Inn ( 575-653-4609; www.ellisstore.com; Hwy 380; r incl breakfast $89-$119) offers three antiques-filled rooms (complete with wood stove) in the main house and five additional rooms in a historic mill on the property. The host – once named New Mexico's 'Chef of the Year' – offers a six-course dinner ($75 per person) served in the cozy dining room Thursday to Saturday. Nonguests are welcome with a reservation.
A few miles west on the road to Capitan, Laughing Sheep Farm and Ranch ( 575-653-4041; www.laughingsheepfarm.com; mains $11-36; 11am-3pm Wed-Sun, 5-8pm Fri & Sat; ) raises sheep, cows and bison – along with vegetables and fruits – then serves them for lunch and dinner. Food is farm-fresh and delicious. The dining room is comfortable and casual, with live fiddle music on weekend nights plus a play-dough table and an easel to keep the kids happy. At the time of research, comfortable, newly built cabins were just opening to overnight guests; call for rates.
About 14 miles south of Lincoln, Hurd Ranch Guest Homes ( 575-653-4331; www.wyethartists.com; 105 La Rinconada, San Patricio; casitas $125-350; ) is a 2500-acre, very rural place in San Patricio that rents six lovely casitas by an apple orchard. Furnished with style and grace, and lots of original art, some units sleep up to six people. They are outfitted with modern conveniences. Owner and artist Michael Hurd runs the Hurd-La Rinconada Gallery on the premises; he also shows the work of his relatives NC and Andrew Wyeth, his mother Henriette Wyeth and his father Peter Hurd. Pets can stay for $10 (per visit).
### Roswell
Whether or not you're a true believer, a visit to Roswell is worth visiting to experience one of America's most enduring, eclectic and fanatical pop-culture phenomena. Sure it's about as cheesy as it gets for some, but conspiracy theorists and _X-Files_ fanatics descend from other worlds into Roswell in real seriousness. Oddly famous as both the country's largest producer of wool and its UFO capital, Roswell has built a tourist industry around the alleged July 1947 UFO crash (see Click here), after which the military quickly closed the area and allowed no more information to filter out for several decades. Was it a flying saucer? The local convention and visitors bureau suggest that Roswell's special blend of climate and culture attracted touring space aliens who wanted a closer look! Decide for yourself.
If you're driving east on Hwy 70/380 from the Sacramento Mountains, enjoy the view. Roswell sits on the western edge of the dry plains, and these are the last big mountains you'll see for a while.
The 'Staked Plains' extending east into Texas were once home to millions of buffalo and many nomadic Native American hunters. White settlers and hunters moved in throughout the late 19th century, and killed some 3.5 million buffalo during a two-year period. Within a few years, the region became desolate and empty; only a few groups of Comanche mixed with other tribes roaming the plains, hunting and trying to avoid confinement on reservations. Roswell, founded in 1871, served as a stopping place for cowboys driving cattle.
#### Sights & Activities
The main west–east drag through town is 2nd St and the main north–south thoroughfare is Main St; their intersection is the heart of downtown.
Roswell
Sights
Goddard Planetarium (see 3)
1Historical Center for Southeast New Mexico A4
2International UFO Museum & Research Center B4
3Roswell Museum & Art Center B3
Sleeping
4Budget Inn B1
Eating
5Farley's B2
6Martin's Capitol Café B4
International UFO Museum
& Research Center MUSEUM
(www.roswellufomuseum.com; 114 N Main St; adult/child $5/$2; 9am-5pm) Serious followers of UFO phenomena (not to mention skeptics or the merely curious) will want to check out this museum and research center. Original photographs and witness statements form the 1947 Roswell Incident Timeline and explain the 'great cover-up.' The library claims to have the most comprehensive UFO-related materials in the world, and we have no reason to be skeptical.
Roswell Museum & Art Center MUSEUM
(www.roswellmuseum.org; 100 W 11th St; admission free; 9am-5pm Mon-Sat, 1-5pm Sun) On a more down-to-earth front, Roswell's excellent museum and art center deserves a visit. Seventeen galleries showcase Southwestern artists including Georgia O'Keeffe, Peter Hurd and Henriette Wyeth, along with an eclectic mix of Native American, Hispanic and Anglo artifacts. A major focus of the museum is space research. The Goddard Planetarium is the reconstructed lab of Robert H Goddard, who launched the first successful liquid fuel rocket in 1926. Goddard spent more than a decade carrying out rocket research in Roswell. A variety of early rocketry paraphernalia is also on display.
Historical Center for Southeast
New Mexico MUSEUM
(www.hssnm.net; 200 N Lea Ave; admission by donation; 1-4pm) Housed in the 1912 mansion of local rancher James Phelps White, this property is well worth seeing. It's on the National Register of Historic Places, and its interior has been carefully restored to its original early-20th-century decor, with period furnishings, photographs and art.
Bitter Lake National Wildlife Refuge WILDLIFE RESERVE
(www.fws.gov/southwest; Pine Lodge Rd; sunrise-sunset) Birders will want to bring their binoculars. Wintering water birds gather at this 38-sq-mile refuge; many birds remain to nest in the summer. To reach the refuge, about 15 miles northeast of Roswell, follow the signed roads from either Hwy 380 or Hwy 285/70.
#### Festivals & Events
As you might imagine, Roswell has a couple of quirky festivals worth checking out.
New Mexico Dairy Day FOOD
In early June, Dairy Day features the Great Milk Carton Boat Race on Lake Van, 20 miles south of Roswell, as well as cheese-sculpting contests, 36ft-long ice cream sundaes, games and sporting events.
UFO Festival QUIRKY
Centers around alien-costume competitions and lectures about UFOs.
Eastern New Mexico State Fair CULTURAL
The main annual event is the State Fair in early October, with rodeo, livestock and agricultural competitions and chile-eating contests.
### THE TRUTH IS OUT THERE...
It's been more than 60 years now since that heady summer of 1947, when an unidentified flying object fell out of the sky, and crash-landed in the desert near Roswell, and the little New Mexican town is still cashing in on the mystery. Those who believe aliens are out there are convinced it was a UFO that crashed the first week of July in that post-WWII baby-making summer, and that the US government has gone to great lengths to cover up the crash. They certainly have a compelling case with this one.
In a 1947 press release, the government identified the object as a crashed disk. A day later, however, it changed its story: now the disk was really just a weather balloon. The feds then confiscated all the previous press releases, cordoned off the area as they collected all the debris, and posted armed guards to escort curious locals from the site of the 'weather-balloon' crash. A local mortician fielded calls from the mortuary office at the government airfield inquiring after small, hermetically sealed coffins for preventing tissue contamination and degeneration.
Now 60-odd years after the incident, the government is still tight-lipped, and Roswell is the story that will never die. There are frequent eyewitness accounts of flying saucers in the sky, and rumor and misinformation continue to swirl about the original crash, fueling all manner of speculation over what really happened in the desert that day. In the early 2000s, Roswell even spawned its own TV series about alien-mutant hybrid teenagers trying to survive as humans while keeping their alien powers alive and attempting to get home.
Now Roswell celebrates the assertions and denials, the mystery and the speculation surrounding the event in an annual UFO Festival (www.roswellufofestival.com). Held on Fourth of July Weekend, it attracts upwards of 20,000 visitors from around the planet – Roswell is now synonymous with UFOs. Interplanetary-travel celebs such as the Duras sisters (known to Trekkies as Klingon warriors from the TV series _Star Trek_ ), as well as past astronauts, often make appearances. Besides enough lectures, films and workshops to make anyone's ears go pointy, the nighttime parade and alien-costume competitions are not to be missed.
#### Sleeping
There are plenty of chain hotels on the north end of main street, plus independent (sometimes sketchy) budget motels west on 2nd St.
Heritage Inn HISTORIC HOTEL $$
( 575-748-2552; www.artesiaheritageinn.com; 209W Main St, Artesia; r incl breakfast from $104; ) The nicest place to stay is actually not in Roswell. If you're traveling between Roswell and Carlsbad and in the mood for slightly upscale digs (this is southeastern New Mexico, don't forget), this turn-of-the-19th-century establishment offers 11 Old West–style rooms in Artesia, about 36 miles south of Roswell.
Budget Inn MOTEL $
( 575-623-6050; 2101 N Main St; r from $35; ) Basic but clean digs, with new pillow-top mattresses and continental breakfast. One of the best values in town.
Bottomless Lakes State Park CAMPGROUND $
(www.nmparks.com; Hwy 409; day-use per vehicle $5, tent/RV sites $10/14) Seven popular lakes in the area provide welcome relief from summer heat. These primitive campsites are among the best available. To reach them, drive 10 miles east of Roswell on Hwy 380, then 5 miles south on Hwy 409. The Lea Lake site has real bathrooms, showers and the only lake you're allowed to swim in.
#### Eating
Wellhead BREWERY $$
(www.thewellhead.com; 332 W Main St, Artesia; mains $8-27; 11am-9pm Mon-Sat) If you're traveling between Roswell and Carlsbad, you'll find some of the region's best food and drink at this modern brewpub restaurant and bar. Housed in a 1905 building and reflecting the town's origins, it's decorated with an oil-drilling theme. Artesia is about 36 miles south of Roswell.
Cowboy Cafe DINER $
(1120 E 2nd St; mains $4-10; 6am-2pm Mon-Sat) One of the few truly local joints left in town, this is a good option for breakfast before hitting the UFO museum or the road.
Martin's Capitol Café NEW MEXICAN $
(110 W 4th St; mains $7-15; 6am-8:30pm Mon-Sat) Although several inexpensive New Mexican restaurants here are good, this one is homestyle and dependable.
Farley's AMERICAN $
(1315 N Main St; mains $7-13; 11am-11pm Sun-Thu, to 1am Fri & Sat) A boisterous barn-like place that stays open late, Farley's has something for everyone: burgers, pizza, chicken and ribs. It also has a big bar with pool tables and music.
Mama Tucker's BAKERY $
(3109 N Main St; donuts $1; 5am-5pm Tue-Fri, 5am-1pm Sat-Mon) If you're cravingsomething sweet, head straight here for homemade donuts, cakes and cookies.
#### Information
Visitors Bureau ( 575-624-0889; www.roswellmysteries.com; 912 N Main St; 8:30am-5:30pm Mon-Fri, 10am-3pm Sat & Sun; )
Eastern New Mexico Medical Center ( 575-622-8170; 405 W Country Club Rd; 24hr emergency)
Police ( 575-624-6770; 128 W 2nd St)
Post office (415 N Pennsylvania Ave)
#### Getting There & Around
Greyhound ( 575-622-2510; www.greyhound.com; 1100 N Virginia Ave) has daily buses to Carlsbad ($28, 1½ hours) and Las Cruces ($49, four hours), from where you can transfer to Albuquerque or El Paso, TX.
### Carlsbad
When Carlsbad Caverns was declared a national monument in 1923, a trickle of tourists turned into a veritable flash flood. Today, hundreds of thousands of visitors come through annually. Carlsbad is situated on the Pecos River about 30 miles north of the Texas state line, and its main thoroughfare is Hwy 285, which becomes Canal St, then S Canal (south of Mermod St) and then National Parks Hwy at the southern end of town.
#### Sights & Activities
Living Desert State Park ZOO
(www.nmparks.com; 1504 Miehls Dr, off Hwy 285; adult/child $5/3; 8am-8pm Jun-Aug, 9am-5pm Sep-May) On the northwestern outskirts of town, this state park is a great place to see and learn about roadrunners, wolves and antelopes, along with desert plants like agave, ocotillo and yucca. The park has a good 1.3-mile trail that showcases different habitats of the Chihuahuan Desert, plus a reptile house.
Carlsbad
Sights
1Carlsbad Museum & Art Center A2
2Carlsbad Riverfront Park B1
Port Jefferson (see 2)
Sleeping
3Stagecoach Inn B4
4Trinity Hotel A2
Eating
5Blue House Bakery & Café A1
6Danny's Place A3
7Lucy's A3
8Red Chimney Pit Barbeque A1
Trinity Restaurant & Wine Bar (see 4)
Lake Carlsbad WATERFRONT
A system of dams and spillways on the Pecos River created the 2-mile Lake Carlsbad, which has a pleasant 4.5-mile trail along its banks. At the north end of Park Dr (or at the east end of Church St), Carlsbad Riverfront Park has a beach and swimming area. At nearby Port Jefferson ( 10am-5pm Mon-Sat late May–early Sep, 10am-5pm Sat & Sun early Sep–Oct), you can rent a paddlewheel boat to tour the river.
Carlsbad Museum & Art Center MUSEUM
(www.nmculture.org; 418 W Fox St; 10am-5pm Mon-Sat) This museum displays Apache artifacts, pioneer memorabilia and art from the renowned Taos School.
#### Sleeping
The nearby national park and mild winters make this a year-round destination; always ask for the best rates. It's mostly chain motels in Carlsbad, plenty of which can be found on Canal St.
Trinity Hotel BOUTIQUE HOTEL $$
( 575-234-9891; www.thetrinityhotel.com; 201 S Canal St; r from $129-199; ) This luxurious new place is Carlsbad's best hotel. It's not exactly 'new' – it's in a renovated building that was once the First National Bank. The sitting room of one suite is inside the old vault! Family-run, it's friendly, and the restaurant is easily Carlsbad's classiest.
Stagecoach Inn MOTEL $
( 575-887-1148; 1819 S Canal St; r from $40; ) One of the best values in town, the Stagecoach has clean rooms, a swimming pool and an on-site playground for kids.
Carlsbad KOA CAMPGROUND $
( 575-457-2000; www.carlsbadkoa.com; 2 MantheiRd; tent/RV sites from $30/45, cabins $57; ) On Hwy 285 about 12 miles north of Carlsbad, this KOA offers the choice of air-conditioned 'kamping kabins' or grassy tent sites. There's a pool, game room, grocery store, laundry, playground and showers here. Ask friendly hosts Scott and Susan Bacher about free rides for the kids in a retired fire truck. The KOA is also dog-friendly, with a park especially for your canine companion.
#### Eating & Drinking
Trinity Restaurant & Wine Bar AMERICAN $$
(www.thetrinityhotel.com; Trinity Hotel, 201 S Canal St; mains breakfast $6-12, lunch $8-12, dinner $10-29; 7-10am, 11am-1:45pm & 5-9pm Mon-Sat, 8am-noon Sun; ) Carlsbad's finest dining features steaks, seafood, and Italian specialties. This is the town's top choice for vegetarians, too, with pastas and salads. Nonkosher carnivores will love the roast pork in a cabernet/green chile reduction. Free wine tastings are held from 3pm to 5pm most days.
Blue House Bakery & Café BREAKFAST $
(609 N Canyon St; mains $3-9; 6am-2pm Tue-Fri, 6am-noon Mon & Sat) This sweet Queen Anne house perks the best coffee and espresso in this quadrant of New Mexico. Its baked goods are pretty darn good too. At lunchtime, the cheery place has good sandwiches made with fresh breads.
Lucy's NEW MEXICAN $$
(701 S Canal St; mains $7-16; 11am-9pm Mon-Thu, to 9:30 Fri & Sat) The most popular place in Carlsbad, Lucy's is usually packed with devoted locals _and_ visitors. Apart from a great Mexican menu, Lucy's serves up tasty margaritas and a good selection of microbrews (and admittedly that may be one reason the place is jumpin').
Red Chimney Pit Barbecue BARBECUE $$
(817 N Canal St; mains $7-15; 11am-2pm, 4:30-8:30pm Mon-Fri) Red Chimney's got quality meats with tasty sauce.
Danny's Place BARBECUE $
(902 S Canal St; mains $6-12; 11am-9pm) It's not quite as good as Red Chimney, but it is open Sundays (rare in Carlsbad).
#### Information
Carlsbad Chamber of Commerce ( 575-887-6516; www.carlsbadchamber.com; 302 S Canal St; 9am-5pm Mon, 8am-5pm Tue-Fri year-round, 9am-3pm Sat May-Sep) Very knowledgeable and helpful with tourist info.
Carlsbad Medical Center ( 575-887-4100; 2430 W Pierce St; 24hr emergency)
National Parks Information Center ( 575-885-8884; 3225 National Parks Hwy; 8am-4:30pm Mon-Fri) Information on both Carlsbad Caverns National Park and Guadalupe Mountains National Park. About a mile south of town.
Police ( 575-885-2111; 405 S Halagueno St)
USFS Ranger Station ( 575-885-4181; 114 S Halagueno; 7:30am-4:30pm Mon-Fri) Info on Sitting Bull Falls and hiking and backpacking in Lincoln National Forest.
#### Getting There & Away
Greyhound ( 575-887-1108; www.greyhound.com; 1000 Canyon St) buses depart daily for Las Cruces ($65, 6 hours) and El Paso, TX ($57, 3 hours); the bus stops at the Allsup's gas station a few miles south of town on Hwy 180.
### SITTING BULL FALLS
An oasis in the desert, Sitting Bull Falls (per vehicle $5; 8:30am-6pm Apr-Sep, to 5pm Oct-Mar) is tucked among the burly canyons of the Guadalupe Mountains, 42 miles southwest of Carlsbad. A spring-fed creek pours 150ft over a limestone cliff, with natural pools below and above the falls that are great for swimming – or at least dunking and cooling off. There are a series of caves behind the waterfalls, which can be explored only with a ranger.
Twenty-six miles of trails around the falls offer the best hiking anywhere near Carlsbad. Though there is no camping in the designated recreation area, backpackers may hike in and camp further up Sitting Bull Canyon, or up Last Chance Canyon, which also usually flows with water. Extended routes from here can take experienced multiday trekkers south all the way into Guadalupe Mountains National Park, in Texas. If you plan on hiking, keep in mind that it gets brutally hot here in summer; it's ideal from late fall to early spring.
Arrange cave walks and pick up trail maps and other info, including a pamphlet about what to do if you encounter a mountain lion, at the Lincoln National Forest office in Carlsbad.
### Carlsbad Caverns National Park
Scores of wondrous caves hide under the hills at this unique national park ( 575-785-2232, bat info 505-785-3012; www.nps.gov/cave; 3225 National Parks Hwy; adult/child $6/free; caves 8:30am-4pm late May–early Sep, 8:30am-3:30pm early Sep–late May), which covers 73 sq miles. The cavern formations are a weird wonderland of stalactites and fantastical geological features. You can ride an elevator from the visitor center (which descends the length of the Empire State Building in under a minute) or take a 2-mile subterranean walk from the cave mouth to the Big Room, an underground chamber 1800ft long, 255ft high and over 800ft below the surface. If you've got kids (or are just feeling goofy), plastic caving helmets with headlamps are sold in the gift shop.
Guided tours ( 877-444-6777; www.recreation.gov; adult $7-20, child $3.50-10) of additional caves are available, and should be reserved well in advance. Bring long sleeves and closed shoes: it gets chilly.
The cave's other claim to fame is the 300,000-plus Mexican free-tailed bat colony that roosts here from mid-May to mid-October. Be here by sunset, when they cyclone out for an all-evening insect feast.
If you want to scramble to lesser-known areas, ask about Wild Cave tours. The last tickets are sold two to 3½ hours before the visitor center closes. Wilderness backpacking trips into the desert are allowed by permit (free); the visitor center sells topographical maps of the 50-plus miles of hiking trails. November to March is the best time for backpacking – summer temperatures are scorching, and the countless rattlesnakes should be sleeping in winter.
Deep within the park's backcountry is Lechugilla Cave. With a depth of 1604ft and a length of some 60 miles, it's the deepest cave and third-longest limestone cave in North America. Sounds incredible –but it's only open to research and exploration teams, with special permission from the park.
## I-40 EAST TO TEXAS
It can be pretty tempting to keep the pedal tothe metal – or set the cruise-control switch –and power on through the eastern half of I-40 without stopping. But if you've got a little time, there are some interesting historical detours, from the days of the dinosaurs to the worst of the Wild West to some of the best of what remains of classic Route 66 kitsch.
### Santa Rosa
Scuba in Santa Rosa? Yup, that's right. Settled in the mid-19th century by Spanish farmers, Santa Rosa's modern claim to fame is, oddly enough, as the scuba diving capital of the Southwest. There's not much else going on here, though.
#### Sights & Activities
Take exit 273 from Route 66/I-40 to reach downtown. The main street begins as Coronado St, then becomes Parker Ave through downtown, before becoming Will Rogers Dr when it passes exits 275 and 277.
Blue Hole DIVING
One of the 10 best spots to dive in the country is, surprisingly, here in li'l ol' Santa Rosa. How could that be? Because of the bell-shaped, 81ft-deep Blue Hole. Fed by a natural spring flowing at 3000 gallons a minute, the water in the hole is both very clear and pretty cool (about 61°F to 64°F, or around 17°C). It's also 80ft in diameter at the surface and 130ft in diameter below the surface. Platforms for diving are suspended about 25ft down. Visit the Santa Rosa Dive Center ( 575-472-3763; www.santarosanm.org; Hwy 40/US 66) to set up a dive. The shop is next to the Hole.
Puerto de Luna HISTORIC SITE
Nine miles south of town along Hwy 91, tiny Puerto de Luna was founded in the 1860s and is one of the oldest settlements in New Mexico. The drive there is pretty, winding through arroyos surrounded by eroded sandstone mesas. In town you'll find an old county courthouse, a village church and a bunch of weathered adobe buildings. It's all quite charming, as long as you're not in a hurry to do something else.
Route 66 Auto Museum MUSEUM
(www.route66automuseum.com; 2766 Rte 66; adult/child under 5 $5/free; 7:30am-6pm Mon-Sat, 10am-5pm Sun Apr-Oct, 8am-5pm Mon-Sat, 10am-5pm Sun Nov-Mar) This museum pays homage to the mother of all roads. It boasts upwards of 35 cars from the 1920s through the 1960s, all in beautiful condition in its exhibit hall, and lots of 1950s memorabilia. It's a fun place; enjoy a milkshake at the '50s-style snack shack. If you're in the market for a beautifully restored old Chevy, the museum doubles as an antique car dealer.
#### Festivals & Events
Annual Custom Car Show CAR SHOW
In keeping with the Route 66 theme, this car show, held in August or September, attracts vintage- and classic-car enthusiasts, as well as folks driving strange things on wheels.
Santa Rosa Fiesta CULTURAL
Homespun, to say the least, the Fiesta has a beauty-queen contest and the bizarre, annual Duck Drop: contestants buy squares and then wait for a duck suspended over the squares to poop – if the poop lands on their square, they win cold cash. Held in the third week of August.
#### Sleeping & Eating
The town is home to a number of long-established family-owned diners and roadside cafes, all with historic allure. If you want to stay the night, choose from your favorite chain hotel off of the I-40 exits. Most hotels and restaurants lie along the main thoroughfare, part of the celebrated Route 66.
Silver Moon DINER $$
(2545 Historic Route 66; mains $9-16; 6am-10pm) A trademark Route 66 eatery that first opened its doors in 1959, Silver Moon serves fantastic homemade _chile rellenos_ and other tasty diner grub dressed up with a New Mexican twist. It's popular with travelers following Route 66's old roadhouse trail, as well as locals who come for a morning coffee and a plate of bacon and eggs.
Joseph's Bar & Grill DINER $$
(865 Historic Route 66; mains $8-20; 7am-10pm Mon-Sat, to 9pm Sun) Route 66 nostalgia lines the walls of this popular place, family-owned since its inception in 1956. Many of the bountiful Mexican and American recipes have been handed down through the generations. Burgers and steaks are as popular as anything smothered in green chile. Joseph's also mixes some serious margaritas.
#### Information
The Chamber of Commerce ( 505-472-3763; www.santarosanm.org; 486 Parker Ave; 8am-5pm Mon-Fri) has tourist information.
#### Getting There & Away
Santa Rosa's downtown is at exit 273 on Route 66/I-40. The town is about 120 miles east of Albuquerque.
### Tucumcari
The biggest town on I-40 between Albuquerque and Amarillo, Tucumcari is a ranching and farming area between the mesas and the plains. It's also home to one of the best-preserved sections of Route 66 in the country. Not surprisingly, it still caters to travelers, with inexpensive motels, several classic pre-interstate buildings and souvenir shops like the Tee Pee Curios.
#### Sights & Activities
Drive the kids down Tucumcari's main street at night, when dozens of old neon signs cast a blazing glow. The bright, flashing signs are relics of Tucumcari's Route 66 heyday, when they were installed by business owners as a crafty form of marketing to get tired travelers to stop for the night. Tucumcari lies barely north of I-40. The main west–east thoroughfare between these exits is old Route 66, called Tucumcari Blvd through downtown. The principal north–south artery is 1st St.
Mesalands Dinosaur Museum MUSEUM
(222 E Laughlin St; adult/child $6.50/4; 10am-6pm Tue-Sat Mar-Aug, noon-5pm Tue-Sat Sep-Feb; ) Well worth a visit is this engaging museum, which showcases real dinosaur bones and has hands-on exhibits for kids. Casts of dinosaur bones are done in bronze (rather than the usual plaster of paris), which not only shows fine detail, but also makes them works of art.
Tucumcari Historical Museum MUSEUM
(416 S Adams St; adult/child $3/1; 9am-3pm Tue-Sat) Several rooms of the historical museum feature reconstructions of early Western interiors, such as a sheriff's office, a classroom and a hospital room. It's an eclectic collection, to say the least, displaying a barbed-wire collection alongside Indian artifacts.
Art Murals WALKING TOUR
The town is also home to 31 life-size and larger murals recording Tucumcari's history throughout the decades. The pieces of art, which adorn buildings on and just north and south of Route 66, are the life work of local painters Doug and Sharon Quarles. Taking the town's mural walk is a great way to stretch your legs and experience Tucumcari's Route 66 legacy. Grab a mural walking map off the website of the chamber of commerce (www.tucumcarinm.com/visitors_guide).
#### Sleeping
Tucumcari has the usual number of chain motels spread along I-40. It also has a some cool old independent motels on historic Route 66.
Blue Swallow Motel HISTORIC MOTEL $
( 575-461-9849; www.blueswallowmotel.com; 815E Tucumcari Blvd; r from $50; ) Spend the night in this beautifully restored Route 66 motel listed on the State and National Registers of Historic Places, and feel the decades melt away. The classic neon sign has been featured in many Route 66 articles and boasts that Blue Swallow offers '100% refrigerated air'. The place has a great lobby, friendly owners and vintage, uniquelydecorated rooms.
Historic Route 66 Motel MOTEL $
( 575-461-1212; www.tucumcarimotel.com; 1620 E Route 66; r from $30; ) When it comes to budget digs, you can't beat this historic motor-court motel with giant plate-glass doors and mesa views. It's nothing splashy, but the 25 rooms are cheap and clean, with comfy beds and quality pillows. Small dogs are welcome, and there's an on-site espresso bar/cafe.
#### Eating & Drinking
Del's Restaurant DINER $$
(www.delsrestaurant.com; 1202 E Tucumcari Blvd; mains $8-15; 11am-9pm) Del's is popular in these here parts simply because it exists. Its New Mexican and American diner fare is mediocre at best and the salad bar is anemic. For breakfast or lunch, try its better sister restaurant, Kix on 66 (www.kixon66.com; 1102 E Tucumcari Blvd; mains $5-10; 6am-2pm; ) with a variety of omelettes and quesadillas, plus an espresso machine.
Pow-Wow Restaurant & Lizard Lounge NEW MEXICAN $$
(801 W Tucumcari Blvd; mains $8-20; 7am-10pm, bar til late Fri & Sat) Though the menu is a bit better than Del's, the real draw here is the lounge. Thursdays are karaoke nights, and on some weekends big-name New Mexican bands, like Little Joe y la Familia, drop by to play a few sets.
### MOVING ON?
For tips, recommendations and reviews, head to shop.lonelyplanet.com to purchase a downloadable PDF of the Texas chapter from Lonely Planet's _USA_ guide.
#### Information
A chamber of commerce ( 575-461-1694; www.tucumcarinm.com; 404 W Tucumcari Blvd) keeps sporadic hours.
#### Getting There & Away
Tucumcari is at the crossroads of Historic Route 66, now I-40, and US Hwy 54. It is 110 miles from Amarillo, TX, and 170 miles from Albuquerque.
### Fort Sumner
If you have a moment to spare, swing through Fort Sumner. The little village that sprang up around old Fort Sumner gets more than a footnote in the history books for two reasons: the disastrous Bosque Redondo Indian Reservation and Billy the Kid's last showdown with Sheriff Pat Garrett.
#### Sights & Activities
Hwy 60 (Sumner Ave) is the main thoroughfare and runs east–west through town; most places of interest lie along it.
Billy the Kid Museum MUSEUM
(www.billythekidmuseumfortsumner.com; 1601 E Sumner Ave; adult/child $5/3; 8:30am-5pm daily mid-May–Sep, 8:30am-5pm Mon-Sat Oct–mid-May, closed first 2 weeks Jan) With more than 60,000 privately owned items on display, this place is more than just a museum about the famous outlaw. It's a veritable shrine, almost a research institution. Indian artifacts and items from late-19th-century frontier life fill many rooms.
Fort Sumner State Monument MUSEUM
(www.nmmonuments.org; Hwy 272; adult/child $5/free; 8:30am-5pm) During the 1860s, Fort Sumner was the heart of the Bosque RedondoIndian Reservation – the destination for Navajos forced from their homeland on the Long Walk (Click here), as well as captured Mescalero Apaches. Some 10,000 Native Americans were imprisoned here in terrible conditions, and about one-third of them died. Navajo call Fort Sumner _H'weeldi_ – the place of suffering. This is also where the Navajo Treaty was signed in 1868, establishing the Navajo Nation as a sovereign people and creating their reservation in their traditional homeland around the Four Corners. The Bosque Redondo Memorial within the Ft. Sumner grounds is informative and worth a visit, but the presentation is a bit sterile, lacking the emotional impact you might expect from an exhibit about such a profound tragedy.
Old Fort Sumner Museum MUSEUM
(Billy the Kid Rd; admission $5; 10am-5pm) This museum, with local history and an emphasis on Billy the Kid, is located near the state monument. Behind the museum you'll find Billy the Kid's Grave and that of Lucien Maxwell. The Kid's tombstone is protected by an iron cage because 'souvenir hunters' kept trying to steal it – even in death he's behind bars.
#### Festivals & Events
Old Fort Days CULTURAL
Held on the second weekend in June, this festival features various athletic events. The purse for the winner of the tombstone race, in which contestants must negotiate an obstacle course while lugging an 80lb tombstone, is $2000.
#### Sleeping & Eating
There are few options in Fort Sumner. If you're looking for a hotel, there's a Super 8 ( 575-355-7888; www.super8.com; 1559 E Sumner Ave; r from $60) on the east end of town. The best restaurant is Sadie's (510 Sumner Ave; mains $5-10; 7:30am-2pm & 5-8pm Thu-Mon) where you can pick up a homemade breakfast burrito or other simple but good New Mexican fare.
#### Information
The chamber of commerce ( 575-355-7705; www.ftsumnerchamber.com; 707 N 4th St; 9am-4pm Mon-Fri) is helpful.
#### Getting There & Away
Fort Sumner is on Hwy 60, 84 miles north of Roswell, 45 miles southwest of Santa Rosa and 60 miles west of Clovis. It is best reached by private vehicle.
Top of section
# Southwestern Colorado
**Includes »**
Pagosa Springs & Around
Durango
Mancos
Mesa Verde National Park
Cortez
Telluride
Ridgway
Ouray & the Million Dollar Hwy
Silverton
Crested Butte
### Why Go?
The West at its most rugged, this is a landscape of twisting canyons and ancient ruins, with burly peaks and gusty high desert plateaus. Centuries of boom, bust and boom – from silver to real estate and resorts – tell part of the story. There's also the lingering mystery of its earliest inhabitants, whose relics have been found at the abandoned cliff dwellings in Mesa Verde National Park.
Southwestern Colorado can be a heady place to play. Some of the finest powder skiing in the world melts to reveal winding singletrack and hiking trails in summer. A sense of remove keeps the Old West alive in wooden plank saloons and aboard the chugging Durango railroad.
With all that fresh mountain air, local attitudes – from the ranch hand to the real estate agent – are undoubtedly relaxed. Dally a bit under these ultra-blue skies and you'll know why.
### When to Go
Jun–Aug Prime time for cycling and hiking the legendary San Juans.
Sep–Nov Cool days in the high desert and fewer crowds in Mesa Verde.
Dec–Apr Powder hounds hit the famed slopes of Telluride.
### Best Places to Stay
»Willowtail Springs (Click here)
»Kelly Place (Click here)
»Wiesbaden (Click here)
»Jersey Jim Lookout Tower (Click here)
»Ruby of Crested Butte (Click here)
### Best Places to Eat
»Kennebec Café (Click here)
»New Sheridan Chop House (Click here)
»Secret Stash (Click here)
»East by Southwest (Click here)
»Absolute Baking & Cafe (Click here)
### Southwestern Colorado Planning
summer at high altitude can be chilly – bring warm clothing and sturdy boots. at lower altitudes, the drier desert climate means mild shoulder seasons ideal for camping and mountain biking, while mountain towns like ouray and telluride are still buried in snow. in late summer, afternoon mountain thunderstorms are typical, so keep your outings early. be sure to use caution anywhere above the tree line, and always have plenty of water on hand, since the high-and-dry climate makes it very easy to get dehydrated.
### DON'T MISS
In Mesa Verde National Park, ranger-led backcountry hikes offer an exclusive peek at america's most mystifying spot. if you're looking to set hearts racing, San Juan four-wheeling offers off-path adrenaline with steep cliff drops, hairpin turns and rugged rockies views.
Powder hounds can grab great late-season deals in the ski town shangri-la of Crested Butte, and foodies can nosh their way through the locavore towns of Durango, Mancos and Telluride.
### Tips for Drivers
»Us 160, from durango to cortez and past mesa verde national park, is the main east–west vein through the region.
»Further north, the fast and convenient us 50 also crosses the state from east to west, linking montrose with pueblo, on the north–south i-25 route, a major thoroughfare.
»In winter conditions, chains or snow tires are required on mountain passes.
»For road conditions, call 303-639-1111 (recorded message) or visit www.cotrip.org.
### TIME ZONE
Colorado runs on Mountain Time (seven hours behind GMT) and observes daylight saving time.
### Fast Facts
»Colorado population: 5 million
»Area: 104,247 sq miles
»Sales tax: 2.9% state sales tax, plus individual city taxes up to 6%
»Durango to Mesa Verde National Park: 66 miles, one hour
»Telluride to Ouray: 50 miles, one hour
»Durango to Denver: 340 miles, five hours
»Pagosa Springs to Santa Fe: 155 miles, two hours
### Powered Up
Thanks to Nikola Tesla, Telluride was the first American city to boast electricity – a key development for the mining that continues today, with the town nesting on the country's biggest uranium belt.
### Resources
»Colorado Tourism ( 800-265-6723; www.colorado.com)
»Edible Edible (www.ediblecommunities.com/sanjuanmountains) Local food and farmers markets.
»14ers (www.14ers.com) Resource for hikers climbing the Rockies' highest summits.
### Southwestern Colorado Highlights
Admiring the ages-old cliff dwellings at Mesa Verde National Park (click here)
Skiing the awesome slopes of spunky Crested Butte (click here)
Carving the snowbound slopes of Telluride (click here)
Appreciating the frozen waterfalls and piping hot springs at rugged Ouray (click here)
Tasting the bouquet of local brews at Durango (click here)
Having fun at Great Sand Dunes National Park, natureÅfs most stunning sandbox (click here)
Poking around friendly and offbeat Mancos (click here)
###### History
Six bands of Utes once resided in a vast area stretching between the Yampa and San Juan Rivers. Unlike other tribes, who migrated to Colorado, their presence here stretches back at least a thousand years. Friction started with gold seekers and settlers entering their lands. Chief Ouray (1833–80), remembered for paving the way to peace between the two parties, actually had little choice but to eventually give up most of the Ute territory.
In 1859, the discovery of gold west of Denver launched the mining era. By the 1870s silver took center stage, making mountain smelter sites thriving towns almost overnight. Colorado relied heavily on its abundant resources until the 20th century, when many mines shut and cities became ghost towns.
Now, millions of visitors flock to Colorado's national parks, historic cities and ski resorts every year. The state boasts the most terrain for skiing in North America. Along with tourism, the military and high-tech industries are major components of the economy. The state is home to a number of high-profile defense-department establishments including the US Air Force Academy and NORAD.
###### Southwestern Colorado Scenic Routes
Replete with stunning scenic byways (www.coloradobyways.org), this region also has the greatest concentration of old mining roads in Colorado. Among the most beautiful is the paved north–south US 550 (known as the Million Dollar Hwy), which connects Durango with Silverton, Ouray and Ridgway.
Some good options for a 4WD trip are the Alpine Loop or Imogene Pass; both start in Ouray (Click here). For beautiful desert scenery, check out the Trail of the Ancients (Click here), accessible by normal vehicles.
#### Information
Colorado Bureau of Land Management ( 303-239-3600; www.co.blm.gov) The state's plentiful natural beauty makes camping one of its best accommodations options. This site offers information on booking public campgrounds.
Colorado Travel & Tourism Authority ( 800-265-6723; www.colorado.com; PO Box 3524, Englewood, CO 80155) Provides statewide tourism information along with free state highway maps.
### Pagosa Springs & Around
POP 1710 / ELEV 7126FT
Pagosa Springs may seem to be a large slice of humble pie, but it has the bragging rights to the biggest snowfall in Colorado – at Wolf Creek Ski Area – nearby. Pagosa, a Ute term for 'boiling water,' refers to the other local draw: hot springs. Natural thermals provide heat for some of the town's 1900 residents.
The town sits east of Durango, on US 160 at the junction with US 84 south to New Mexico. The historic downtown, with most visitor services, is near the intersection of Hot Springs Blvd and US 160. Condos and vacation rentals flank a winding series of roads 2 miles to the west, over a small rise.
#### Sights & Activities
Fred Harman Art Museum & the Red Ryder Roundup MUSEUM
( 970-731-5785; www.harmanartmuseum.com; 85 Harman Park Dr; adult/child $4/0.50; 10:30am-5pm Mon-Sat; ) Fred Harman's comic- book hero was born in Pagosa Springs and today his home is a kitschy and offbeat roadside attraction.
Pagosa Springs' biggest annual event is the Red Ryder Roundup, a carnival with a rodeo and art show and ending in fireworks. It's held near 4th of July.
Springs Resort & Spa SPA
( 970-264-4168; www.pagosahotsprings.com; 165 Hot Springs Blvd; adult/child from $20/12; 7am-1am Jun-Aug, to 11pm Sun-Thu & to 1am Fri & Sat Sep-May; ) These glorious pools along the San Juan River have healing, mineral-rich waters from the Great Pagosa Aquifer, the largest and deepest hot mineral spring in the world. Man-made pools are a little fanciful but look fairly natural, and the views are lovely. Temperatures vary from 83°F to 111°F (28°C to 49°C).
The terraced pink adobe hotel (rooms from $189) features a spa, offers ski packages and welcomes pets. The cheapest rooms are nothing special, while sprawling deluxe rooms feature thicker mattresses, higher thread-count sheets and kitchenettes.
Pagosa Outside RAFTING
( 970-264-4202; www.pagosaoutside.com; 350 Pagosa St; rafting from $59; 10am-6pm, reduced hr winter; ) In the springtime, check out this outfitter's white-water trips (Class III) on the San Juan and Piedra Rivers. The most exciting travels Mesa Canyon, a good spot to sight eagles and other wildlife.
Rivers mellow in summer and the focus turns to river tubing ($15 for two hours, and mountain-biking trips, including a thrilling singletrack route at Turkey Creek, and rentals ($35 per day).
### LAKE CITY
Whichever road you take to spectacular Lake City, it's worth the drive. Located on two scenic and historic byways – the Silver Thread (Hwy 149) and the 4WD-only Alpine Loop (see Click here) – this stress-free mountain community makes the perfect summer day trip or overnight stop. Art galleries and funky shops line the main drag, and there are romantic lodgings and delicious eateries around the Victorian-style historic downtown.
But the weirdness starts every year at the end of June, when the town celebrates Alferd Packer Days, a homage to the man who is alleged to have eaten members of his own hiking party in the nearby mountains in 1874. Totally offbeat, the festival includes a mystery-meat cook-off, a bone-throwing contest and coffin races down the main street.
Don't miss one of the most photographed waterfalls in the state. North Creek Falls tumble 100 odd feet, crashing through the slot canyon into the Rio Grande River. This booming treasure is hidden south of Lake City in a box canyon off Forest Rd 510, reached via Hwy 149 after crossing Spring Creek Pass.
Lake City is primarily a summer destination. Check the city website (www.lakecity.com) for year-round lodging and services. It's 112 miles north of Pagosa Springs via Hwy 149.
Wolf Creek Ski Area SNOW SPORTS
( 970-264-5639; www.wolfcreekski.com; lift ticket adult/child $52/28; Nov–mid-Apr) With more than 450in of snow per year, hitting Wolf Creek on a powder day feels like riding a tidal wave of snow. Located 25 miles north of Pagosa Springs on US 160, this family-owned ski area is one of Colorado's last and best-kept secrets, never crowded and lacking the glitz of larger resorts. Seven lifts service 50 trails, from wide-open bowls to steep tree glades.
Chimney Rock Archaeological Area ARCHAEOLOGICAL SITE
( visitor cabin 970-883-5359, off-season 970-264-2287; www.chimneyrockco.org; Hwy 151; per vehicle $10, guided tours adult/child $10/5; 9am-4:30pm mid-May–late Sep, additional evening hr for special events, tours at 9:30am, 10:30am, 1pm & 2pm; ) Like the architects of the elaborate structures in Chaco Canyon – with which this community was connected – the people of the Chimney Rock Archaeological Area were dedicated astronomers and this was a place of spiritual significance. Remains of 100 permanent structures are at the base of two large red-rock buttes.
Today, the rock monuments remain, though the thriving religious and commercial center has been reduced to sketches in stone. The largest pair of buildings, the Great Kiva and Great House, are impressive examples of Chacoan architecture. Designated an Archaeological Area and National Historic Site in 1970, the entire area covers more than 4000 acres of the San Juan National Forest land. If the local politicos get their way, Chimney Rock Archaeological Area will soon be designated a National Monument.
#### Sleeping & Eating
With the hot springs as a year-round draw, hotels hold rates fairly steady, though are usually cheaper than Durango. Motels and new hotels sprawl out from the city center on US 160. Usually the further away lodging sits from the hot springs, the better the deal.
Fireside Inn Cabins CABINS $$
( 888-264-9204; www.firesidecabins.com; 1600 E Hwy 160; cabins from $125, 2-bedroom cabins from $174; ) Hands down our favorite – each log cabin comes with a Webber grill and planters of wild flowers. Pine interiors have immaculate kitchenettes, quilts, a flat screen TV and wood floors. The San Juan River runs through the back of the property. Equestrians can use the corral, and games available at the central office are great for families.
Pagosa Huts CABINS $
(www.pagosa-huts.com; San Juan National Forest; cabins $60; ) These remote, basic huts are perfect for people trying to get out into the national forest, and they are available to both hikers and recreational motorists. Getting here is a little rough – the roads can be a mess in the spring – but they offer excellent solitude. Inquire about availability and exact location through the website.
Alpine Inn Motel MOTEL $
( 970-731-4005; www.alpineinnofpagosasprings.com; 8 Solomon Dr; d $69; ) A converted chain motel, this roadside option is excellent value. The rooms, each with dark carpet and balconies, are a standard size, but the owners are great guides to the local area and there's a deluxe continental breakfast.
Pagosa Brewing Company BREWPUB $$
( 970-731-2739; www.pagosabrewing.com; 118 N Pagosa Blvd; mains $8-12; 11am-10pm Mon-Sat; ) Brewmaster Tony Simmons is a professional beer judge, and the Poor Richard's Ale is structured with astute standards – the corn and molasses mix is inspired by the tipple of Ben Franklin. With made-from-scratch pub food (including free-range beef) and picnic tables in a rustic courtyard, it's a fun dinner spot.
JJ's Riverwalk Restaurant Pub CONTEMPORARY AMERICAN $$$
( 970-264-9100; 356 E Hwy 160; mains $15-40) Overlooking the San Juan River, JJ's has a great vibe, a decent wine list and pleasant service. It can be very spendy, but the menu includes early-bird cheap meals and a nightly happy hour. In summer, patio seating allows you to watch the kayakers paddling by.
#### Information
Pagosa Springs Area Chamber of Commerce ( 970-264-2360; www.visitpagosasprings.com; 402 San Juan St; 9am-5pm Mon-Fri) The Pagosa Springs Area Chamber of Commerce operates a large visitor center located across the bridge from US Hwy 160.
USFS Pagosa Ranger Station ( 970-264-2268; 180 Pagosa St; 8am-4:30pm Mon-Fri)
#### Getting There & Around
Pagosa Springs is at the junction of US 160 and US 84.
### Durango
POP 16,700 / ELEV 6580FT
An archetypal old Colorado mining town, Durango is a regional darling nothing short of delightful. Its graceful hotels, Victorian-era saloons and tree-lined streets of sleepy bungalows invite you to pedal around soaking up all the good vibes. There is plenty to do outdoors. Style-wise, Durango is torn between its ragtime past and a cool, cutting- edge future where townie bikes, caffeine and farmers markets rule.
The town's historic central precinct is home to boutiques, bars, restaurants and theater halls. Foodies will revel in the innovative organic and locavore fare that is making it the best place to eat in the state. But there's also interesting galleries and live music that, combined with a relaxed and congenial local populace, make it a great place to visit.
Durango is also an ideal base for exploring the enigmatic ruins at Mesa Verde National Park, 35 miles to the west.
Most visitors' facilities are along Main Ave, including the 1882 Durango & Silverton Narrow Gauge Railroad Depot (at the south end of town). Motels are mostly north of the town center. The compact downtown is easy to walk in a few hours.
#### Sights & Activities
Durango & Silverton Narrow Gauge Railroad TRAIN RIDE
( 970-247-2733, toll-free 877-872-4607; www.durangotrain.com; 479 Main Ave; adult/child return from $83/49; departure at 8am, 8:30am, 9:15am, 10am; ) Riding the Durango & Silverton Narrow Gauge Railroad is a Durango must. These vintage steam locomotives have been making the scenic 45-mile trip north to Silverton (3½ hours each way) for over 125 years. The dazzling journey allows two hours for exploring Silverton. This trip operates only from May through October. Check online for different winter options.
### PEDALING DURANGO
Bike geeks take note: Durango is home to some of the world's best cyclists, who regularly ride the hundreds of local trails ranging from steep singletracks to scenic road rides. Start easy on the Old Railroad Grade Trail, a 12.2-mile loop that uses both US Hwy 160 and a dirt road following the old rail tracks. From Durango, take Hwy 160 west through the town of Hesperus. Turn right into the Cherry Creek Picnic Area and the trailhead. For a more technical ride, try Dry Fork Loop, accessible from Lightner Creek just west of town. It has some great drops, blind corners and copious vegetation.
Big Corral Riding Stable HORSEBACK RIDING
( 970-884-9235; www.vallecitolakeoutfitter.com; 17716 County Rd 501, Bayfield) Highly recommended by locals, this outfitter does day rides and overnight horseback camping for the whole family in the gorgeous Weminiuche Wilderness. If you're short on time, try the two-hour breakfast ride (including sausage, pancakes and cowboy coffee) with views of Vallecito Lake. Located 25 miles northeast of Durango.
Durango Mountain Resort SNOW SPORTS
( 970-247-9000; www.durangomountainresort.com; 1 Skier Pl; lift tickets adult/child from $65/36; mid-Nov–Mar; ) Durango Mountain Resort, 25 miles north on US 550, is Durango's winter highlight. The resort, also known as Purgatory, offers 1200 skiable acres of varying difficulty and boasts 260in of snow per year. Two terrain parks offer plenty of opportunities for snowboarders to catch big air.
Check local grocery stores and newspapers for promotions and two-for-one lift tickets and other ski season specials before purchasing directly from the ticket window.
Trimble Spa & Natural Hot Springs HOT SPRINGS
( 970-247-0111, toll-free 877-811-7111; www.trimblehotsprings.com; 6475 County Rd 203; day pass adult/child $15/9.50; 10am-9pm Sun-Thu, 10am-10pm Fri & Sat; ) For a pampering massage or just a post-hike soak in natural hot springs. Phone or check the website for last-minute specials, which sometimes include two-for-one deals and other discounts. It's 5 miles north of Durango.
Durango Soaring Club GLIDING
(Val-Air Gliderport; 970-247-9037; www.soardurango.com; 27290 US Hwy 550 North; 20min per person from $100; 9am-6pm mid-May–mid-Oct; ) One- and two-person gliding flights highlight the spectacular San Juan scenery. On summer afternoons, when the earth is warmed, the chance of catching rising thermal air currents is best.
Mild to Wild Rafting RAFTING
( 970-247-4789, toll-free 800-567-6745; www.mild2wildrafting.com; 50 Animas View Dr; trips from $55; ) Offers all levels of rafting on the Animas River; the more adventurous (and experienced) run the upper Animas, which boasts Class III to Class V rapids.
Duranglers FISHING
( 970-385-4081, toll-free 800-347-4346; www.duranglers.com; 923 Main Ave; day trip 1-person/2-person $325/350) They won't put the trout on your hook, but Duranglers will do everything to bring you to that gilded moment, serving beginners to experts.
#### Festivals & Events
San Juan Brewfest BEER
(www.cookmanfood.com/brewfest; Main Ave, btwn 12th & 13th Sts; admission $20; early Sep; ) With bands, food and a carnival atmosphere, this event showcases 30-odd specialist brewers from Durango and the region. Attendees (must be aged 21 and over to taste) can vote for the People's Choice award.
#### Sleeping
Strater Hotel HOTEL $$
( 970-247-4431; www.strater.com; 699 Main Ave; d $169-189; ) The past lives large in this historical Durango hotel with walnut antiques, hand-stenciled wallpapers and relics ranging from a Stradivarius violin to a gold-plated Winchester. Rooms lean toward the romantic, with comfortable beds amid antiques, crystal and lace. The boast-worthy staff goes out of its way to assist with inquiries.
The hot tub is a romantic plus (reserved by the hour), as is the summertime melodrama (theater) the hotel runs. In winter, rates drop by more than 50%, making it a virtual steal. Look online.
Hometown Hostel HOSTEL $
( 970-385-4115; www.durangohometownhostel.com; 736 Goeglein Gulch Rd; dm $30; reception 3:30-8pm; ) The bee's knees of hostels, this suburban-style house sits on the winding road up to the college, next to a convenient bike path. A better class of hostel, it's all-inclusive, with linen, towels, lockers and wi-fi. There are two single-sex dorms and a larger mixed dorm, and a great common kitchen and lounge area. Room rates fall with extended stays.
Rochester House HOTEL $$
( 970-385-1920, toll-free 800-664-1920; www.rochesterhotel.com; 721 E 2nd Ave; d $169-219; ) Movie posters and marquee lights adorn the hallways of these two spacious but slightly worn, yet attractive homes. All guests check in at Leland house, across the street. Still, you can't beat the cool townie bikes, available for spins around town. Pet rooms come with direct access outside and some rooms have kitchenettes.
General Palmer Hotel HOTEL $$
( 970-247-4747, toll-free 800-523-3358; www.generalpalmer.com; 567 Main Ave; d incl breakfast $105-195; ) With turn-of-the-century elegance, this 1898 Victorian has a damsel's taste of floral prints, pewter four-post beds and teddies on every bed. Rooms are small but elegant, and if you tire of TV, there's a collection of board games at the front desk. Check out the cozy library and the relaxing solarium.
Siesta Motel MOTEL $
( 970-247-0741; www.durangosiestamotel.com; 3475 N Main Ave; d $58; ) This family-owned motel is one of the town's cheaper options, sparkling clean and spacious but admittedly dated. If you're self-catering, there's a little courtyard with a BBQ grill.
#### Eating
East by Southwest FUSION, SUSHI $$
( 970-247-5533; http://eastbysouthwest.com; 160 E College Dr; sushi $4-13, mains $12-24; 11:30am-3pm, 5-10pm Mon-Sat, 5-10pm Sun; ) Low-lit but vibrant, it's packed with locals on date night. Skip the standards for goosebump-good innovations like sashimi with jalapeño or rolls with mango and wasabi honey. Fish is fresh and endangered species are absent from the menu. Fusion plates include Thai, Vietnamese and Indonesian, well matched with creative martinis or sake cocktails. For a deal, grab the happy-hour food specials (5pm to 6:30pm) for around $6.
Randy's MODERN AMERICAN $$$
( 970-247-9083; www.randysrestaurant.com; 152 E College Dr; mains $20-25; 5-10pm) Intimate and extremely popular, this upscale spot goes eclectic with seafood and steak, with refreshing lighter fare and specialties like garlic polenta fries. Between 5pm and 6pm, early birds score the same menu for $12 to $14. Happy hour runs from 5pm to 7pm.
Durango Diner DINER $$
( 970-247-9889; www.durangodiner.com; 957 Main Ave; mains $7-18; 6am-2pm Mon-Sat, 6am-1pm Sun; ) Enjoy the open view of the griddle at this loveable greasy spoon with button-cute servers and monstrous plates of eggs, smothered burritos or French toast. It's a local institution.
Cyprus Cafe MEDITERRANEAN $$$
( 970-385-6884; www.cypruscafe.com; 725 E Second Ave; mains $13-29; 11:30am-2:30pm, 5-9pm, closed Sun; ) Nothing says summer like live jazz on the patio at this little Mediterranean cafe, a favorite of the foodie press. Quality ingredients include locally raised vegetables, wild seafood and natural meats. Favorites include warm duck salad with green olives, oranges and spinach and the Colorado trout with quinoa pilaf. For smaller bites, check out Eno, their wine and coffee bar next door.
Jean Pierre Bakery FRENCH, BAKERY $$$
( 970-247-7700; www.jeanpierrebakery.com; 601 Main Ave; mains $15-35; 8am-9pm; ) A charming patisserie serving mouthwatering delicacies made from scratch. Dinner is a much more formal affair. Prices are dear, but at $15, the soup-and-sandwich lunch special with a sumptuous French pastry (we recommend the sticky pecan roll) is a deal.
Olde Tymers Café BURGERS $
( 970-259-2990; www.otcdgo.com; 1000 Main Ave; mains $4-10; 11am-10pm; ) Voted as having the best burger in Durango by the local paper, these cozy booths host the college crowd for other American classics too, like fried chicken and mashed potatoes. Ask about the cheap daily specials.
### KENNEBEC CAFÉ
This countryside romantic cafe ( 970-247-5674; www.kennebeccafe.com; 4 County Rd 124; mains $10-29; 11am-3pm, 5-9pm Tue-Fri, 8am-3pm, 5-9pm Sat & Sun) may flaunt Euro style, but it bares American overtones, with local Ska brews on tap, as well as an extensive wine list. Think tasty and creative – Chef Miguel Carillo serves up Duck Two Ways (seared with a pomegranate glaze) and poblano chiles stuffed with strip steak. Weekend brunch makes playful twists on old favorites, best enjoyed on the patio. It's located in Hesperus, 10 miles west of Durango on Highway 140.
#### Drinking & Entertainment
Ska Brewing Company BREWERY
( 970-247-5792; www.skabrewing.com; 225 Girard St; 11am-3pm Mon-Wed, 11am-3pm & 5-8pm Thu, 11am-8pm Fri) Big on flavor and variety, these are the best beers in town. The small, friendly tasting-room bar, once mainly a production facility, packs with an after-work crowd. Call for dates of weekly BBQs with live music and free food.
Steamworks Brewing BREWERY
( 970-259-9200; www.steamworksbrewing.com; 801 E 2nd Ave; mains $10-15; 1pm-midnight Mon-Fri, 11am-2am Sat & Sun) DJs and live music pump up the volume at this industrial microbrewery, with high sloping rafters and metal pipes. College kids fill the large bar area, but there's also a separate dining room with a Cajun-influenced menu.
Durango Brewing Co BREWERY
( 970-247-3396; www.durangobrewing.com; 3000 Main Ave; tap room 9am-5pm) While the ambiance is nothing special, serious beer fans can appreciate that these guys concentrate on the brews. There's tap-room tastings and it's open seven days a week.
Diamond Belle Saloon BAR
( 970-376-7150; www.strater.com; 699 Main Ave; 11am-late; ) A rowdy corner of the historic Strater Hotel, this elegant old-time bar has waitresses flashing Victorian-era fishnets and live ragtime that keeps out-of-town visitors packed in, standing room only, at happy hour. Half-price appetizers and drink specials run from 4pm to 6pm. Also in Strater, The Office serves cocktails in an upscale and much more low-key atmosphere.
Henry Strater Theatre LIVE MUSIC
( 970-375-7160; www.henrystratertheatre.com; 699 Main Ave; adult/child from $20/18; ) Internationally renown, producing old-world music-hall shows, live bands, comedy, community theatre and more for nearly 50 years.
#### Shopping
Durango may be the best place to shop in the region for sporting gear and outdoor fashions (locals will take prAna over Prada any day). There are also delightful boutiques and galleries along Main Ave.
Pedal the Peaks SPORTING GOODS
( 970-259-6880; www.pedalthepeaks.biz; 598b Main Ave; full-suspension rentals $80; 9am-5pm Mon-Sat, 10am-5pm Sun; ) This specialist bike store offers the works from mountain- and road-bike sales and rentals, custom-worked cycles, trail maps and accessories. The staff are all hardcore riders, and their friendly advice and local knowledge are second to none.
2nd Avenue Sports SPORTING GOODS
( 970-247-4511; www.2ndavesports.com; 600 E 2nd Ave; 9am-6pm Mon-Sat, 10am-5pm Sun) Skiing and extensive cycling and mountain-biking gear for sale and rental.
Maria's Bookshop BOOKS
( 970-247-1438; www.mariasbookshop.com; 960 Main Ave; 9am-9pm) A good general bookstore – independently owned and well stocked; does e-reader orders too.
#### Information
Durango Area Tourism Office ( 970-247-3500, toll-free 800-525-8855; www.durango.org; 111 S Camino del Rio; 8am-5pm Mon-Fri; ) Located south of town, at the Santa Rita exit from US 550.
Mercy Regional Medical Center ( 970-247-4311; www.mercydurango.org; 1010 Three Springs Ave) Outpatient and 24-hour emergency care.
San Juan-Rio Grande National Forest Headquarters ( 970-247-4874; www.fs.fed.us/r2/sanjuan; 15 Burnett Ct; 8am-5pm Mon-Sat) Offers camping and hiking information and maps. It's about a half-mile west on US Hwy 160.
#### Getting There & Away
Durango lies at the junction of US Hwy 160 and US Hwy 550, 42 miles east of Cortez, 49 miles west of Pagosa Springs and 190 miles north of Albuquerque in New Mexico.
AIR Durango–La Plata County Airport (DRO; 970-247-8143; www.flydurango.com; 1000 Airport Rd) Durango–La Plata County Airport is 18 miles southeast of Durango via US Hwy 160 and Hwy 172. Both United and Frontier Airlines have direct flights to Denver; US Airways flies to Phoenix.
BUS Greyhound buses run daily from the Durango Bus Center north to Grand Junction and south to Albuquerque, NM.
#### Getting Around
Check the website of Durango Transit ( 970-259-5438; www.getarounddurango.com) for local travel information. All Durango buses are fitted with bicycle racks. Free, the bright-red T shuttle bus trundles up and down Main St.
### Mancos
POP 1260 / ELEV 7028FT
At 10am, tiny Mancos may feel like another Colorado ghost town, but poke around and you'll find an offbeat and inviting community. Downtown has historic homes, art and crafts cooperatives and landmark buildings, while the countryside offers spacious views and ranch-style B&B options. Mesa Verde National Park is just 7 miles to the west, so if visiting the park is on your itinerary, staying in Mancos makes an appealing alternative to Cortez's rather nondescript motels.
#### Sleeping
Willowtail Springs LODGE, CABINS $$$
( 800-698-0603; www.willowtailsprings.com; 10451 County Rd 39; cabins $249-279; ) Peggy and Lee, artist and T'ai Chi master, have crafted a setting that inspires and helps you to slow down. Way down, to the pace of the largemouth bass in their pond. Intimate and spectacular, these exquisite camps sit within 60 acres of gardens and ponderosa forest.
Two immaculate cabins and a spacious lake house (sleeping six) feature warm and exotic decor (note the real remnant beehive!) There are also clawfoot tubs, Peggy's fabulous original art and a canoe hitched up to the dock. Kitchens are stocked with organic goodies and extras include candlelight chef dinners, reasonable catered meals and massages. It's also a wildlife sanctuary (raptors are released here) and, for roamers, a little slice of heaven. It's well outside of town; get directions from the website.
Jersey Jim Lookout Tower LOOKOUT TOWER $
( 970-533-7060; www.fs.fed.us/r2/recreation /rentals; r $40; mid-May–mid-Oct) How about spending the night in a former fire-lookout tower? Standing 55ft above a meadow 14 miles north of Mancos at an elevation of 9800ft, this place is on the National Historic Lookout Register and comes with an Osborne Fire Finder and topographic map.
The tower accommodates up to four adults with a two-night minimum stay. Bring your own bedding and water. There is a functioning kitchen. The reservation office opens on the first workday of March (1pm to 5pm) and the entire season is typically booked within days.
Flagstone Meadows Ranch Bed & Breakfast B&B $$
( 970-533-9838; www.flagstonemeadows.com; 38080 Rd K-4; d incl breakfast $115-125) A welcoming Western-ranch home with knotty pine walls, quilted beds, cathedral ceilings and a stone fireplace. The Navajo-speaking host offers a wealth of local knowledge, and guests enjoy long views of the snowy La Plata range.
Enchanted Mesa Motel MOTEL $
( 970-533-7729; www.enchantedmesamotel.com; 862 W Grand Ave; r from $45; ) Hipper than most independent motels, this place has shiny lamps, solid wooden furniture and a play area out front for the kids. Best of all, you can shoot pool while waiting for your whites to dry at the laundry room billiards table.
#### Eating & Drinking
Absolute Baking & Cafe BREAKFAST, SANDWICHES $
( 970-533-1200; 110 S Main St; mains $6-8; 7am-2pm; ) The screen door is always swinging open at this town hot spot with giant breakfasts. Try the green chile on eggs—it's made from scratch, as are the organic breads and pastries. Lunch includes salads, big sammies and local, grass-fed beef burgers. Grab a bag for the trail, but don't forgo a square of gooey, fresh carrot cake.
If you're in the market for a new read, the cafe has a decent collection of used books for sale; so grab a cup of coffee, chat with friendly wait staff and just chill out.
Millwood Junction STEAKHOUSE $$
( 970-533-7338; www.millwoodjunction.com; cnr Main St & Railroad Ave; mains $10-20; 11am-2pm daily, 5:30-10:30pm Mon-Fri; ) A popular steak and seafood dinner joint, though the food isn't always spot on. The restaurant often doubles as a club, showcasing live music.
Fahrenheit Coffee Roasters COFFEE SHOP
(201 W Grand Ave; 7am-5pm Mon-Sat, 7am-2pm Sun; ) Surrounded by the aroma of fresh roasted beans, this espresso house also serves slices of homemade pie and breakfast burritos to go.
Arborena WINE BAR
( 970-533-1381; 114 W Grand Ave; 4-9pm Mon, Thu-Sat) A welcome alternative to another brewery, in this stylish art gallery you can sip wines by the glass, accompanied by cheese plates, baguettes and salads. Thursday is Girls' Night Out – women save a dollar on drinks.
Columbine Bar BAR
( 970-533-7397; 123 W Grand Ave; 10am-2am) This smoky old saloon, established in 1903, is one of Colorado's oldest continuously operating bars. Join locals shooting pool over pints of ice-cold local brews.
Mancos Valley Distillery DISTILLERY
(www.mancosvalleydistillery.com; 116 N Main St; hours vary) If you're interested in tasting something really local, make your way to this alleyway where artisan distiller Ian James crafts delicate rum (and chocolate). With sporadic hours, check the website.
#### Information
Mancos Valley Visitors Center ( 702-533-7434; www.mancosvalley.com; 101 E Bauer St; 9am-5pm Mon-Fri) Historic displays and a walking-tour map are available at the visitor center. It also has information on outdoor activities and local ranches that offer horseback rides and Western-style overnight trips.
### Mesa Verde National Park
More than 700 years after its inhabitants left, the mystery behind Mesa Verde ( 970-529-4465; www.nps.gov/meve; 7-day pass private cars/motorcycles $15/8 Jun-Sep, $10/5 low season) remains. This civilization of Ancestral Puebloans (see Click here) abandoned the area in 1300. Today their last known home is preserved as Mesa Verde. Amateur anthropologists will love it; the focus on preserving cultural relics makes Mesa Verde unique among American national parks.
Ancestral Puebloan sites are found throughout the canyons and mesas of the park, perched on a high plateau south of Cortez and Mancos, though many remain off-limits to visitors. The NPS strictly enforces the Antiquities Act, which prohibits the removal or destruction of any antiquities and prohibits public access to many of the approximately 4000 known Ancestral Puebloan sites.
If you only have a few hours, the best approach is a stop at the visitor center and a drive around Wetherill Mesa combined with a short walk to the easily accessible Spruce Tree House, the park's best-preserved cliff dwelling. If you have a day or more, take the ranger-led tours of Cliff Palace and Balcony House, explore Wetherill Mesa, linger around the museum or participate in one of the campfire programs run at Morefield Campground.
The park occupies a mesa, with North Rim summit at Park Point (8571ft) tower ing more than 2000ft above the Montezuma Valley. From Park Point the mesa gently slopes southward to a 6000ft elevation above the Mancos River in the Ute Mountain Tribal Park. Parallel canyons, typically 500ft below the rim, dissect the mesa-top and carry the drainage southward. Mesa Verde National Park occupies 81 sq miles of the northernmost portion of the mesa and contains the largest and most frequented cliff dwellings and surface sites.
Planned for 2012, the new Mesa Verde Visitor and Research Center, located just beyond the park entrance, will replace the Far View Visitor Center. The cutting-edge LEED-certified compound will feature a 7000-sq-ft visitor center featuring exhibits and a repository for the park's 3 million artifacts.
###### History
A US army lieutenant recorded spectacular cliff dwellings in the canyons of Mesa Verde in 1849–50. The large number of sites on Ute tribal land, and their relative inaccessibility, protected the majority of these antiquities from pothunters.
The first scientific investigation of the sites in 1874 failed to identify Cliff Palace, the largest cliff dwelling in North America. Discovery of this 'magnificent city' occurred only when local cowboys Richard Wetherill and Charlie Mason were searching for stray cattle in 1888. The cowboys exploited their discovery for the next 18 years by guiding both amateur and trained archaeologists to the site, particularly to collect the distinctive black-on-white pottery.
### PARK TIPS
The park is busiest over 4th of July, Memorial Day and Labor Day weekends. On busy days, visitors are allowed one tour only. Assure your spot by buying tickets one day in advance (there is often a 45-minute wait in line in summer). The best information can be found in the latest visitor's guide, available online at www.nps.gov/meve/planyourvisit.
When artifacts started being shipped overseas, Virginia McClurg of Colorado Springs began a long campaign to preserve the site and its contents. McClurg's efforts led Congress to protect artifacts on federal land, with the passage of the Antiquities Act establishing Mesa Verde National Park in 1906.
The park entrance is off US 160, midway between Cortez and Mancos. Near the entrance, the new Mesa Verde Visitor and Research Center opens in 2012. From here it's about 21 miles to park headquarters, Chapin Mesa Museum and Spruce Tree House. Along the way are Morefield Campground (4 miles), the panoramic viewpoint at Park Point (8 miles) and the Far View Lodge – about 11 miles. Towed vehicles are not allowed beyond Morefield Campground.
South from park headquarters, Mesa Top Rd consists of two one-way circuits. Turn left about a quarter mile from the start of Mesa Top Rd to visit Cliff Palace and Balcony House on the east loop. From the junction with the main road at Far View Visitor Center, the 12-mile mountainous Wetherill Mesa Rd snakes along the North Rim, acting as a natural barrier to tour buses and indifferent travelers. The road is open only from Memorial Day in late May to Labor Day in early September.
#### Sights
##### PARK POINT
With panoramic views, the fire lookout at Park Point (8571ft) has the highest elevation in the park. To the north are the 14,000ft peaks of the San Juan Mountains; in the northeast is the 12,000ft La Plata range; to the southwest, beyond the southward sloping Mesa Verde plateau, is the distant volcanic plug of Shiprock; and to the west is the prone, humanlike profile of Sleeping Ute Mountain.
##### CHAPIN MESA
Chapin Mesa features the most dense clusters of remnants of Ancestral Puebloan settlements. It's a unique opportunity to see and compare examples of all phases of construction – from pothouses to Pueblo villages to the elaborate multiroom cities tucked into cliff recesses. Pamphlets describing the most excavated sites are available at either the visitor center or Chapin Mesa Museum.
On the upper portion of Chapin Mesa, the Far View Sites were the most densely settled area in Mesa Verde after AD 1100. The large-walled Pueblo sites at Far View House enclose a central kiva and planned room layout that was originally two stories high. To the north is a small row of rooms and an attached circular tower that likely used to extend just above the adjacent 'pygmy forest' of piñon pine and juniper trees. This tower is one of 57 in Mesa Verde that may once have served as watchtowers, religious structures or astronomical observatories for agricultural schedules.
South from park headquarters, the 6-mile Mesa Top Rd circuit connects 10 excavated mesa-top sites, three accessible cliff dwellings and many vantages of inaccessible cliff dwellings from the mesa rim. It's open 8am to sunset.
Chapin Mesa Museum MUSEUM
( 970-529-4475; www.nps.gov/meve; Chapin Mesa Rd; admission included with park entry; 8am-6:30pm Apr–mid-Oct, 8am-5pm mid-Oct–Apr) A good first stop, with detailed dioramas and exhibits pertaining to the park. When park headquarters are closed on weekends, staff at the museum provide information.
Spruce Tree House ARCHAEOLOGICAL SITE
(Chapin Mesa Rd; admission included with park entry) The most accessible of the archaeological sites, although the paved half-mile round-trip access path is still a moderately steep climb. Spruce Tree House was once home to 60 or 80 people and its construction began around AD 1210. Like other sites, old walls and houses have been stabilized.
Rangers are on hand to answer questions and offer free guided tours from November to April at 10am, 1pm and 3:30pm.
##### CLIFF PALACE & MESA TOP LOOPS
This is the most visited part of the park. Access to the major Ancestral Puebloan sites is only by ranger-led tour, and tickets must be pre-purchased in person from the visitor center, Morefield Ranger Station or the Colorado Welcome Center in Cortez. These tours are well-worth it; purchase several days ahead to ensure your spot in high season.
Cliff Palace ARCHAEOLOGICAL SITE
(Cliff Palace Loop; one-hour guided tour $3) The only way to see the superb Cliff Palace is to take an hour-long ranger-led tour that retraces the steps taken by the Ancestral Puebloans. This grand representative of engineering achievement, with 217 rooms and 23 kivas, provided shelter for 250 or 300 people.
Its inhabitants were without running water. However, springs across the canyon, below Sun Temple, were most likely their primary water sources. The use of small 'chinking' stones between the large blocks is strikingly similar to Ancestral Puebloan construction at distant Chaco Canyon.
Balcony House ARCHAEOLOGICAL SITE
(Cliff Palace Loop; one-hour guided tour $3) Tickets are required for the one-hour guided tours of Balcony House, on the east side of the Cliff Palace Loop. The tour could prove a challenge for those with a fear of heights or small places. But it includes outstanding views of Soda Canyon, 600ft below the sandstone overhang that once served as the ceiling for 35 to 40 rooms.
Visitors must descend a 100ft-long staircase into the canyon, then climb a 32ft-tall ladder, crawl through a 12ft-long tunnel and climb an additional 60ft of ladders and stone steps to get out. It's not recommended for people with medical problems. The most physical tour in the park, it's also the most rewarding, not to mention fun!
##### WETHERILL MESA
The less-frequented western portion of Mesa Verde offers a comprehensive display of Ancestral Pueblo relics. The Badger House Community consists of a short trail connecting four excavated surface sites depicting various phases of Ancestral Puebloan development.
Long House ARCHAEOLOGICAL SITE
(Wetherill Mesa Rd; one-hour guided tour $3) On the Wetherill Mesa side of the canyon is Long House. It's a strenuous place to visit and can only be done as part of a ranger-led guided tour (organized from the visitor center). Access involves climbing three ladders – two at 15ft and one at 4ft – and a 0.75-mile hike, and there's an aggregate 130ft elevation to descend and ascend.
Step House ARCHAEOLOGICAL SITE
(Wetherill mesa rd; admission included with park entry) step house was initially occupied by modified basketmaker peoples residing in pithouses, and later became the site of a classic pueblo-period masonry complex with rooms and kivas. the 0.75-mile trail to step house involves a 100ft descent and ascent.
### UTE MOUNTAIN TRIBAL PARK
If Mesa Verde leaves you intrigued but wanting a more intimate experience, this alternative has been getting rave reviews. The park ( 970-749-1452; www.utemountainute.com; Morning Star Lane; half-day/full-day tours per person $28/47; by appointment) features a number of fascinating archaeological sites from both Utes and Ancient Puebloans, including petroglyphs and cliff dwellings, accessed only through tours led by Ute tribal members. While half-day tours are suitable to all, full-day tours are physically demanding; visitors hike 3 miles into the backcountry and up ladders to cliff dwellings. It's best to use transportation provided by the tribal park ($10 per person) to avoid 80 miles of wear and tear on your vehicle.
Book in advance or stop by Ute Mountain Casino, Hotel & Resort ( hotel reservations 800-258-8007; 3 Weeminuche Dr; d $75-95, sites $30), near Sleeping Ute Mountain, for information. There's also primitive camping and cabin rentals.
#### Activities
Hiking
Hiking is a great way to explore the park, but follow the rules. backcountry access is specifically forbidden and fines are imposed on anyone caught wandering off designated trails or entering cliff dwellings without a ranger. please respect these necessary regulations, so that these fragile and irreplaceable archaeological sights and artifacts remain protected for centuries to come.
Always carry water and wear appropriate footwear. trails – some cliffside – can be muddy and slippery after rain or snow. most, except the soda canyon trail, are strenuous and involve steep elevation changes. register at the respective trailheads before venturing out.
The 2.8-mile Petroglyph Loop Trail is accessed from spruce tree house. it follows a path beneath the edge of a plateau before making a short climb to the top of the mesa, where you'll have good views of the spruce and navajo canyons. this is the only trail in the park where you can view petroglyphs.
The 2.1-mile Spruce Canyon Loop Trail also begins at spruce tree house and descends to the bottom of spruce tree canyon. it's a great way to see the canyon bottoms of mesa verde.
Cycling
Finding convenient parking at the many stops along mesa top rd is no problem for those with bikes. but only the hardy will want to enter the park by bike and immediately face the grueling 4-mile ascent to morefield campground, quickly followed by a narrow tunnel ride to reach the north rim. an easier option is to unlimber your muscles and mount up at morefield or park headquarters.
Skiing & Snowshoeing
In winter, mesa verde's crowds are replaced with blue skies and snows that drape the cliff dwellings. sometimes there is enough snow to ski or snowshoe after a snowstorm (although colorado's dry climate and sunshine cause it to melt quickly). before Setting out, check the current conditions by calling park headquarters.
Two park roads have been designated for cross-country skiing and snowshoeing when weather permits. The Cliff Palace Loop Rd is a 6-mile relatively flat loop located off the mesa top loop rd. the road is closed to vehicles after the first snowfall, so you won't have to worry about vehicular traffic. park at the closed gate and glide 1 mile to the cliff palace overlook, continuing on past numerous other scenic stopping points.
The Morefield Campground Loop Rds offer multiple miles of relatively flat terrain. the campground is closed in winter, but skiers and snowshoers can park at the gate and explore to their heart's content.
#### TOURS
Park concessionaire Aramark (www.visitmesaverde.com; adult/child $35/17.50) offers ranger-led bus tours that depart far View Lodge at 1pm daily.
### SCENIC DRIVE: TRAIL OF THE ANCIENTS
An arid moonscape with cliff dwellings, pottery shreds and rock art, the Trail of the Ancients traces the territory of the Ancestral Puebloans. The 114-mile drive uses Hwy 145, Hwy 184 and US 160. Begin in Cortez and either head northwest toward Hovenweep National Monument on the Utah border (which, like Mesa Verde, contains dense clusters of Ancestral Puebloan dwellings) or southwest toward Four Corners, where Colorado, Utah, Arizona and New Mexico meet. Allow three hours for driving.
Highly recommended, the Mesa Verde Institute (www.mesaverdeinstitute.org) runs ranger-led backcountry hikes. The only way to access restricted backcountry, they have proved duly popular, usually selling out. With participants limited to 10 or 12 people, these trips offer a very intimate look at the sites. Tickets may be purchased at the visitor center or online. Also check the website for new or limited-time offerings.
Square House Hiking Tour HIKING
(per person $20; 8am, Sep–mid-October) The park's most popular ranger-led hike, this strenuous 1-mile hike takes two hours but includes exposure to cliffs, rocky slopes, climbing a 20ft ladder and two shorter ladders. One highlight is seeing one of only two original kiva roofs in the park.
Oak Tree House and Fire Temple HIKING
(per person $20; departs 8am late May-early Sep; ) This strenuous 1-mile hike takes two hours, features some exposure and requires a 15ft ladder climb. Meet at the Sun Temple (Mesa Top Loop Rd).
Spring House Hiking Tour HIKING
(per person $40; 8am, May 4-Sep 30) For serious hikers only, this 8-hour, 8-mile round-trip has steep drop-offs, switchbacks and an elevation change of 1500ft. Remote sites are part of the itinerary. Wear hiking boots and bring plenty of water and sunscreen.
#### Festivals & Events
12 Hours of Mesa Verde MOUNTAIN-BIKE RACE
(www.12hoursofmesaverde.com; per rider early-bird/regular $65/80; May) In this popular 12-hour relay-endurance bike event, teams race against each other over an incredible network of trails across the national park. All proceeds raised go to the Montezuma County Partners –a mentoring program for youths at risk.
#### Sleeping
Nearby Cortez, Mancos or Durango (36 miles to the east) have plenty of accommodations. Within the national park, visitors can stay at the lodge or camp. Stay overnight to catch sites during the best viewing hours, participate in evening programs and enjoy the sunset over Sleeping Ute Mountain.
Morefield Campground CAMPING $
( 970-529-4465; www.nps.gov/meve; North Rim Rd; campsite $20, canvas tents from $40; May–mid-Oct) Deluxe campers will dig the big canvas tents kitted out with two cots and a lantern. The park's camping option, located 4 miles from the entrance gate, also has 445 regular tent sites on grassy grounds conveniently located near Morefield Village. The village has a general store, gas station, restaurant, free showers and laundry. Free evening campfire programs take place nightly from Memorial Day (May) to Labor Day (September) at the Morefield Campground Amphitheater.
Far View Lodge LODGE $$
( 970-529-4421, toll-free 800-449-2288; www.visitmesaverde.com; North Rim Rd; r from $119; mid-Apr–Oct; ) Perched on a mesa-top 15 miles inside the park entrance, this tasteful Pueblo-style lodge has 150 rooms, some with kiva fireplaces. Southwestern-style kiva rooms are a worthy upgrade, with balconies, pounded copper sinks and bright patterned blankets. Don't miss sunset over the mesa from your private balcony. Standard rooms don't have air-con (or TV) and summer daytimes can be hot.
#### Eating
Metate Room CONTEMPORARY AMERICAN $$
( 800-449-2288; www.visitmesaverde.com; North Rim Rd; mains $15-25; 5-7:30pm year-round, & 7-10am Apr–mid-Oct; ) With lovely views, this innovative restaurant in the Far View Lodge offers regional flavors with some innovation, with dishes like cinnamon chile pork, elk shepherd's pie and trout crusted in pine nuts. You can also get local Colorado beers.
Far View Terrace Café CAFE FOOD $
( 970-529-4421, toll-free 800-449-2288; www.visitmesaverde.com; North Rim Rd; dishes from $5; 7-10am, 11am-3pm & 5-8pm May–mid-Oct; ) In Far View Lodge, a self-service place with reasonably priced meals. Don't miss the house special – the Navajo taco.
#### Information
MAPS Good maps are issued to visitors at the national park gate on entry. Quality topographical maps can be bought at the visitor center and the museum as well as in stores in Durango and Cortez.
TOURIST INFORMATION Mesa Verde Visitor & Research Center ( 800-305-6053, 970-529-5034; www.nps.gov/meve; North Rim Rd; 8am-7pm daily Jun-early Sep, 8am-5pm early Sep–mid-Oct, closed mid-Oct–May; ) Visitor information and tickets for tours of Cliff Palace, Balcony House or Long House. Note: before the center is completed in 2012, visitors should use the Far View Visitor Center, located 15 miles from the entrance.
Mesa Verde Museum Association ( 970-529-4445, toll-free 800-305-6053; www.mesaverde.org; Chapin Mesa Rd; 8am-6:30pm Apr–mid-Oct, 8am-5pm mid-Oct–Apr; ) Attached to the Chapin Mesa Museum, this nonprofit organization sponsors research activities and exhibits. It has an excellent selection of materials on the Ancestral Puebloans and modern tribes in the American Southwest, and has books, posters and glossy calendars for sale.
Park Headquarters ( 970-529-4465; www.nps.gov/meve; Chapin Mesa Rd; 7-day park entry per vehicle $15, cyclists, hikers & motorcyclists $8; 8am-5pm Mon-Fri; ) The Mesa Verde National Park entrance is off US 160, midway between Cortez and Mancos. From the entrance it is 21 miles to the park headquarters. You can get road information and the word on park closures (many areas are closed in winter).
#### Getting There & Around
Mesa Verde is best accessed by private vehicle. In the park, a new biodiesel tram (free; 9:20am-3:30pm daily, every 30min) shuttles visitors around Wetherill Mesa, starting at the ranger kiosk; park here.
### Cortez
POP 8640 / ELEV 6201FT
Cortez fails to beguile, but its location, 10 miles west of Mesa Verde National Park, makes it a logical base, and the surrounding area holds quiet appeal. Mountain bikers will covet the hundreds of great singletrack rides nearby.
Typical of small-town Colorado, downtown Cortez is lined with trinket and rifle shops; family-style restaurants dishing up meat and potatoes; and the requisite microbrewery. The edges of the town are jam-packed with independent motels and fast-food outlets. Far-off mountain vistas complete the picture.
#### Sights & Activities
Cultural Park MUSEUM
( 10am-9pm Mon-Sat summer, to 5pm winter) An outdoor space at the Cortez Cultural Center with art, weaving demonstrations and a Navajo hogan. Summer evening programs feature Native American dancessix nights a week at 7:30pm, followed at 8:30pm by cultural programs such as Native American storytellers.
Cortez Cultural Center MUSEUM
( 702-565-1151; www.cortezculturalcenter.org; 25N Market St; 10am-9pm Mon-Sat May-Oct, to 5pm Nov-Apr; ) Exhibits on the Ancestral Puebloans, as well as visiting art displays, make this museum worthy of a visit if you have a few hours to spare.
Crow Canyon Archaeology Center ARCHAEOLOGICAL SITE
( 970-565-8975, 800-422-8975; www.crowcanyon.org; 23390 Rd K; adult/child $55/30; 9am-5pm Wed & Thu Jun–mid-Sep; ) An excellent way to learn about Ancestral Puebloan culture and the significance of regional artifacts first-hand; daylong programs visit an excavation site west of town. In weeklong sessions, guests share traditional Pueblo hogans and study excavation field and lab techniques. It's 3 miles north of Cortez.
Kokopelli Bike & Board BIKE RENTALS
( 970-565-4408; www.kokopellibike.com; 30 W Main St; per day $20; 9am-6pm Mon-Fri, to 5pm Sat) The friendly staff at this local bike shop are happy to talk trails, they also rent and repair mountain bikes. For some pre-trip planning, visit the shop's website with great trail descriptions.
#### Sleeping
Budget motels dot the main drag; expect winter discounts around 50%. Sadly, the only campground in town not right next to a highway or dedicated to RVs is the Cortez-Mesa Verde KOA ( 970-565-9301; 27432 E Hwy 160; sites $25-32, cabins $50; Apr-Oct; ) at the east end of town.
### MOUNTAIN BIKING THE FOUR CORNERS
Cortez offers some epic mountain-bike trails among piñon-juniper woodland and over the otherworldly slickrock mesa. Some ideas include Sand Canyon, an 18-mile trail starting at the same-named archaeological site west of Cortez. For advanced riders, the 27-mile Stoner Mesa Loop has splendid views. For details, check out _Mountain and Road Bike Routes for the Cortez-Dolores-Mancos Area._ The staff at Kokopelli Bike & Board are helpful.
Kelly Place B&B $$
( 970-565-3125; www.kellyplace.com; 14663 Montezuma County Rd G; r & cabins $80-155, 2-person campsite/RV site $40/50; ) It is pretty rare to find a B&B with archaeological ruins and a network of desert trails with nary another soul in sight. Founded by late botanist George Kelly, this lovely adobe-style guest lodge is situated on 40 acres of orchards, red-rock canyon and Indian ruins abutting Canyon of the Ancients, 15 miles west of Cortez. A pamphlet given to guests helps to locate and understand the ruins, in addition to identifying local plants. Rooms are tasteful and rates (even camping) include an enormous buffet breakfast.
There is a range of cabins, the best sports a private flagstone patio and whirlpool tub. Kelly Place also offers horseback riding, cultural tours and archaeological programs. At night put a DVD on the big-screen TV in the communal lounge and chill with a glass of wine or a tasty microbrew; the lodge serves both.
Tomahawk Lodge LODGE $
( 970-565-8521, 800-643-7705; www.angelfire.com/co2/tomahawk; 728 S Broadway; r from $75; ) Friendly hosts welcome you at this clean, good-value place. It feels more personable than the average motel with unique Native American art on the walls and a pool out front.
Best Western Turquoise Inn & Suites HOTEL $$
( 970-565-3778; www.bestwestern.com; 535 E Main St; r from $130; ) With two swimming pools, this is a good choice for families (kids stay free, and the restaurant has a kids' menu). Rooms here are spacious, and bigger families can grab a two-room suite. If you're exploring Mesa Verde all day and just want an affordable and clean, if slightly bland, hotel to crash at night, this central Best Western will do the trick.
#### Eating & Drinking
Main Street Brewery & Restaurant PUB $$
( 970-544-9112; 21 E Main St; mains $8-15; lunch & dinner; ) A cozy spot with German-style house-brewed beers listed on the wall, right next to the hand-painted murals. Beers are excellent and a large menu features everything from southwestern cuisine to Mexican and Italian, with the requisite burgers and pizzas. There's also a downstairs game room with billiards.
Stonefish Sushi & More JAPANESE $$
( 970-565-9244; 16 W Main St; mains $10-16; 4:30-9pm Mon-Thu, to 10pm Sat) With blues on the box and a high tin ceiling, this is southwestern sushi. The rolls are standard fare, but specialties, like the Colorado rancher seared beef and wasabi, liven things up. Cool light fixtures, black tiles and globe-shaped fish tanks behind the bar complete the scene.
Nero's Italian Restaurant ITALIAN $$$
( 970-565-7366; 303 W Main St; mains $14-25; 5-9pm Mon-Sat) Though splashed in southwest decor, this local favorite is known for well-prepared Italian dishes. Favorites include the half Hudson Valley duckling with garlic and honey glaze and the pecan raviolis. The menu is extensive, with good options for kids.
#### Information
Colorado Welcome Center ( 970-565-4048; 928 E Main St; 9am-5pm Sep-May, to 6pm Jun-Aug) Maps, brochures and some excellent pamphlets on local activities like fishing and mountain biking. Also sells tickets to popular backcountry ranger tours at Mesa Verde National Park.
Southwest Memorial Hospital ( 970-565-6666; 1311 N Mildred Rd) Provides emergency services.
#### Getting There & Around
Cortez is easier to reach by car from Phoenix, AZ, or Albuquerque, NM, than from Denver (379 miles away by the shortest route). East of Cortez, US Hwy 160 passes Mesa Verde National Park on the way to Durango – the largest city in the region.
Cortez Municipal Airport ( 970-565-7458; 22874 County Rd F) is served by United Express, which offers daily turboprop flights to Denver. The airport is 2 miles south of town off US 160/666.
### Dolores
POP 920 / ELEV 6936FT
Scenic Dolores, sandwiched between the walls of a narrow canyon of the same name, has a treasure trove of Native American artifacts and sits near the sublime river of the same name – only rafted in spring. But on a more permanent basis, the McPhee Lake boasts the best angling in the southwest. Food and lodging options here are slim.
#### Sights & Activities
The Bureau of Land Management manages the Anasazi Heritage Center ( 970-882-5600; 27501 Hwy 184; admission $3, free Dec-Feb; 9am-5pm Mar-Nov, 10am-4pm Dec-Feb; ), a must-see for anyone touring the area's archaeological sites. It's 3 miles west of town, with hands-on exhibits including weaving, corn grinding, tree-ring analysis and an introduction to the way in which archaeologists examine potsherds. You can walk through the Dominguez Pueblo, a roofless site from the 1100s that sits in front of the museum, and compare its relative simplicity to the Escalante Pueblo, a Chacoan structure on a nearby hillside.
Dolores is home to McPhee Lake, a reservoir that's the second-largest body of water in Colorado. Located in a canyon of the Dolores River, McPhee offers many angling spots accessible only by boat. In skinny, tree-lined side canyons, wakeless boating zones allow for still-water fishing. With the best catch ratio in all of southwest Colorado, it's a great place to teach younger anglers. Make sure you have a valid Colorado fishing license.
#### Sleeping & Eating
Find out about nearby campsites in the San Juan National Forest from the USFS Dolores Ranger Station ( 970-882-7296; 29211 Hwy 184; 8am-5pm Mon-Fri), which has the best options.
Dolores River RV Park RV PARK $
( 970-882-7761; www.doloresriverrvparkandcabins.com; 18680 Hwy 145; tent/RV sites $25/35, cabins $45; ) Has pleasant though overpriced sites, 1.5 miles east of town.
Rio Grande Southern Hotel HOTEL $$
( 866-882-3026; www.rgshotel.com; 101 S 5th St; r incl breakfast $85-110; ) Norman Rockwell prints and an old-world front desk beckon guests at this National Historic Landmark which is by far the best sleeping option in town. A cozy library and small, antique-filled guest rooms add to the cluttery charm. It's rumored that Zane Gray stayed in room 4 while writing _Riders of the Purple Sage._
Rio Grande Southern Restaurant AMERICAN $$
( 866-882-3026; www.rgshotel.com; 101 S 5th St; mains $5-15; 7am-8pm Wed-Sat; ) Downstairs from the historic hotel, is former mayor cooks a standard American menu, with weekly specials including a fish fry and Chicago pizza night.
#### Getting There & Away
Dolores is 11 miles north of Cortez on Hwy 145, also known as Railroad Ave.
### San Juan Mountains
In autumn, yellow aspens dot the San Juans and cool air carries the sharp scent of pine. Day-to-day tensions tend to dissipate into serene, blue-sky days as you amble among towering peaks, picturesque towns and old mines.
The 236-mile San Juan Skyway climbs to the top of the world as it twists and turns past a series of 'fourteeners' (peaks exceeding 14,000ft). Places like Telluride, Durango and Silverton have storied pasts of boom and bust. The San Juan Skyway leads you past both churling rapids primed for descent and quiet pockets of the Animas River almost made for fly-fishing. In the summer, there's a rousing, rowdy soundtrack of bluegrass, jazz and folk, when local towns host renowned festivals.
From Ridgway follow US 550 south to Ouray and then over Red Mountain Pass to Silverton. Continue heading south on US 550 until you hit Durango. From here, you can head west on US 160 to the ruins at Mesa Verde, then head north on Rte 145 toward Telluride before following Rte 62 back to Ridgway. To drive the entire byway, allow at least one or two days.
### Telluride
POP 2400 / ELEV 8750FT
Surrounded on three sides by mastodon peaks, exclusive Telluride is quite literally cut off from the hubbub of the outside world. Once a rough mining town, today it's dirtbag-meets-diva – mixing the few who can afford the real estate with those scratching out a slope-side living for the sport of it. The town center still has palpable old-time charm, though locals often villainize the recently developed Mountain Village, whose ready-made attractions have a touch of Vegas. Yet idealism remains the Telluride mantra. Shreds of paradise persist with the longtime town free box where you can swap unwanted items (across from the post office), the freedom of luxuriant powder days and bonhomie of its infamous festivals.
Colorado Ave, also known as Main St, has most of the restaurants, bars and shops. You can walk everywhere, so leave your car at the intercept parking lot at the south end of Mahoney Dr (near the visitor center) or at your lodgings.
From town you can reach the ski mountain via two lifts and the gondola. The latter also links Telluride with Mountain Village, the basefor the Telluride Ski Resort. Located 7 miles from town along Hwy 145, Mountain Village is a 20-minute drive east, but only 12 minutes away by gondola (free for foot passengers).
Ajax Peak, a glacial headwall, rises up behind the town to form the end of the U-shaped valley. To the right (or south) on Ajax Peak, Colorado's highest waterfall, Bridal Veil Falls, cascades 365ft down; a switchback trail leads to a restored Victorian powerhouse atop the falls. To the south, Mt Wilson reaches 14,246ft among a group of rugged peaks that form the Lizard Head Wilderness Area.
#### Activities
Backcountry skiers should look into the incredible San Juan Hut system. In summer, the area has plenty of 4WD routes and some steep but gorgeous hikes.
Telluride Ski Resort SNOW SPORTS
( 970-728-7533, 888-288-7360; www.tellurideskiresort.com; 565 Mountain Village Blvd; lift tickets $98) Covering three distinct areas, Telluride Ski Resort is served by 16 lifts. Much of the terrain is for advanced and intermediate skiers,but there's still ample choice for beginners.
Telluride Ski & Snowboarding School SNOW SPORTS
( 970-728-7507; www.tellurideskiresort.com; 565 Mountain Village Blvd; full-day adult group lessons $170; ) Private and group lessons feature good teachers; there are classes for children and women-only clinics.
Telluride Flyfishers FISHING
( 800-294-9269; www.tellurideflyfishers.com; half-day for 2 $280) Housed in Telluride Sports, this outfit offers fishing guides and instruction.
Ride with Roudy HORSEBACK RIDING
( 970-728-9611; www.ridewithroudy.com; County Rd 43Zs; 2hr trips adult/child $85/45; ) If there ever were a local personality, it's Roudy. On the scene for 30-plus years, he offers all-season trail rides through the surrounding hills with a good dose of hospitality. Call for an appointment and pricing details.
Telluride Nordic Center SNOW SPORTS
( 970-728-1144; www.telluridetrails.org; 500 E Colorado Ave) Offers instruction and rentals. Public cross-country trails are in Town Park, along the San Miguel River and the Telluride Valley floor west of town.
Paragon Ski & Sport SPORTS RENTAL
( 970-728-4525; www.paragontelluride.com; 213W Colorado Ave) A one-stop shop for outdoor activities in Telluride, with three town branches and a huge selection of rental bikes.
Easy Rider Bike & Sport BIKE RENTAL
( 970-728-4734; 101 W Colorado Ave) A full-service shop with bike rentals, maps and information.
#### Festivals & Events
Mountainfilm FILM
(www.mountainfilm.org; Memorial Day weekend; prices vary) A spirited, four-day screening of outdoor adventure and environmental films that will get you in the mountain mood.
Telluride Bluegrass Festival MUSIC FESTIVAL
( 800-624-2422; www.planetbluegrass.com; 4-daypass $185; late Jun) A wildly rollicking festival attracting thousands for a music-filled weekend. Stalls sell all sorts of food and local microbrews to keep you happy, and acts continue well into the night. Camping out for the four-day festival is very popular. Check out the website for info on sites, shuttle services and combo ticket-and-camping packages – it's all very organized!
Telluride Mushroom Festival FOOD
(www.tellurideinstitute.org) Fungiphiles sprout up at this festival in late August.
Telluride Film Festival FILM
( 603-433-9202; www.telluridefilmfestival.com;entry $25-780) Held in early September, national and international films are premiered throughout town, and the event attracts big-name stars. Some talks and showings are free. For more information visit the film festival website.
Brews & Blues Festival BEER, MUSIC
(www.tellurideblues.com; mid-Sep) Telluride's festival season comes to a raucous end at this mid-September event, where blues musicians take to the stage and microbrews fill the bellies of fans.
#### Sleeping
Aside from camping, there are no cheap places to stay in Telluride. During summer, festival times or winter peak seasons, guests pay dearly. Yet, off-season rates drop up to 30%.
Some of the huge properties in Mountain Village can offer a decent rate if you book online, but none have the character ofthe smaller hotels downtown. Most wintervisitors stay in vacation rentals – there are scores of them. To book, contact Telluride Alpine Lodging ( 888-893-0158; www.telluridelodging.com; 324 W Colorado Ave).
### TELLURIDE CAMPGROUNDS
Right in Telluride Town Park, Telluride Town Park Campground ( 970-728-2173; 500 E Colorado Ave; campsites $20; mid-May–mid-Oct; ) offers 42 campsites, showers and swimming and tennis from mid-May to October. Developed campsites cost $20 and are all on a first-come, first-served basis.
Two campgrounds in the Uncompahgre National Forest are within 15 miles of Telluride on Hwy 145 and cost $20. Sunshine Campground ( 970-327-4261; off County Rd 145; sites $20 late May–late Sep) is the nearest and best and offers 15 first-come, first-served campsites; facilities at Matterhorn Campground ( 970-327-4261; Hwy 145; sites $20; May-Sep; ), a bit further up the hill, include showers and electrical hookups for some of the 27 campsites.
Hotel Columbia HOTEL $$$
( 970-728-0660, toll-free 800-201-9505; www.columbiatelluride.com; 300 W San Juan Ave; d $350; ) Since spendy digs are a given in Telluride, skiers might as well stay right across the street from the gondola. Locally owned and operated, this stylish and swank hotel pampers. Store your gear in the ski and boot storage and head directly to a room with espresso maker, fireplace and heated tile floors. With shampoo dispensers and recycling, it's also pretty eco-friendly.
Other highlights include a rooftop hot tub and fitness room. Breakfast is included, but food at the connected Cosmopolitan is also excellent – many say it's the best dining room in Telluride.
New Sheridan Hotel HOTEL $$
( 970-728-4351, 800-200-1891; www.newsheridan.com; 231 W Colorado Ave; d from $199; ) Elegant and understated, this historic brick hotel (erected in 1895) provides a lovely base camp for exploring Telluride. High-ceiling rooms feature crisp linens and snug flannel throws. Check out the hot-tub deck with mountain views. In the bull's eye of downtown, the location is perfect, but some rooms are small for the price.
Inn at Lost Creek BOUTIQUE HOTEL $$
( 970-728-5678; www.innatlostcreek.com; 119 LostCreek Lane; r from $189; ) Across from Lumière but with a more relaxed decor, this lush boutique-style hotel knows cozy. At the bottom of Telluride's main lift, it's also very convenient. Service is personalized, and impeccable rooms have an alpine style of hardwoods, southwestern designs and molded tin. There are also two rooftop spas. Check the website for packages.
Lumière HOTEL $$$
( 907-369-0400, 866-530-9466; www.lumierehotels.com; 118 Lost Creek Lane; d from $325, studio from $799; ) In Mountain Village, this ski-in, ski-out luxury lodge commands breathtaking views of the San Juans. Think plush and fluff, with seven-layer bedding, Asian-inspired contempo design and suites with top-of-the-line appliances that few probably even use. In the morning, guests enjoy an elegant breakfast reception. But even with the hip sushi bar and luxuriant spa menu, its greatest appeal is the location, which zips you from the slopes to a bubble bath in minutes.
Victorian Inn LODGE $$
( 970-728-6601; www.tellurideinn.com; 401 W Pacific Ave; r from $159; ) The smell of fresh cinnamon rolls greets visitors at one of Telluride's better deals, offering comfortable rooms (some with kitchenettes) and a hot tub and dry sauna in a nice garden area. Staff are friendly and guests get lift-ticket discounts. Kids aged 12 years and under stay free, and you can't beat the downtown location.
Aspen Street Inn BOUTIQUE HOTEL $$
( 970-728-3001, toll-free 800-537-4781; www.telluridehotels.com; 330 W Pacific Ave; d from $195; ) Near the chairlift, this small hotel has carpeted country-style rooms. Prices are steep for the dog-eared B&B vibe, but loyal visitors rave about the hospitality. Snacks are served in the stone- and wood-lined common room and the back patio is a lovely setting for the hot tub.
#### Eating
Meals and even groceries can be pricey in Telluride, so check out the hot dog stand or taco truck on Colorado Ave for quick fixes. Gaga for sustainability, many local restaurants offer grass-fed beef or natural meat; we indicate those with the greatest commitment to sustainability.
New Sheridan Chop House MODERN AMERICAN $$$
( 970-728-4531; www.newsheridan.com; 231 W Colorado Ave; mains $19-90; 5pm-2am) With superb service and a chic decor of embroidered velvet benches, this is an easy pick for an intimate dinner. Diners can start with a cheese plate, but from there the menu gets Western. Pasta comes with a creamy wild mushroom and sage sauce. Meat eaters should try the elk shortloin in a hard cider reduction. For a treat, top it off with a flourless dark chocolate cake in fresh caramel sauce.
Cosmopolitan MODERN AMERICAN $$$
( 970-728-0660; www.columbiatelluride.com; 300 W San Juan Ave; mains from $20; dinner) The on-site restaurant at the Hotel Columbia is one of Telluride's most respected for fine modern dining – can you resist Himalayan yak ribeye or lobster corn dogs? The food is certainly inventive, which makes up for sometimes snooty service.
La Cocina de Luz MEXICAN, ORGANIC $$
(www.lacocinatelluride.com; 123 E Colorado Ave; mains $9-19; 9am-9pm; ) As they lovingly serve two Colorado favorites (organic + Mexican), it's no wonder that the lunch line is 10 people deep on a slow day at this healthy taquería. There's delicious details too, like handmade tortillas and margaritas with organic lime and agave nectar. With vegan, gluten-free options too.
The Butcher & The Baker CAFE FOOD $$
( 970-728-3334; 217 E Colorado Ave; mains $8-14; 7am-7pm Mon-Sat, 8am-2pm Sun; ) Two veterans of upscale catering started this heartbreakingly cute cafe, and no one beats it for breakfast. Hearty sandwiches with local meats are the perfect takeout for the trail and there are heaps of baked goods and fresh sides.
There TAPAS $
( 970-728-1213; http://therebars.com; 627 W Pacific Ave; appetizers from $4; 3pm-late) A popular local caterer opened this hip social alcove for nibbling. East-meets-West in yummy soy paper wraps with asparagus, duck ramen and sashimi tostadas, paired with original cocktails. We liked the jalapeño kiss.
221 South Oak MODERN AMERICAN $$$
( 970-728-9505; www.221southoak.com; 221 S Oak St; mains $19-25; 5-10pm; ) A local favorite, with small, seasonal menus playful with world flavors. In a cozy historic home, dine on watermelon, blueberry and feta salad in summer and five-spice shortribs with sweet potato wontons in winter. Vegetarian menu available upon request.
La Marmotte FRENCH $$$
( 970-728-6232; www.lamarmotte.com; 150 W San Juan Ave; mains from $20; 5pm-late Tue-Sat) Seasonal plates of French cuisine, white linen and candlelit warmth contrast with this rustic 19th-century icehouse. Dishes like the coq au vin with bacon mashed potatoes are both smart and satisfying. There's some organic options and an extensive wine list. Parents should check out their Friday-night winter babysitting options.
Baked in Telluride BAKERY $
( 970-728-4775; www.bakedintelluride.com; 127 S Fir St; mains $6-10; 5:30am-10pm) Back in action after a fire closure, this Telluride institution boasts the West's best bagel, sourdough wheat-crust pizza and some hearty soups and salads. The front deck is a fishbowl of local activity and the vibe is happy casual.
Honga's Lotus Petal ASIAN $$$
( 970-728-5134; www.hongaslotuspetal.com; 135 E Colorado Ave; mains $17-33) For pan-Asian cuisine, beat it to this two-story dining space. Prices are dear but the presentation – ranging from sushi to curries – is lovely. The Korean short ribs just about fall off the bone. So lively and fresh, we can even forgive the pan flutes.
Clark's Market SELF-CATERING
(www.clarksmarket.com; 700 W Colorado Ave; 7am-9pm) The nicest market in town stocks specialty goods and scores of treats, with fresh fruit and deli meats.
#### Drinking
Smugglers Brewery & Grille PUB
( 970-728-0919; www.smugglersbrew.com; 225 S Pine St; 11am-2am; ) Beer-lovers will feel right at home at casual Smugglers, a great place to hang out, sample local brew and eat fried stuff.
New Sheridan Bar BAR
( 970-728-3911; www.newsheridan.com; 231 W Colorado Ave; 5pm-2am) Well worth a visit in low season for some real local flavor and opinions. At other times, it becomes a rush hour of beautiful ones. But there's old bullet holes in the wall and the plucky survival of the bar itself, even as the adjoining hotel sold off chandeliers and fine furnishings to pay the heating bills during waning mining fortunes.
Last Dollar Saloon BAR
( 970-728-4800; www.lastdollarsaloon.com; 100 E Colorado Ave; 3pm-2am) All local color – forget about cocktails and grab a cold can of beer at this longtime late-night favorite, popular when everything else closes. With pool tables and darts.
#### Entertainment
Fly Me to the Moon Saloon LIVE MUSIC
( 970-728-6666; 132 E Colorado Ave; 3pm-2am) Let your hair down and kick up your heels to the tunes of live bands at this saloon, the best place in Telluride to party hard.
Sheridan Opera House THEATER
( 970-728-4539; www.sheridanoperahouse.com; 110 N Oak St; ) This historic venue has a burlesque charm and is always the center of Telluride's cultural life. It hosts the Telluride Repertory Theater, and frequently has special performances for children.
#### Shopping
In addition to boutique sporting gear, shoppers will find upscale shops and art galleries (featuring artists of renown) all over town; pick up a local shopping guide.
Telluride Sports SPORTING GOODS
( 970-728-4477; www.telluridesports.com; 150 WColorado Ave; 8am-8pm) With several branches and associated shops in Mountain Village, this main outfitter covers everything outdoors, has topographical and USFS maps, sporting supplies and loads of local information.
Between The Covers BOOKS
( 970-728-4504; www.btwn-the-covers.com; 224W Colorado Ave) With a doting staff, great local reads and creaking floors, this bookstore is a terrific place to browse. For a mean espresso milk shake, go to the coffee counter in back.
#### Information
Telluride Central Reservations ( 888-355-8743; 630 W Colorado Ave) Handles accommodations and festival tickets. Located in the same building as the visitor center.
Telluride Library ( 970-728-4519; www.telluridelibrary.org; 100 W Pacific Ave; 10am-8pm Mon-Thu, 10am-6pm Fri & Sat, 12-5pm Sun; ) With free wi-fi, maps, hiking guides and flyers on local happenings, this is a worthy pit stop, especially with kids. In summer they sponsor a free film series in Mountain Village.
Telluride Medical Center ( 970-728-3848; 500 W Pacific Ave) Handles skiing accidents, medical problems and emergencies.
Telluride Visitor Center ( 888-353-5473, 970-728-3041; www.telluride.com; 630 W Colorado Ave; 9am-5pm winter, to 7pm summer) This well-stocked visitor center has local info in all seasons. Restrooms and an ATM make it an all-round useful spot.
#### Getting There & Around
Commuter aircraft serve the mesa-top Telluride airport ( 970-778-5051; www.tellurideairport.com; Last Dollar Rd), 5 miles east of town on Hwy 145. If weather is poor flights may be diverted to Montrose, 65 miles north. For car rental, National and Budget both have airport locations.
In ski season Montrose Regional Airport has direct flights to and from Denver (on United), Houston, Phoenix and limited cities on the East Coast.
Shared shuttles from Telluride airport to town or Mountain Village cost $15. Shuttles between the Montrose airport and Telluride cost $48. Contact Telluride Express ( 970-728-6000; www.tellurideexpress.com).
### Ridgway
POP 810 / ELEV 6985FT
Ridgway, with its local quirk, zesty history and scandalous views of Mt Sneffels, is hard to just blow through. Before it got so hip, the town also served the backdrop for John Wayne's 1969 cowboy classic, _True Grit._
It sits at the crossroads of US 550, which goes south to Durango, and Hwy 62, which leads to Telluride, but the downtown is tucked away on the west side of the Uncompahgre River. Through town Hwy 62 is called Sherman and all the perpendicular streets are named for his daughters. Ridgway Area Chamber of Commerce has a lot of information about local activities in the area.
### COLORADO'S HAUTE ROUTE
An exceptional way to enjoy hundreds of miles of singletrack in summer or virgin powder slopes in winter, San Juan Hut Systems ( 970-626-3033; www.sanjuanhuts.com; per person $30) continues the European tradition of hut-to-hut adventures with five backcountry mountain huts. Bring just your food, flashlight and sleeping bag – amenities include padded bunks, propane stoves, wood stoves for heating and firewood.
Mountain-biking routes go from Durango or Telluride to Moab, winding through high alpine and desert regions. Or pick one hut as your base for a few days of backcountry skiing or riding. There's terrain for all levels, though skiers should have knowledge of snow and avalanche conditions or go with a guide.
The website has helpful tips and information on rental skis, bikes and (optional) guides based in Ridgway or Ouray.
#### Sights & Activities
Chicks with Picks CLIMBING INSTRUCTION
( 970-316-1403, office 970-626-4424; www.chickswithpicks.net; 163 County Rd 12; prices vary) Arming women with ice tools and crampons, this group of renowned women athletes gives excellent instruction for all-comers (beginners included) in rockclimbing, bouldering and ice climbing. Programs are fun and change frequently, with multiday excursions or town-based courses. Clinics also hit the road.
Ridgway Railroad Museum MUSEUM
( 970-626-5181; www.ridgwayrailroadmuseum.org;150 Racecourse Rd; 10am-6pm May-Sep, reduced hr Oct-Apr; ) Ridgway's Rio Grande Southern Railroad connected to Durango with the narrow-gauge 'Galloping Goose', a kind of hybrid train and truck that saved the struggling Rio Grand Southern for a number of years, featured here.
Riggs Fly Shop & Guide Service FLY-FISHING
( 970-626-4460, toll-free 888-626-4460; www.fishrigs.com; Suite 2, 565 Sherman St; half-day fishing tours per person from $225; ) Good guided fly-fishing from half-day beginners' trips to multiday campouts for more experienced fisherfolk. There's also white-water rafting and other regional soft-adventure itineraries.
Ridgway State Park & Recreation Area FISHING
( 970-626-5822; www.parks.state.co.us/parks/ridgway; 28555 US Hwy 550; dawn-dusk) With a reservoir stocked with loads of rainbow trout, as well as German brown, kokanee, yellow perch and the occasional large-mouth bass. There's also hiking and campsites, 12 miles north of town.
#### Sleeping & Eating
Ridgway State Park & Recreation Area CAMPING $
( 800-678-2267; www.parks.state.co.us/parks/ridgway; 28555 US Hwy 550; tent/RV/yurt sites $16/$20/70; ) With almost 300 available sites, these three campgrounds offer good availability with gorgeous water views, hiking and fishing. If you're tent camping, these 25 sites are 'walk in' but the path is short and a free wheelbarrow is offered to transport your stuff. For a comfortable alternative, check out the cool canvas yurts. Services include rest rooms with coin-op showers and a playground for kids. You can book online or over the phone.
Chipeta Sun Lodge & Spa LODGE $$$
( 970-626-3737; www.chipeta.com; 304 S Lena St; r $125-235; ) Swank and southwestern, this adobe-style lodge offers a nice upscale getaway. Rooms feature hand-painted Mexican tiles, fireplaces, rough-hewn log beds and decks with a view. In-room magazines invite you to linger and wonderful public areas include a solarium and hot tubs. There's also an on-site spa and yoga classes. Check the website for ski, soak and stay deals.
Kate's Place BREAKFAST $$
( 970-626-9800; 615 W Clinton St; mains $9-13; 7am-2pm; ) Consider yourself lucky if the morning starts with a chorizo-stuffed breakfast burrito and white cheddar grits from Kate's, the best breakfast joint for miles. But the restaurant's dedication to local farmers, warm interior and friendly wait staff seal the deal.
True Grit Cafe AMERICAN $$
( 970-626-5739; 123 N Lena Ave; mains $8-15; lunch & dinner) Scenes from the original _True Grit_ were filmed at this loud cafe, but come for the burgers, roast beef, and peach pie. It's friendly, with a crackling fire warming patrons in the winter.
#### Information
Ridgway Area Chamber of Commerce ( 970-626-5181, 800-220-4959; www.ridgwaycolorado.com; 150 Racecourse Rd; 9am-5pm Mon-Fri)
### Ouray & the Million Dollar Hwy
POP 940 / ELEV 7760FT
With gorgeous icefalls draping the box canyon and soothing hot springs that dot the valley floor, Ouray is one privilegedplace, even for Colorado. For ice-climbers, it's a world-class destination, but hikers and 4WD fans can also appreciate its rugged and sometimes stunning charms. The town is a well-preserved quarter-mile mining village sandwiched between imposing peaks.
Between Silverton and Ouray, US 550 is known as the Million Dollar Hwy because the roadbed fill contains valuable ore. One of the state's most memorable drives, this breathtaking stretch passes old mine head-frames and larger-than-life alpine scenery. Though paved, the road is scary in rain or snow, so take extra care.
#### Sights
Little Ouray, 'the Switzerland of America,' is very picturesque and littered with old houses and buildings. The visitor center and museum ( 970-325-4576; www.ouraycountyhistoricalsociety.org; 420 6th Ave; adult/child $5/1; 1-4:30pm Thu-Sat Apr 14-May 14, 10am-4:30pm Mon-Sat & noon-4:30pm Sun May 15-Sep 30, 10am-4:30pm Thu-Sat Oct 1-30, closed Dec 1-Apr 14; ) issue a free leaflet with details of an excellent walking tour that takes in two-dozen buildings and houses constructed between 1880 and 1904.
Bird-watchers come to Ouray to sight rare birds, including warblers, sparrows and grosbeaks. Box Canyon Falls has the USA's most accessible colony of protected black swifts. The visitor center has resources for bird-watchers, and the excellent Buckskin Booksellers ( 970-325-4071; www.buckskinbooksellers.com; 505 Main St; 9am-5pm Mon-Sat; ) has books and guides.
### SCENIC DRIVES: SAN JUAN ROUTES
For the following we suggest a high-clearance 4WD vehicle and some four-wheeling skills.
Alpine Loop
Demanding but fantastic fun, this 63-mile drive into the remote and rugged heart of the San Juan Mountains begins in Ouray and travels east to Lake City before looping back. Along the way you'll cross two 12,000ft mountain passes, with spectacular scenery and abandoned mining haunts. Allow six hours.
Imogene Pass
Every year, runners tackle this rough 16-mile mining road, but you might feel that driving it is enough. Ultra-scenic, it connects Ouray with Telluride. Built in 1880, it's one of the San Juans' highest passes, linking two important mining sites.
In Ouray, head south on Main St and turn right on Bird Camp Rd (City Rd 361). Pass Bird Camp Mine, once one of the San Juans' most prolific, climbing high into the mountains. You will have to cross streams, and at times the road snakes precariously close to sheer cliff drops offering a thrilling adrenaline rush. Eventually the route opens, reaching high alpine meadows before the summit of Imogene Pass (13,114ft). Descending toward Telluride, you'll pass the abandoned Tomboy Mine, which once had a population as large as present-day Ouray. The pass is open only in summer. Allow three hours one way.
#### Activities
Ouray Ice Park ICE CLIMBING
( 970-325-4061; www.ourayicepark.com; Hwy 361; 7am-5pm mid-Dec–March; ) Enthusiasts from around the globe come to ice climb at the world's first public ice park, spanning a 2-mile stretch of the Uncompahgre Gorge. The sublime (if chilly) experience offers something for all skill levels.
Ouray Hot Springs HOT SPRINGS
( 970-325-7073; www.ourayhotsprings.com; 1220Main St; adult/child $10/8; 10am-10pm Jun-Aug, noon-9pm Mon-Fri & 11am-9pm Sat & Sun Sep-May; ) For a healing soak, try this crystal-clear natural spring water. It's free of the sulphur smells plaguing other hot springs around here, and the giant pool features a variety of soaking areas at temperatures from 96°F to 106°F (36°C to 41°C). The complex also offers a gym and massage service.
Ouray Mule Carriage Co CARRIAGE TOURS
( 970-708-4946; www.ouraymule.com; 834 Main St; adult/child $15/5; hourly departures 1-6pm Jun-Aug; ) Clip-clopping along Main Street, this nine-person dray (been in the same family since 1944) takes visitors on interpretive tours of old town.
Ouray Livery HORSEBACK RIDING
( 970-708-7051, 970-325-4340; www.ouraylivery.com; 834 Main St; tour of Ouray 2hr riding $60; ) The Ouray Livery offers short carriage and stagecoach tours as well as horseback riding in the mountains. This group has special-use permits to tour the Grand Mesa, Uncompahgre and Gunnison National Forests.
San Juan Scenic Jeep Tours 4WD, FISHING
( 970-325-0090, 888-624-8403; www.historicwesternhotel.com; 210 7th Ave; adult/child half-day $54/27, full day $108/54; ) The friendly folks at the Historic Western Hotel offer off-road tours of the nearby peaks and valleys. Hiking, hunting and fishing drop-offs and pick-ups can be arranged.
San Juan Mountain Guides CLIMBING, SKIING
( 970-325-4925, 866-525-4925; www.ourayclimbing.com; 474 Main St; ) Ouray's own professional guiding and climbing group is certified with the International Federation of Mountain Guides Association (IFMGA). It specializes in ice and rock climbing and wilderness backcountry skiing.
#### Festivals & Events
Ouray Ice Festival ICE CLIMBING
( 970-325-4288; www.ourayicefestival.com; donation for evening events $15; Jan; ) The Ouray Ice Festival features four days of climbing competitions, dinners, slide shows and clinics in January. There's even a climbing wall set up for kids. You can watch the competitions for free, but to check out the various evening events you will need to make a donation to the ice park. Once inside you'll get free brews from popular Colorado microbrewer New Belgium.
#### Sleeping
Wiesbaden HOTEL $$
( 970-325-4347; www.wiesbadenhotsprings.com; 625 5th St; r from $132; ) Quirky, quaint and new age, Wiesbaden even boasts a natural indoor vapor cave, which, in another era, was frequented by Chief Ouray. Rooms with quilted bedcovers are cozy and romantic, but the sunlit suite with a natural rock wall tops all. In the morning, guests roam in thick robes, drinking the free organic coffee or tea, post-soak, or awaiting their massage. The on-site Aveda salon also provides soothing facials to make your mountain detox complete. Outside, there's a spacious hot-spring pool (included) and a private, clothing-optional soaking tub with a waterfall, reserved for $35 per hour.
Beaumont Hotel HOTEL $$$
( 970-325-7000; www.beaumonthotel.com; 505 Main St; r $169-259; ) With magnificent four-post beds, clawfoot tubs and hand-carved mirrors, this 1886 hotel underwent extensive renovations to revive the glamour it posed a century ago. Word has it that Oprah stayed here, and you'll probably like it too. There's also a spa and boutiques, but due to the fragile decor, pets and kids under 16 years old are not allowed.
Box Canyon Lodge & Hot Springs LODGE $$
( 800-327-5080, 970-325-4981; www.boxcanyonouray.com; 45 3rd Ave; d $159; ) It's not every hotel that offers geothermal heat, and these pineboard rooms prove spacious and fresh. Spring-fed barrel hot tubs are perfect for a romantic stargazing soak. With good hospitality that includes free apples and bottled water, it's popular, so book ahead.
Amphitheater Forest Service Campground CAMPING $
( 877-444-6777; www.ouraycolorado.com/amphitheater; US Hwy 550; tent sites $16; Jun-Aug; ) With great tent sites under the trees, this high-altitude campground is a score. On holiday weekends a three-night minimum applies. South of town on Hwy 550, take a signposted left-hand turn.
St Elmo Hotel HOTEL $$
( 970-325-4951, toll-free 866-243-1502; www.stelmohotel.com; 426 Main St; d incl breakfast $139-165; ) Effusively feminine, this 1897 hotel is a showpiece of the Ouray museum's historic walking tour. Nine unique renovated rooms have floral wallpaper and period furnishings. Guests have access to a hot tub and sauna and there's even some of Ouray's best dining, Bon Ton Restaurant, on-site downstairs.
Ouray Victoria Inn HOTEL $$
( 970-325-7222, toll-free 800-846-8729; www.victorianinnouray.com; 50 3rd Ave; d incl breakfast $145; ) Refurbished in 2009, 'The Vic' has a terrific setting next to Box Canyon Park on the Uncompahgre riverfront near the Ouray Ice Park. Rooms have cable TV, fridges and coffeemakers, some with balconies and splendid views. Kids will appreciate the deluxe swing set with climbing holds. Rates vary widely by season, but low-season rates are a steal.
Historic Western Hotel, Restaurant & Saloon HOTEL $
( 970-325-4645; www.historicwesternhotel.com; 210 7th Ave; r without/with bath $55/95; ) Open by reservation in shoulderseason, this somewhat threadbare Wild West boardinghouse serves all budgets. The second-floor verandah commands stunning views of the Uncompahgre Gorge, while the saloon serves affordable meals and grog in a timeless setting.
#### Eating & Drinking
Buen Tiempo Mexican Restaurant & Cantina MEXICAN $$
( 970-325-4544; 515 Main St; mains $7-19; 6-10pm; ) Bursting with locals at bar stools and families filling the booths, this is a good-time spot. From the chile-rubbed sirloin to the posole served with warm tortillas, Buen Tiempo delivers. Start with a signature margarita, served with chips and spicy homemade salsa. You can end with a satisfying scoop of deep-fried ice cream. But if you want to find out how the dollars got on the ceiling, it will cost you.
Bulow's Bistro at the Beaumont MODERN AMERICAN $$
( 970-325-7000; www.beaumonthotel.com/dine.html; 505 Main St; mains $10-26; closed Sun; ) Replacing a more upscale establishment, this popular contemporary bistro offers everything from baguettes to a well-seared rib eye steak, and there's a children's menu as well. Both the restaurant and the outdoor courtyard are lovely and you can choose from the wine cellar's 300 vintages from all over the world.
Bon Ton Restaurant FRENCH, ITALIAN $$$
( 970-325-4951; www.stelmohotel.com; 426 Main St; mains $15-36; 6-11pm; ) Bon Ton has been cooking in a beautiful room under the historic St Elmo Hotel for as long as anyone can remember. In fact, supper has been served at this location for nearly a century. The French-Italian menu includes house specialties of escargot and crawfish tails, and tortellini with bacon and shallots. The wine list is extensive.
Ouray Brewery BREWERY
( 970-325-7388; ouraybrewery.com; 607 Main St; 11am-9pm) With chairlift bar stools, this pub earns stripes in brews, if not in bar food. Why must so many landlocked menus insist on shrimp?
#### Information
Ouray Chamber Resort Association ( 970-325-4746, 800-228-1876; www.ouraycolorado.com; 1230 Main St; 10am-5pm Mon-Sat, 10am-3pm Sun; ) The visitor center is at the Ouray hot-springs pool.
Post office ( 970-325-4302; 620 Main St; 9am-4:30pm Mon-Sat)
#### Getting There & Away
Ouray is on Hwy 550, 70 miles north of Durango, 24 miles north of Silverton and 37 miles south of Montrose. There are no bus services in the area.
### Silverton
POP 530 / ELEV 9318FT
Ringed by snowy peaks and steeped in sooty tales of a tawdry mining town, Silverton would seem more at home in Alaska than the lower 48. But here it is. Whether you're into snowmobiling, biking, fly-fishing, beer on tap or just basking in some very high altitude sunshine, Silverton delivers.
It's a two-street town, but only one is paved. Greene St is where you'll find most businesses. Still unpaved, notorious Blair St runs parallel to Greene and is a blast from the past. During the silver rush, Blair St was home to thriving brothels and boozing establishments.
A tourist town by day in summer, once the final Durango-bound steam train departs it reverts to local turf. Visit in winter for a real treat. Snowmobiles become the main means of transportation, and town becomes a playground for intrepid travelers, most of them serious powder hounds.
One of Silverton's highlights is just getting here from Ouray on the Million Dollar Hwy – an awe-inspiring stretch of road that's one of Colorado's best road trips.
#### Sights & Activities
Silverton Railroad Depot NARROW-GAUGE RAILWAY
( 970-387-5416, toll-free 877-872-4607; www.durangotrain.com; 12th St; adult/child return from $83/49; departures 2pm, 2:45pm & 3:30pm; ) Buy one-way and return tickets for the brilliant Durango & Silverton Narrow Gauge Railroad at the Silverton terminus or online. A ticket provides admission to the on-site Silverton Freight Yard Museum. The train service offers combination train-bus return trips (with the bus route much quicker). Hikers use the train to access the Durango and Weminuche Wilderness trailheads.
Silverton Museum MUSEUM
( 970-387-5838; www.silvertonhistoricsociety.org; 1557 Greene St; adult/child $5/free; 10am-4pm Jun-Oct; ) Installed in the original 1902 San Juan County Jail, with an interesting collection of local artifacts and ephemera.
Silverton Mountain Ski Area SKIING
( 970-387-5706; www.silvertonmountain.com; StateHwy 110; daily lift ticket $49, all-day guide & lift ticket $99) Not for newbies, this is one of the most interesting and innovative ski mountains in the US – a single lift takes advanced and expert backcountry skiers up to the summit of an area of ungroomed ski runs. Numbers are limited and the mountain designates unguided and the more exclusive guided days.
The lift rises from the 10,400ft base to 12,300ft. Imagine heli-skiing _sans_ helicopter. You really need to know your stuff – the easiest terrain here is comparable to skiing double blacks at other resorts.
Kendall Mountain Recreation Area SKIING
( 970-387-5522; www.skikendall.com; Kendall Pl; daily lift tickets adult/child $15/10; 11am-4pm Fri & Sat Dec-Feb; ) Managed by the town, with just one double 1050ft chairlift and four runs, all suitable for beginners. People goof around on sleds and tubes, and it's cheap and family-friendly. Rent gear from the Kendall Mountain Community Center.
San Juan Backcountry TOURS
( 970-387-5565, toll-free 800-494-8687; www.sanjuanbackcountry.com; 1119 Greene St; 2hr tours adult/child $60/40; May-Oct) Offering both 4WD tours and rentals, these folks get you out and into the brilliant San Juan Mountain wilderness areas around Silverton, often in modified open-top Chevy Suburbans.
#### Sleeping
Wyman Hotel & Inn B&B $$$
( 970-387-5372; www.thewyman.com; 1371 GreeneSt; d incl breakfast $125-230; ) A handsome sandstone on the National Register of Historic Places, this 1902 building brims with personality. Local memorabilia lines long halls with room after room of canopy beds, Victorian-era wallpaper and chandelier lamps. Every room is distinct, none more so than the caboose that you can rent out back. Includes a full breakfast plus afternoon wine and cheese tasting.
Inn of the Rockies at the Historic Alma House B&B $$
( 970-387-5336, toll-free 800-267-5336; www.innoftherockies.com; 220 E 10th St; r incl breakfast from $110; ) Opened by a local named Alma in 1898, this inn has nine unique rooms furnished with Victorian antiques. You can't beat the hospitality or the New Orleans-inspired breakfasts, served in a chandelier-lit dining room. There's also a garden hot tub.
Bent Elbow HOTEL $$
( 970-387-5775, toll-free 877-387-5775; www.thebent.com; 1114 Blair St; d $100-145; ) Located on notorious Blair St, these creaky rooms once served as a bordello. For what you get these days, prices are a little steep, but the decoration is pleasingly quaint and Western.
Locals say the restaurant (mains $6 to $12) has the best cooking in town. It's a cheerful dining room with a gorgeous old wood shotgun bar that serves Western American fare.
Silver Summit RV Park CAMPING $
( 970-387-0240, toll-free 800-352-1637; www.silversummitrvpark.com; 640 Mineral St; RV sites $36 plus electricity $3; May 15-Oct 15; ) A mixed business running rental Jeeps out of the RV park headquarters (two-/four-door Jeep Wranglers $155/185). The park has good facilities including a laundry, hot tub, fire pit and free wi-fi.
Red Mountain Motel & RV Park MOTEL, CAMPING $
( 970-382-5512, toll-free 800-970-5512; www.redmtmotelrvpk.com; 664 Greene St; motel r from $78, cabins from $70, RV/tent sites $38/20; year-round; ) Standard, with warm and tiny log cabins fully outfitted with little kitchenettes. The managers seem keen to make sure guests and customers have a good time. The river, with good fishing, is just a few minutes' walk away. Jeep and ATV rental are available, as well as guided tours, snowmobiling, fishing and hunting.
#### Eating & Drinking
Stellar Bakery & Pizzeria CAFE $$
( 970-387-9940; 1260 Blair St; mains $8-15; 11am-10pm; ) Great for lunch or dinner, with signature stellar pizzas, friendly service and an easy atmosphere. Beers by the bottle are available and there's also a selection of fresh baked quiches, pastas and salads.
Handlebars AMERICAN $$
( 970-387-5395; www.handlebarssilverton.com; 117 13th St; mains $10-20; lunch & dinner, May-Oct; ) Steeped in Wild West kitsch, this place still serves worthy baby-back ribs basted in a secret BBQ sauce and other Western fare. The decor, a mishmash of old mining artifacts, mounted animal heads and cowboy memorabilia, gives this place a ramshackle museum-meets-garage-sale feel.
After dinner, kick it up on the dance floor to the sounds of live rock and country music.
Montanya Distillers BAR
(www.montanyadistillers.com; 1332 Blair St; mains $8-20; 11:30am-7pm) Finding handcrafted rum in the Rockies is like digging up a nugget of gold. This smart and inviting shoebox is run by hip female bartenders with a lazy pour. They're known to invite you for the first shot and talk you into organic tamales, free popcorn and exotic cocktails handmade with homemade syrups and award-winning rum. It's worth it just for the cozy, fun atmosphere. Note: low season hours change.
Silverton Brewery & Restaurant BREWERY
( 970-387-5033; www.silvertonbrewing.com; 1333Greene St; 11:30am-10pm) This hugely popular brewery consistently wins a thumbs-up for its brews, food and atmosphere. The food (mains $7 to $19) is a clever mix of comfort favorites. The beer bratwurst with homemade sauerkraut is a house specialty.
#### Information
Silverton Chamber of Commerce & Visitor Center ( 970-387-5654, toll-free 800-752-4494; www.silvertoncolorado.com; 414 Greene St; 9am-5pm; ) The Silverton Chamber of Commerce & Visitor Center provides information about the town and surrounds. It's staffed by friendly volunteers and you can buy tickets for the Durango & Silverton Narrow Gauge Railroad here.
#### Getting There & Away
Silverton is on Hwy 550 midway between Montrose, about 60 miles to the north, and Durango, some 48 miles to the south. Other than private car, the only way to get to and from Silverton is by using the Durango & Silverton Narrow Gauge Railroad or the private buses that run its return journeys.
### Black Canyon of the Gunnison National Park
The Colorado Rockies are most famous for their mountains, but the Black Canyon of the Gunnison National Park ( 970-249-1915, 800-873-0244; www.nps.gov/blca; 7-day admission per vehicle $15; 8am-6pm summer, 8:30am-4pm fall, winter & spring; ) is the inverse of this geographic feature – a massive yawning chasm etched out over millions of years by volcanic uplift and the flow of the Gunnison River.
A dark, narrow gash above the Gunnison River leads down a 2000ft chasm that's as eerie as it is spectacular. Sheer, deep and narrow, it earned its name because sunlight only touches the canyon floor when the sun is directly overhead. No other canyon in America combines the narrow openings, sheer walls and dizzying depths of the Black Canyon, and a peek over the edge evokes a sense of awe (and vertigo) for most.
Two miles past the park entrance on South Rim Drive, South Rim Visitor Center ( 970-249-1915, 800-873-0244; www.nps.gov/blca; 8:30am-4pm fall, winter & spring, 8am-6pm summer) is well stocked with books and maps, and enthusiastic National Parks Service staff offer a wealth of information on hiking, fishing and rock climbing.
The park spans 32,950 acres. Head to the 6 mile-long South Rim Rd, which takes you to 11 overlooks at the edge of the canyon, some reached via short trails up to 1.5 miles long (round-trip). At the narrowest part of Black Canyon, Chasm View is 1100ft across yet 1800ft deep. Rock climbers are frequently seen on the opposing North Wall. Colorado's highest cliff face is the 2300ft Painted Wall. To challenge your senses, cycle along the smooth pavement running parallel to the rim's 2000ft drop-off. You definitely get a better feel for the place than when trapped in a car.
In summer the East Portal Rd is open. This steep, winding hairpin route takes you into the canyon and down to the river level where there are picnic shelters and superb views up the gorge and the craggy cliff faces. This area is popular with fly-fishers.
For a surreal experience, visit Black Canyon's South Rim in winter. The stillness of the snow-drenched plateau is broken only by the icy roar of the river at the bottom of the canyon, far, far below.
The park has three campgrounds although only one is open all year round. Water is trucked into the park and only the East Portal Campground ( 970-249-1915; www.nps.gov/blca; sites $12; spring to fall) has river-water access. Firewood is not provided and may not be collected in the national park –campers must bring their own firewood into the campgrounds. Rangers at the visitor center can issue a backcountry permit, if you want to descend one of the South Rim's three unmarked routes to the infrequently visited riverside campsites.
The park is 12 miles east of the US Hwy 550 junction with US Hwy 50. Exit at Hwy 347 – well marked with a big brown sign for the national park – and head north for 7 miles.
### GREAT SAND DUNES NATIONAL PARK
A strange sight, the country's youngest national park features 55 miles of towering Sahara-like dunes tucked against the looming peaks of the Sangre de Cristo range. Sandboarding, or just running down them full speed, is heaps of fun. The visitor center ( 719-378-6399; www.nps.gov/grsa; 11999 Hwy 150; adult $3; 8:30am-6:30pm summer, 9am-4:30pm winter, to 5pm spring & fall) provides information. Camp in Pinyon Flats Campground (www.recreation.gov; Great Sand Dunes National Park; sites $14; year-round; ).
The park is 164 miles (approximately 3¼ hrs) from Crested Butte and 114 miles (2¼ hours) from Pagosa Springs, Colorado. From Crested Butte, take CO-135 to CO-114 south, then head east toward Mosca and follow the signs to the park. The visitors center is 3 miles north of the park entrance; access to the dunes is another mile along the road.
### Crested Butte
POP 1680 / ELEV 8885FT
Powder-bound Crested Butte has retained its rural character better than most Colorado ski resorts. Ringed by three wilderness areas, this remote former mining village is counted among Colorado's best ski resorts (some say _the_ best). The old town center features beautifully preserved Victorian-era buildings refitted with hip shops and businesses. Strolling two-wheel traffic matches the laid-back, happy attitude.
In winter, the scene centers around Mt Crested Butte, the conical ski mountain emerging from the valley floor. But come summer, these rolling hills become the state wildflower capital (according to the Colorado State Senate), and many mountain- bikers' fave for sweet alpine singletrack.
#### Sights & Activities
Crested Butte Mountain Heritage Museum MUSEUM
( 970-349-1880; www.crestedbuttemuseum.com; 331 Elk Ave; adult/child $3/free; 10am-8pm summer, noon-6pm winter; ) In one of the oldest buildings in Crested Butte, a worthwhile visit for the Mountain Bike Hall of Fame or to see a terrific model railway. Exhibits range from geology to mining and early home life.
Crested Butte Center for the Arts PERFORMANCE SPACE
( 970-349-7487; www.crestedbuttearts.org; 606 6th St; prices vary; 10am-6pm; ) With shifting exhibitions of local artists and a stellar schedule of live music and performance pieces, there's always something lively and interesting happening here.
Crested Butte Mountain Resort SKIING
( 970-349-2222; www.skicb.com; 12 Snowmass Rd; lift ticket adult/child $87/44; ) Catering mostly to intermediates and experts, Crested Butte Mountain Resort sits 2 miles north of the town at the base of the impressive mountain of the same name. Surrounded by forests, rugged mountain peaks, and the West Elk, Raggeds and Maroon Bells-Snowmass Wilderness Areas, the scenery is breathtaking. It's comprised of several hotels and apartment buildings, with variable accommodations rates.
Crested Butte Nordic Center CROSS-COUNTRY SKIING
( 970-349-1707; www.cbnordic.org; 620 2nd St; day passes adult/child $15/10; 8:30am-5pm; ) With 50km of groomed cross-country ski trails around Crested Butte, this center issues day and season passes, manages hut rental and organizes events and races. Ski rentals and lessons are available, in addition to ice-skating, snowshoeing and guided tours of the alpine region.
Adaptive Sports Center OUTDOOR ACTIVITIES
( 970-349-2296; www.adaptivesports.org; 10 Crested Butte Way; ) This nonprofit group helps people with disabilities participate in outdoors activities and adventure sports.
Fantasy Ranch HORSEBACK RIDING
( 970-349-5425, toll-free 888-688-3488; www.fantasyranchoutfitters.com; 935 Gothic Rd; 1½hr/3hr/day rides $55/85/120; ) Offers short trail rides (guests over seven years and under 240lbs), wilderness day rides and multiday pack trips. One highlight is a stunning ride from Crested Butte to Aspen round-trip.
### MOVING ON?
For tips, recommendations and reviews, head to shop.lonelyplanet.com to purchase a downloadable PDF of the Rocky Mountains chapter from Lonely Planet's _USA_ guide.
Alpineer MOUNTAIN BIKING
( 970-349-5210; www.alpineer.com; 419 6th St; bike rental per day $20-50; ) Serves the mountain-biking mecca with maps, information and rentals. It also rents out skis and hiking and camping equipment.
Crested Butte Guides OUTDOOR ACTIVITIES
( 970-349-5430; www.crestedbutteguides.com; off Elk Ave) Guide service for hardcore backcountry skiing, ice climbing or mountaineering. With over a decade of experience, these guys can get you into (and out of) some seriously remote wilderness. They can also provide equipment.
Black Tie Ski Rentals SNOW SPORTS
( 970-349-0722, toll-free 888-349-0722; www.blacktieskis.com; Unit A/719 4th St; 7:30am-10pm winter; ) Black Tie rents skis, skiing equipment and snowboards.
#### Sleeping
Visitors to Crested Butte can stay either in the main town, better for restaurants and nightlife, or in one of the many options at the mountain resort. Some of the Crested Butte Mountain Resort hotels and apartment buildings close over the shoulder seasons in spring and fall, but others offer great discounts and longer-stay incentives – check websites, compare prices and bargain. If you've come for the hiking, mountain biking or to enjoy the wildflowers, you can do very well at these times.
Ruby of Crested Butte B&B $$$
( 800-390-1338; www.therubyofcrestedbutte.com;624 Gothic Ave; d $129-249, suite $199-349; ) Thoughtfully outfitted, down to the bowls of jellybeans and nuts in the stylish communal lounge. Rooms are brilliant, with heated floors, high-definition flat-screen TVs with DVD players (and a library), iPod docks and deluxe linens. There's also a Jacuzzi, library, ski-gear drying room, free wi-fi and use of retro townie bikes. Hosts help with dinner reservations and other services. Pets get a first-class treatment that includes their own bed, bowls and treats.
Crested Butte International Hostel HOSTEL $
( 970-349-0588, toll-free 888-389-0588; www.crestedbuttehostel.com; 615 Teocalli Ave; dm $25-31,r $65-110; ) For the privacy of a hotel with the lively ambience of a hostel, grab a room here. One of Colorado's nicest hostels, the best private rooms have their own baths. Dorm bunks come with reading lamps and lockable drawers, and the communal area has a stone fireplace and comfortable couches. Rates vary with the season, with winter being high season. Extended stays attract discounts.
Inn at Crested Butte BOUTIQUE HOTEL $$
( 970-349-2111, toll-free 877-343-211; www.innatcrestedbutte.net; 510 Whiterock Ave; d $130-200; ) This recently refurbished hoteloffers smart, modern rooms. Some have balcony views over Mt Crested Butte, and all feature antiques, flat-screen TVs, coffeemakers and minibars. Especially if you get a king-sized bed, space can seem cramped.
Elevation Hotel & Spa HOTEL $$$
( 970-349-2222; www.skicb.com; 500 Gothic Rd; r from $200; ) At the base of Crested Butte Mountain Resort and just steps from a major chairlift, this swank address offers oversized luxury rooms ready for first call on powder days. Check online for specials, particularly at the start or end of the season.
The Atmosphere Restaurant is a trendy place for dining, while the hotel's slope-side deck is the spot for a beer by the fire pit while you watch snowboarders whizz by.
Crested Butte Mountain Resort Properties RENTAL AGENCY
(CBMR Properties; 888-223-2631; www.skicb.com) This property-management group, part of the Crested Butte Mountain Resort, handles reservations for dozens of the lodges, hotels and apartment buildings at the resort.
#### Eating & Drinking
Secret Stash PIZZA $$
( 970-349-6245; www.thesecretstash.com; 21 Elk Ave; mains $8-20; 5-10pm; ) A locals go-to place, this pizza and calzone joint has phenomenal food and a hip interior where you can sit on the floor upstairs or park yourself in a velvety chair on the lower level and catch up on the gossip. The Notorious Fig pizza (with Asiago, fresh figs, prosciutto and truffle oil) won a pizza world championship. We think you'd like it too. Exotic cocktails are also a house specialty.
Soupçon FRENCH $$$
( 970-349-5448; www.soupconcrestedbutte.com;127 Elk Ave; mains $17-32; 6-10:30pm; ) Specializing in seduction, this petite French bistro occupies an ambient old mining cabin with just a few tables. Chef Jason has worked with big New York City names and keeps it fresh with local meat and organic produce. Reserve ahead.
Avalanche Bar & Grill PUB $$
(www.avalanchebarandgrill.com; off Gothic Rd; mains $7-19; 7:30am-9pm winter, from 11:30am summer; ) One of the favorite _après ski_ venues, Avalanche is right on the slopes. Test your hunger against their encyclopedic menu of American comfort foods (tuna melts, burgers, club sandwiches, pizzas) as well as an impressive lineup of desserts and beverages. There's a kids menu too.
Camp 4 Coffee COFFEE SHOP $
(www.camp4coffee.com; 402 1/2 Elk Ave) Grab your caffeine fix at this serious local roaster,the cutest cabin in town, shingled with licenseplates (just as local miners once did when they couldn't afford to patch their roofs).
Princess Wine Bar WINE BAR
( 970-349-0210; 218 Elk St; 8am-midnight; ) Intimate and perfect for conversation over some sampling of the select regional wine list. There's regular live acoustic music featuring local singer-songwriters. A popular _après ski_ spot.
#### Entertainment
On CB's lively music scene, most bands play Eldo Brewery ( 970-349-6125; www.eldoBrewery.com; 215 Elk Ave; cover charge varies; 3pm-late, music from 10:30pm; ), a popular microbrewery. Nightclub/sushi-bar Lobar ( 970-349-0480; www.thelobar.com; 303 Elk Ave; occasional cover charge) goes disco late-night, complete with mirror balls DJs and sometimes live music.
The best community theatre is Crested Butte Mountain Theatre ( 970-349-0366; www.cbmountaintheatre.org; 403 2nd St; prices vary; vary; ), for bargains check out a dress rehearsal show.
#### Information
Crested Butte Visitor Center ( 970-349-6438; www.cbchamber.com; 601 Elk Ave; 9am-3pm) Crested Butte's visitor center is packed with information and staffed by helpful people.
Post office ( 970-349-5568; www.usps.com; 217 Elk Ave; 7:30am-4:30pm Mon-Fri, 10am-1pm Sat)
#### Getting There & Away
Crested Butte is a 30-minute drive from Gunnison. The trip from Ouray to Crested Butte takes a little less than three hours.
Top of section
# Utah
**Includes »**
Moab & Southeastern Utah
Monument Valley
Canyonlands National Park
Arches National Park
Capitol Reef National Park
Bryce Canyon National Park & Around
Zion National Park
Salt Lake City
Wasatch Mountains
Park City
### Why Go?
Though not everyone knows it, Utah is one of nature's most perfect playgrounds. The state's rocky terrain comes ready-made for hiking, biking, rafting, rappelling, rock climbing, skiing, snowmobile riding, horseback pack-tripping, four-wheel driving... Need we go on? More than 65% of the lands are public, including 12 national parks and monuments.
Southern Utah is defined by red-rock cliffs, sorbet-colored spindles and seemingly endless sandstone desert. The forest- and snow-covered peaks of the Wasatch Mountains dominate northern Utah. Interspersed you'll find old pioneer buildings, ancient rock art and ruins, and traces of dinosaurs.
Mormon-influenced rural towns can be quiet and conservative, but the rugged beauty has attracted outdoorsy progressives as well. Salt Lake City (SLC) and Park City especially, have vibrant nightlife and foodie scenes. So pull on your boots or rent a jeep: Utah's wild and scenic hinterlands await. We'll meet you later at the nearest boho coffeehouse.
### When to Go
May The mild weather makes this an excellent time to hike, especially in southern Utah.
Oct Colorful autumn leaves come out, but a welcome touch of warmth lingers.
Jan–Mar Powder hounds gear up for the skiing at SLC and Park City mountain resorts.
### Best Places to Stay
»Sundance Resort (Click here)
»Torrey Schoolhouse B&B (Click here)
»Quail Park Lodge (Click here)
»Under the Eaves Inn (Click here)
»Sorrel River Ranch (Click here)
### Best Places to Eat
»Café Diablo (Click here)
»Hell's Backbone Grill (Click here)
»Parallel 88 (Click here)
»Love Muffin (Click here)
»Talisker (Click here)
### Utah Planning
Utah is not a large state, but it is largely rural. That means unless you are staying in Salt Lake City or Park City, you'll need a car. If you're headed to the parks in southern Utah, your cheapest bet may be to fly into Las Vegas and rent a ride there.
### DON'T MISS
Sure, some of Utah's rugged beauty can be seen roadside. But one of the great things about the state is how much of it is set aside for public use. You'll gain a whole new perspective – and appreciation – of the terrain if you delve deeper. Not-to-be-missed outdoor adventures are available for all skill levels, and outfitters are there to help. Challenge yourself by rappelling into the narrow canyons around Zion National Park or mountain biking on the steep and sinister Slick Rock Trail in Moab. Or take it easy on your body (though not your vehicle) by going off-pavement along one of the state's many 4WD roads. Whether you're rafting on the Colorado River or skiing fresh powder in the Wasatch Mountains, you'll see the state in a whole new way.
### Fast Facts
»Population: 2.9 million
»Area: 84,900 sq miles
»Time Zone: Mountain Standard Time
»Sales Tax: 4.7%
»SLC to Moab: 235 miles, 4 hours
»St George to SLC: 304 miles, 4¼ hours
»Zion to Moab: 359 miles, 5½ hours
### TIME ZONE
Utah is on Mountain Standard Time (generally seven hours behind GMT), but does follow daylight saving time from mid-March to early November. Note that if you're traveling into Arizona, there's an hour's difference spring to fall.
### Liquor Laws
Although a few unusual liquor laws remain, regulations have relaxed recently. For more information, see Click here.
### Resources
»Utah Office of Tourism ( 800-200-1160; www.utah.com) Free Utah Travel Guide; website in six languages.
»Utah State Parks & Recreation Department ( 877-887-2757; www.stateparks.utah.gov) Info about the 40-plus state parks.
### Tips for Drivers
»Driving between major cities can be quite a speedy affair. The three interstate freeways have a 75mph limit.
»Cruising in from Denver on I-70? Make sure you get gas in Green River (345 miles, 5¼ hours). The 104 miles between there and Salina is the largest stretch of US interstate without services.
»When traveling between Las Vegas and SLC, consider a scenic detour east on Hwy 9 at St George to Hwy 89 north. It's longer (365 miles, seven hours, St George to SLC; compared with 303 miles and 4¼ hours on the I-15), but you'll pass through some stunning red-rock country.
»In general, plan to take your time on smaller roads and byways. The state has some daunting geographic features. Switchbacks, steep inclines, reduced speed limits – and stunning views – are all part of the experience.
### Utah Highlights
Hiking to the heights of Angels Landing or Observation Point at Zion National Park (Click here)
Stopping at every amphitheater overlook in colorful Bryce Canyon National Park (Click here)
Using tiny rustic towns like Bluff (Click here), Boulder (Click here) and Torrey (Click here) as basecamps for adventure
Cruising the state's incredibly scenic byways, especially Hwy 12 (Click here)
Dining in style after a day slopeside in Park City (Click here)
Hiring an outfitter in Moab (Click here) to guide you into the backcountry by bike or 4WD
Searching out ancient rock art and ruin sites such as Newspaper Rock (Click here)
###### History
Traces of the Ancestral Puebloan and Fremont people can today be seen in the rock art and ruins they left behind. But it was the modern Ute, Paiute and Navajo tribes who were living here when European explorers first trickled in. Larger numbers of settlers didn't arrive until after second Mormon church president Brigham Young declared 'This is the place!' upon seeing Salt Lake Valley in 1847. The faithful pioneers fled to this territory, then part of Mexico, to escape religious persecution in the east. They then set about attempting to settle every inch of land, no matter how inhospitable, which resulted in skirmishes with Native Americans – and more than one abandoned ghost town. (One group was so determined that it lowered its wagons by rope through a hole in the rock to continue on an impassible mountain trail; see Click here.)
For nearly 50 years after the United States acquired the land, the Utah Territory's petitions for statehood were rejected due to the Mormon practice of polygamy, or the takingof multiple wives. Tensions and prosecutions mounted until 1890 when Mormon leader Wilford Woodruff officially discontinued the practice. (For more, see Click here.) In 1896 Utah became the 45th state. About the same time, Utah's remote backcountry served as the perfect hideout for notorious Old West 'bad men', such as native son Butch Cassidy, and the last spike of the first intercontinental railroad was driven here.
Throughout the 20th century the influence of the modern Mormon church, now called the Church of Jesus Christ of Latter-Day Saints (LDS), was pervasive in state government. Though it's still a conservative state, LDS supremacy may be waning –less than 60% of today's population claims church membership (the lowest percentage to date). The urban/rural split may be more telling for future politics: roughly 75% of state residents now live along the urbanized Wasatch Front surrounding Salt Lake City.
###### Scenic Drives
Roads in Utah are often attractions in and of themselves. State-designated Scenic Byways (www.byways.org) twist and turn through the landscape past stunning views. It goes without saying that every main drive in a national park is a knock-out.
### NO SMOKING ALLOWED
Utah is pretty much a smoke-free state. All lodgings are required to have nonsmoking rooms, but most have nothing else (exceptions are noted in the text). Restaurants, and even some bars, also prohibit lighting up.
Scenic Byway 12 (Hwy 12) The best overall drive in the state for sheer variety: from sculpted slickrock to vivid red canyons and forested mountain tops (Click here).
Zion Park Scenic Byway (Hwy 9) Runs through red-rock country, and Zion National Park, between I-15 and Hwy 89 (Click here).
Markagaunt High Plateau Scenic Byway (Hwy 14) High elevation vistas, pine forests and Cedar Breaks National Monument are en route (Click here).
Nine Mile Canyon Rd A rough and rugged back road leads to a virtual gallery of ancient rock art and ruins (Click here).
Flaming Gorge-Uintas Scenic Byway (Hwy 191) Travel through geologic time on this road; as you head north, the roadside rocks get older (Click here).
Burr Trail Rd Dramatic paved backcountry road that skirts cliffs, canyons, buttes, mesas and monoliths on its way to the Waterpocket Fold (Click here).
Cottonwood Canyon Rd A 4WD trek through the heart of Grand Staircase-Escalante National Monument (Click here).
Mirror Lake Hwy (Rte 150) This high-alpine road cruises beneath 12,000ft peaks before dropping into Wyoming (Click here).
###### Utah Street Layout
Most towns in Utah follow a street grid system, in which numbered streets radiate from a central hub (or zero point), usually the intersection of Main and Center Sts. Addresses indicate where you are in relation to that hub.
## MOAB & SOUTHEASTERN UTAH
Experience the earth's beauty at its most elemental in this rocky-and-rugged desert corner of the Colorado Plateau. Beyond the few pine-clad mountains, there's little vegetation to hide the impressive handi work of time, water and wind: the thousands of red-rock spans in Arches NationalPark, the sheer-walled river gorges from Canyonlands to Lake Powell, and the stunning buttes and mesas of Monument Valley. The town of Moab is the best base for adventure, with as much four-wheeling, white-knuckle rafting, outfitter-guided fun as you can handle. Or you can lose the crowd while looking for Ancestral Puebloan rock art and dwellings in miles of isolated and undeveloped lands.
Note that many regional restaurants and shops – some motels even – close or have variable hours after the May to late October high season.
### Bluff
Tiny tot Bluff isn't much more than a spot in the road. But a few great motels and a handful of restaurants, surrounded by stunning red rock, make it a cool little base for exploring the far southwestern corner of the state. From here you can easily reach Moki Dugway (30 miles), Hovenweep National Monument (40 miles), Monument Valley (47 miles) and Natural Bridges National Monument (61 miles), just to mention a few area sights, as well as explore the surrounding Bureau of Land Management (BLM) wilderness.
There's no visitor center here at the crossroads of Hwys 191 N and 163. You can log onto www.bluff-utah.org, but local business owners and staff are your best resource (they know the hikes betterthan an office worker could, anyway). To preserve the night sky, Bluff has no streetlights.
#### Sights & Activities
The BLM field office in Monticello has information about the public lands surrounding Bluff. Local motel Recapture Lodge also sells topographic maps for hiking; a public trail leads down from the lodging to the San Juan River.
Bluff Fort HISTORIC SITE
(www.hirf.org/bluff.asp; 5 E Hwy 191; admission by donation; 9am-6pm Mon-Sat) Descendants of the original pioneers have re-created the original log cabin settlement near the few remaining historic buildings in Bluff.
Sand Island Petroglyphs ARCHAEOLOGICAL SITE
(www.blm.gov; Sand Island Rd, off Hwy 163) On BLM land 3 miles west of Bluff, these freely accessible petroglyphs were created between 800 and 2500 years ago. The nearby campground boat launch is the starting point for San Juan River adventures.
Far Out Expeditions ADVENTURE TOUR
( 435-672-2294; www.faroutexpeditions.com; full-day from $165) Interested in remote ruins and rock art? Vaughn Hadenfeldt leads much sought after single- and multiday hikes into the desert surrounds.
Wild Rivers Expeditions RAFTING
( 800-422-7654; www.riversandruins.com; day tripadult/child $165/120) Float through the San Juan River canyons with this history- and geology-minded outfitter; you'll also get to stop and see petroglyphs.
Buckhorn Llama ADVENTURE TOUR
( 435-672-2466; www.llamapack.com; per day from $300) Llama-supported multiday pack trips into hard-to-reach wilderness.
#### Sleeping
Recapture Lodge MOTEL $
( 435-672-2281; www.recapturelodge.com; Hwy 191; r incl breakfast $70; ) This locally owned, rustic motel makes the best base for area adventures. Super-knowledgeable staff help out with trip planning and present educational slide shows in season. Thankfully there's plenty of shade around the pool and on the property's 3½ miles of walking trails.
### PUBLIC LANDS
Public lands – national and state parks and monuments, national forests and Bureau of Land Management (BLM) lands – are Utah's most precious natural resource for visitors. Check out www.publiclands.org.
Desert Rose Inn MOTEL $$
( 435-672-2303, 888-475-7673; www.desertroseinn.com; Hwy 191; r $99-119, cabins $129-159; ) Wood porches wrap completely around a dramatic, two-story log building at the edge of town. Quilts on pine beds add to the comfort of extra large rooms and cabins.
Sand Island Campground CAMPGROUND $
( 435-587-1500; www.blm.gov; Sand Island Rd; tent & RV sites $10; May-Oct) The San Juan River location helps cool things off at these 27 first-come, first-served sites. Pit toilets and drinking water only; no hookups, no showers.
Far Out Bunkhouse GUESTHOUSE $
( 435-672-2294; www.faroutexpeditions.com; cnr7th East & Mulberry Sts; 1 or 2 in room $90) Two private six-bunk rooms available in a guesthouse run by the eponymous hiking outfitter.
Kokopelli Inn MOTEL $
( 435-672-2322, 877-342-6099; www.kokoinn.com; Hwy 191; r $62-72; ) Basic, 26-room motel.
### CAN I GET A DRINK IN UTAH?
Absolutely. You always could, it's just gotten easier in recent years. Private club memberships are no more: a bar is now a bar (no minors allowed), and you don't have to order food to consume alcohol in one of them. As far as restaurants go, few have full liquor licenses, and most places that serve dinner also have beer and wine only. Either way, if you're in a restaurant, you have to order food to drink there. Some rules to remember:
»Mixed drinks and wine are available only after midday; 3.2% alcohol beer can be served starting at 10am.
»Mixed drinks cannot contain more than 1.5 ounces of a primary liquor, or 2.5 ounces total including secondary alcohol. Sorry, no Long Island Iced Teas or double shots.
»Packaged liquor can only be sold at state-run liquor stores; grocery and convenience stores can sell 3.2% alcohol beer and malt beverages. Both are open Monday through Saturday only.
#### Eating
San Juan River Kitchen NEW MEXICAN $$
(75 E Main St; lunch $8-13, dinner $9-20; 11am-9pm Tue-Sun) The inventive, regionally-sourced Mexican-American dishes here use organic ingredients whenever possible. Don't skip the homemade chipotle chocolate ice cream for desert.
Comb Ridge Coffee CAFE $
(Hwy 191; baked goods $2-6; 7am-3pm Wed-Sun, varies Nov-Feb; ) Grab an espresso, muffin or stack of blue-corn pancakes inside this arty, adobe cafe-gallery.
Twin Rocks Cafe NATIVE AMERICAN $-$$
(913 E Navajo Twins Dr; mains $6-14; 7am-9pm) At Twin Rocks you can try fry bread (deep-fried dough) with any of your three daily meals: as part of a breakfast sandwich, wrapped up as a Navajo taco at lunch or accompanying stew with dinner.
Cottonwood Steakhouse STEAKHOUSE $$-$$$
(cnr Main & 4th West Sts; mains $18-25; 5-10pm Mar-Nov) Yee-haw! Sure it's pricey, but you're paying for Wild West-style fun to go with your outdoor-grilled rib-eye steak, pardner.
### Hovenweep National Monument
This area straddling the Utah-Colorado state line was home to a sizeable Ancestral Puebloan population before abandonment in the late 1200s (perhaps because of drought and deforestation). Since 1923, six sets of sites have been protected as a national monument (www.nps.gov/hove; 7-day per vehicle $6; trails sunrise-sunset, visitor center 8am-5pm).
The Square Tower Group near the visitor center is what people are generally referring to when speaking of Hovenweep. Pick up the interpretive guide ($1), essential for understanding the unexcavated ruins. Stronghold House is reachable from a paved, wheelchair-accessible path and from there you overlook the rest of the ruins. To get a closer look, you'll have to hike down into the canyon (and back up); follow the trail clockwise to best see the ruins unfold around every corner. Most of the eight brick towers and unit houses were constructed between 1230 and 1275. The masonry skills it took to piece together such tall structures on such little ledges definitely inspires admiration.
The other sections of the park require 4WD and/or lengthy hikes. Ask for a map at the visitor center, where there's also a nice 30-site campground (tent & RV sites $10) with water and toilets; no hookups. Otherwise, there's a whole lotta nothin' else out here. The closest store is the Hatch Trading Post (County Rd 414), an atmospheric white-brick building that sells a few sundries and some Native American crafts. Other than that, supplies are in Blanding (45 miles), Bluff (40 miles) and Cortez, Colorado (43 miles).
The best route to the park is paved Hwy 262. From the turnoff east at Hwy 191 follow the signs; it's a 28-mile drive to the main entrance (past Hatch Trading Post). Use caution traveling on any unpaved roads here: all become treacherous in wet weather. From Hovenweep, Mesa Verde National Park (Click here) is 75 miles east in Colorado.
### Valley of the Gods
Up and over, through and around: the 17-mile unpaved road that leads through Valley of the Gods is like a do-it-yourself roller coaster – amid some mind-blowing scenery. In other states, this incredible butte-filled valley would be a national park, but such are the riches of Utah that here it is merely a BLM-administered area (www.blm.gov). Locals call it 'mini-Monument Valley'. The field office in Monticello puts out a BLM pamphlet, available online, identifying a few of the sandstone monoliths and pinnacles that have been named over the years, including Seven Sailors, Lady on a Tub and Rooster Butte.
Free, dispersed camping among the rock giants is a dramatic – if shade-free – prospect. In such an isolated, uninhabited place, the night sky is incredible. Or you could spend a secluded night at one of the very few pioneer ranches in the area, now the Valley of the Gods B&B ( 970-749-1164; www.valleyofthegods.cjb.net; off Hwy 261; r incl breakfast $85-115), 6.5 miles north of Hwy 163. Simple, rustic beds feel right at home in exposed wood-and-stone rooms. Water is trucked in and solar power is harnessed out of necessity (leave your hair dryer at home).
A high-clearance vehicle is advised for driving the Valley of the Gods (County Rd 242). This author's little Volkswagen GTI made it on a very dry day, but don't try it without a 4WD if it has rained recently. Allow an hour for the 17-mile loop connecting Hwys 261 and 163. The nearest services are in Mexican Hat, 7 miles southwest of the Hwy 163 turnoff.
### IN SEARCH OF ANCIENT AMERICA
Cliff dwellings, centuries-old rock art and artifacts – the southern part of the state is a great place to explore the ancient, Ancestral Puebloan cultures. Top sites include:
»Hovenweep National Monument (Click here)
»Anasazi State Park Museum (Click here)
»Edge of the Cedars State Park (Click here)
»Great Gallery, Canyonlands – Horseshoe Canyon (Click here)
»Newspaper Rock (Click here)
»Grand Gulch Primitive Area (Click here)
But there's far more than that to explore: small ruins and petroglyphs are to be found all across BLM lands. We recommend you hire an outfitter in Bluff, Moab, Torrey, Boulder or Escalante – especially if you're an inexperienced backcountry hiker or don't have a 4WD. Their experience and knowledge will take you far.
If you're well aware that you need at least a gallon of water per person per day, know how to negotiate rock and sand in your high-clearance SUV and can read a topographic map, you may want to explore on your own. Ask locals for tips (hint: you can also suss out the ruin symbols on the _Delorme Utah Atlas & Gazetteer_). In the far southeast, a good place to start is off Comb Wash Rd (linking Hwys 95 and 163) near Bluff, as is Montezuma Canyon Rd, north of Hovenweep.
A few things to keep in mind:
»Take only pictures – do not remove any artifacts you find, it's against the law. Not only will touching or moving items contaminate future study, you'll ruin the amazing experience for the next visitor.
»Tread lightly – though sandstone structures seem sturdy, climbing on building walls causes irreparable damage. Don't do it.
»Respect the spiritual and historical value of these places – they are sacred to many Native Americans.
»Leave no trace – pack out anything you pack in. You leave the least effect on the area's ecology if you walk on slickrock or in dry washes.
### Mexican Hat
The settlement of Mexican Hat is named after a sombrero-shaped rock off Hwy 163. The town is little more than a handful of simple lodgings, a couple of places to eat and a store or two on the north bank of the San Juan River. The south bank marks the edge of the Navajo Reservation. Monument Valley is 20 miles to the south; Bluff 27 miles to the east. The cliffside San Juan Inn ( 435-683-2220, 800-447-2022; www.sanjuaninn.net; Hwy 163; r $85; ) perches high above the river. The motel rooms are pretty basic, but they're the nicest in town. You can buy Navajo crafts, books and beer on site at the trading post ( 7am-9pm). The year-round Old River Grille (mains $7-15; 7am-8pm) has southwestern home-cooking and the only full liquor license for at least 50 miles.
### Monument Valley
From Mexican Hat, Hwy 163 winds southwest and enters the Navajo Reservation and (after 22 miles) Monument Valley, on the Arizona state line. Though you'll recognize it instantly from TV commercials and Hollywood movies (remember where Forrest Gump stopped his cross-country run?), nothing compares with seeing the sheer chocolate-red buttes and colossal mesas for real. To get close, you must visit the Monument Valley Navajo Tribal Park. For details about the park and places to stay, such as Goulding's Lodge (a motel-lodge restaurant-grocery trading-post museum-tour operator), see Click here.
### Goosenecks State Park
If instead of heading south to Medicine Hat you turn north on Hwy 261, you'll come to a 4-mile paved road that turns west to Goosenecks State Park. The attraction here is the mesmerizing view of the San Juan River. From above, the serpentine path carved by years of running water is dramatically evident. You can see how the river snaked back on its course, leaving gooseneck-shaped spits of land untouched. The park itself doesn't have much to speak of: there are pit toilets, picnic tables and free campsites, but frequent high winds discourage staying long.
### Moki Dugway & Around
Ready for a ride? Eleven miles north of Goosenecks, Moki Dugway is a roughly paved, hairpin-turn-filled section of Hwy 261 that ascends 1100ft in just 3 miles (you descend traveling south). Miners dug out the extreme switchbacks in the 1950s to transport uranium ore. Today it's a way to Lake Powell, and to some hair-raising fun. Wide pullouts allow a few overviews, but for most of the time you cannot see what's around the sharp corners. The dugway is not for anyone who's height sensitive (or for those in a vehicle more than 28ft long).
### LOCAL PASSPORTS
Southeastern Utah national parks sell a local passport (per vehicle $25) that's good for a year's entry to Arches and Canyonlands National Parks, plus Hovenweep and Natural Bridges National Monuments. Federal park passes (www.nps.gov/findapark/passes.htm; per vehicle adult/senior $80/10), available online and at parks, allow year-long access to all federal recreation lands in Utah and beyond – and are a great way to support the Southwest's amazing parks.
Past the northern end of the dugway, take the first western-traveling road to Muley Point Overlook. This sweeping cliff-edge viewpoint looks south to Monument Valley and other stunning landmarks in Arizona. Payattention, the unsigned turnoff is easy to miss.
Follow Hwy 261 further north to the wild and twisting canyons of Cedar Mesa and Grand Gulch Primitive Area (www.blm.gov), both hugely popular with backcountry hikers. The BLM-administered area also contains hundreds of Ancestral Puebloan sites, many of which have been vandalized by pot hunters. (It bears repeating that all prehistoric sites are protected by law, and authorities are cracking down on offenders.) The 4-mile one-way Kane Gulch (600ft elevation change) leads to a great view of the Junction Ruin cliff dwelling. To hike in most canyons you need a $2 day-use permit ($8 overnight). In season (March to June 15, September and October) some walk-in permits are available at the Kane Gulch Ranger Station (Hwy 261, 4 miles south of Hwy 95; 8am-noon Mar–mid-Nov), but the number is strictly limited so make advance reservations by calling the Monticello Field Office ( 435-587-1510). Off season, self-serve permits are available at trailheads. Know that this is difficult country with primitive trails; the nearest water is 10 miles away at Natural Bridges National Monument.
### BUTLER WASH & MULE CANYON RUINS
The drive along Hwy 95 between Blanding and Natural Bridges provides an excellent opportunity to see isolated Ancestral Puebloan ruins. No need to be a backcountry trekker here: it's only a half-mile hike to Butler Wash Ruins (14 miles west of Blanding), a 20-room cliff dwelling. Scramble over the slickrock boulders (follow the cairns) and you're rewarded with an overlook of the sacred kivas, habitation and storage rooms that were used c 1300.
Though not as well preserved, the base of the tower, kiva and 12-room Mule Canyon Ruins (20 miles west of Blanding) are more easily accessed. Follow the signs to the parking lot just steps from the masonry remains. The pottery found here links the population (c 1000 to 1150) to the Mesa Verde group in southern Colorado; Butler Wash relates to the Kayenta group of northern Arizona. Both are on freely accessible BLM-administered land.
### Natural Bridges National Monument
In 1908 Natural Bridges National Monument (www.nps.gov/nabr; Hwy 275; 7-day per vehicle $6; 24hr, visitor center 8am-6pm Apr-Sep, 8am-5pm Oct-Mar) became Utah's first National Park Service (NPS) land. The highlight is a dark-stained, white sandstone canyon with three giant natural bridges.
The oldest – beautifully delicate Owachomo Bridge – spans 180ft and rises over 100ft above ground, but is only 9ft thick. Kachina Bridge is the youngest and spans 204ft. The 268ft span of Sipapu Bridge makes the top five of any 'largest in the US' list (the other four are in Utah, too). All three bridges are visible from a 9-mile winding loop road with easy-access overlooks. Most visitors never venture below the canyon rim, but they should. Descents may be a little steep, but distances are short; the longest is just over half a mile one-way. Enthusiastic hikers can take a longer trail that joins all three bridges (8 miles). Don't skip the 0.3-mile trail to the Horsecollar Ruin cliff dwelling overlook. The elevation here is 6500ft; trails are open all year, but steeper sections may be closed after heavy rains or snow.
The 12 first-come, first-served sites at the campground (tent & RV sites $10), almost half a mile past the visitor center, are fairly sheltered among scraggly trees and red sand. The stars are a real attraction here – this has been designated an International Dark Sky Park and is one of the darkest in the country. There are pit toilets and grills, but wateris available only at the visitor center; no hookups. The campground fills on summer afternoons, after which you are directed to camp in a designated area along Hwy 275. No backcountry camping is allowed. Towed trailers are not suitable for the loop drive.
The nearest services are in Blanding, 47 miles to the east. If you continue west onHwy 95 from Natural Bridges, and followHwy 276, the services of Lake Powell's Bullfrog Marina are 140 miles away.
### Blanding
Two specialized museums elevate small, agriculturally-oriented Blanding a little above its totally dull name. Still, it's best to visit as a day trip, or en route between Bluff (22 miles) and Moab (75 miles). Both the motels and the (alcohol-free) restaurants are, well...bland.
Blanding Visitor Center ( 435-678-3662; www.blandingutah.org; cnr Hwy 191 N & 200 East; 8am-7pm Mon-Sat) has some areawide information. If you're here, the small pioneer artifact collection is worth a look.
Edge of the Cedars State Park Museum (www.stateparks.utah.gov; 660 W 400 N; admission $5; 9am-5pm Mon-Sat) houses a treasure trove of ancient Native American artifacts and pottery gathered from across southeastern Utah. Informative displays provide a good overview of area cultures. Outside, you can climb down into a preserved ceremonial kiva built by the Ancestral Puebloans c 1100. The encroaching subdivision makes you wonder what other sites remain hidden under neighborhood houses.
Born of a private owner's personal collection, the Dinosaur Museum (www.dinosaur-museum.org; 754 S 200 West; adult/child $3/1.50; 9am-5pm Mon-Sat mid-Apr–mid-Oct) is actually quite large. Mummified remains and fossils come from around the world, but most interesting is the collection of old dinosaur-movie-related exhibits.
Fatboyz Grillin (164 N Hwy 191; mains $10-16; 11am-9pm Mon-Sat, noon-9pm Sun) has blue-plate specials, like lasagna and pot roast, in addition to good barbecue. For a sweet treat with a side of novelty, head to Old Bank Creamery (30 W 100 S; 11-7pm Jun-Aug) in a tiny 100-year-old stone bank. Innovative flavors include cotton candy and peanut-butter cup.
### Monticello
Monticello (mon-ti- _sell_ -o) sits up in the foothills of the Abajo (or Blue) Mountains, and is a bit cooler than other towns in the region. As the seat of San Juan County, it is the place to get information about the far southeast corner of Utah. Here you're midway between Moab (54 miles) and Bluff (47 miles); both have better places to stay but this is the closesttown to the Canyonlands' Needles District.
Just west of town, Manti–La Sal NationalForest (www.fs.fed.us/r4/mantilasal) rises to 11,360ft at Abajo Peak. Hundreds of trail miles crisscross the 1.4-million-acre park. Here, spruce- and fir-covered slopes offer respite from the heat (expect about a 10°F, or 6°C, drop in temperature for every 1000ft you ascend), and spring wildflowers and fall color are a novelty in the arid canyonlands.
Talking Stones ( 435-587-2881; www.talkingstonestours.com; full-day from $150) leads rock-art tours and excursions into the Abajo Mountains. Abajo Haven Guest Ranch ( 435-979-3126; www.abajohaven.com; 5440 N Cedar Edge Ln; cabins $70) is already up in the mountains; guest cabin rental includes a free tour to private Native American sites.
Other places to stay include Canyonlands Lodge at Blue Mountain ( 435-220-1050; www.canyonlandslodge.com; Hwy 191; r $89-119, cabins $119-179; ), a giant log lodge adjacent to the national forest 10 miles south of town, and Inn at the Canyons ( 435-587-2458; www.monticellocanyonlandsinn.com; 533 N Main St; r $75-85; ), with modernized motel rooms on the main drag.
Peace Tree Juice Café (516 N Main St; mains $5-14; 7:30am-4pm daily, plus 5-9pm May-Sep) is a great place for full breakfasts, organic espresso, smoothies, lunch wraps or healthy, flavorful dinners (in season). Slow service hasn't stopped Lamplight Restaurant (655 E Central St; mains $7-18; 5-10pm Mon-Sat) from being the local choice for pasta, steaks and seafood for eons.
San Juan Visitor Center ( 435-587-3235, 800-574-4386; www.southeastutah.com; 117 S Main St; 10am-4pm Mon-Fri Nov–mid-Mar, 8am-5pm daily mid-Mar–Oct) has general information on attractions, forest service and other public lands in the region. (Many of its brochures are available online, too.) The BLM Monticello Field Office ( 435-587-1510; 435 N Main St; 7:45am-noon & 1-4:30pm Mon-Fri) is the place to inquire about area backcountry BLM hiking, driving, camping and permits. Buy topographic maps here. And if you like to get way, way off the beaten path on multiday hikes, ask about the brilliantly empty Dark Canyon Primitive Area.
From Monticello there's a shortcut to Canyonlands National Park – Needles District (22 miles instead of the main route's 34 miles). Take County Rd 101 (Abajo Dr) west to Harts Draw Rd (closed in winter); after 17 scenic miles you join Hwy 211 near Newspaper Rock Recreation Area. Befitting the region's religiousness, Hwy 666, which goes to Colorado, was officially renamed Hwy 491 in 2003.
### NEWSPAPER ROCK RECREATION AREA
This small, free recreation area showcases a single large sandstone rock panel packed with more than 300 petroglyphs attributed to Ute and Ancestral Puebloan groups during a 2000-year period. The many red-rock figures etched out of a black 'desert varnish' surface make for great photos (evening sidelight is best). The site, about 12 miles along Hwy 211 from Hwy 191, is usually visited as a short stop on the way to the Needles section of Canyonlands National Park (8 miles further).
### Canyonlands National Park
A 527-sq-mile vision of ancient earth, Canyonlands is Utah's largest national park. Vast serpentine canyons tipped with white cliffs loom high over the Colorado and Green Rivers, their waters a stunning 1000ft below the rim rock. Skyward-jutting needles and spires, deep craters, blue-hued mesas and majestic buttes dot the landscape. Overlooks are easy enough to reach. To explore further you'll need to contend with difficult dirt roads, great distances and limited water resources.
The Colorado and Green Rivers form a Y that divides the park into three separate districts, inaccessible to one another from within the park. Cradled atop the Y is the most developed and visited district, Island in the Sky (30 miles/45 minutes from Moab). Think of this as the overview section of the park, where you look down from viewpoints into the incredible canyons that make up the other sections. The thin hoodoos, sculpted sandstone and epic 4WD trails of the Needles District are 75 miles/90 minutes south of Moab. Serious skill is required to traverse the 4WD-only roads of the most inaccessible section, the Maze (130 miles/3½ hours from Moab).
###### Fees & Permits
In addition to the park entrance fee (Island & Needles sections only, 7-day per vehicle $10), permits are required for overnight backpacking, mountain biking, 4WD trips and river trips. Designated camp areas abut most trails; open-zone camping is permitted in some places. Horses are allowed on all 4WD trails. Permits are valid for 14 days and are issued at the visitor center or ranger station where your trip begins. Reservations are available by fax or mail from the NPS Reservations Office ( 435-259-4351; fax 435-259-4285; www.nps.gov/cany/planyourvisit/backcountrypermits.htm; 2282 SW Resource Blvd, Moab, UT 84532; 8:30am-noon Mon-Fri) up to two weeks ahead. A few space-available permits may be available same-day, but advanced reservations are essential for spring and fall trips. Costs are as follows:
Backpackers $15 per group
General mountain bike or 4WD day-use $30 for up to three vehicles
Needles Area 4WD day-use $5 per vehicle
River trips $30 per group in Cataract Canyon, $20 elsewhere; plus $20 per person fee
###### Regulations
Canyonlands follows most of the national park hiking and backcountry use regulations. A few rules to note:
»No ATVs allowed. Other four-wheel-drive vehicles, mountain bikes and street-legal motorbikes are permitted on dirt roads.
»Backcountry campfires are allowed only along river corridors; use a fire pan, burn only driftwood or downed tamarisk, and pack out unburnt debris.
»Free or clean-aid rock climbing is allowed, except at archaeological sites or on most named features marked on US Geological Survey (USGS) maps. Check with rangers.
#### Information
Island in the Sky and the Needles District have visitor centers, listed in the respective sections below. Many of the brochures from the Canyonlands NPS (www.nps.gov/cany/planyourvisit/brochures.htm) are available online. The information center in Moab also covers the park.
#### Getting Around
The easiest way to tour Canyonlands is by car. Traveling between districts takes two to six hours, so plan to visit no more than one per day. Speed limits vary but are generally between 25mph and 40mph. Outfitters in Moab have hiker shuttles and guide rafting, hiking, biking and 4WD tours in the park.
##### CANYONLANDS – ISLAND IN THE SKY
You'll comprehend space in new ways atop the appropriately named Island in the Sky. This 6000ft-high flat-topped mesa drops precipitously on all sides, providing some of the longest, most enthralling vistas of any park in southern Utah. The 11,500ft Henry Mountains bookend panoramic views in the west, and the 12,700ft La Sal Mountains are to the east. Here you can stand beneath a sparkling blue sky and watch thunderheads inundating far-off regions while you contemplate applying more sunscreen. The island sits atop a sandstone bench called the White Rim, which indeed forms a white border 1200ft below the red mesa top and 1500ft above the river canyon bottom. An impressive 4WD road descends from the overlook level.
The complimentary video at the visitor center provides great insight into the nature of the park. And a reminder to keep your park entry receipt – admission to Island in the Sky includes entry to Needles, too.
Overlooks and trails line each road. Most trails at least partially follow cairns over slickrock. Bring lots of water and watch for cliff edges!
#### Sights & Activities
Ask rangers about longer hikes off the mesa that are strenuous, steep and require advance planning. There's one major, hard-to-follow backpacking route: the Syncline Loop (8.3 miles, five to seven hours).
Scenic Drive DRIVING TOUR
From the visitor center the road leads past numerous overlooks and trailheads, ending after 12 miles at Grand View Point – one of the Southwest's most sweeping views, rivaled only by the Grand Canyon and nearby Dead Horse Point State Park. Halfway there, a paved spur leads (past Aztec Butte) northwest 5 miles to Upheaval Dome trailhead. An informative driving tour CD rents for $5 from the visitor center.
White Rim Road MOUNTAIN BIKING, DRIVING TOUR
Blazed by uranium prospectors in the 1950s, primitive White Rim Rd encircling Island in the Sky is the top choice for 4WD and mountain-biking trips. This 70-mile route is accessed near the visitor center via steeply descending Shafer Trail Rd. It generally takes two to three days in a vehicle or three to four days by bike. Since the route lacks any water sources, cyclists should team up with a 4WD support vehicle or travel with a Moab outfitter. Permits are required and rangers do patrol. _A Naturalist's Guide to the White Rim Trail_ , by David Williams and Damian Fagon, is a good resource.
Several easy trails pack a lot of punch:
Mesa Arch Nature Trail HIKING
Hike this half-mile loop at sunrise, when the arch, dramatically hung over the very edge of the rim, glows a fiery red.
Upheaval Dome HIKING
Here, a half-mile spur leads to an overlook of a geological wonder that was possibly the result of a meteorite strike 60 million years ago.
White Rim Overlook Trail HIKING
A mile before Grand View Point, this is a good spot for a picnic and a 1.8-mile round-trip hike.
Grand View Trail HIKING
At the end of the road, the trail follows a 2-mile round-trip course at rim's edge. Even if you don't hike, Grand View Point Overlook is a must-see.
Aztec Butte Trail HIKING
Back near the Y in the road, this moderate 2-mile round-trip climbs slickrock to stellar views and an ancient granary ruin.
#### Sleeping
Backcountry camping in the Island is mostly open-zone (not in prescribed areas), but is still permit-limited. Nearby Dead Horse Point State Park also has camping; food, fuel and lodging are available in Moab.
Willow Flat Campground CAMPGROUND $
(tent & RV sites $10) Seven miles from the visitor center, the first-come, first-served, 12-site Willow Flat Campground has vault toilets but no water, and no hookups. Bring firewood and don't expect shade. Arrive early to claim a site during spring and fall.
#### Information
Island in the Sky Visitor Center (www.nps.gov/cany/island; Hwy 313; 8am-6pm Mar-Oct, 9am-4:30pm Nov-Feb) Get books, maps, permits and campground information here. Schedules are posted daily for ranger-led lectures and hikes.
##### CANYONLANDS – NEEDLES DISTRICT
Named for the spires of orange-and-white sandstone jutting skyward from the desert floor, the Needles District's otherworldly terrain is so different from Island in the Sky, it's hard to believe they're part of the same park. Despite having paved access roads, theNeedles receives only half as many visitors as the Island. Why? It takes 90 minutes to drive from Moab, and once you arrive, you have to work harder to appreciate the wonders – in short, you have to get out of the car and walk. Expend a little energy, though, and the payoff is huge: peaceful solitude and the opportunity to participate in,not just observe, the vastness of canyon country. Morning light is best for viewing the rock spires.
Needles Visitor Center lies 2.5 miles insidepark boundaries and provides drinking water. Hold on to your receipt, admission (7-day per vehicle $10) includes entry to Island in the Sky.
#### Sights & Activities
Needles has a couple of short trails (none wheelchair accessible), but getting off the beaten path is this section's premier attraction. Many challenging day-hikes connect in a series of loops, some requiring route-finding skills. And 50 miles of 4WD and mountain-biking roads (permit required, see Click here) crisscross the park. Know what you're doing, or risk damaging your vehicle and endangering yourself. Towing fees run from $1000 to $2000 – really. If you're renting a 4WD vehicle, check the insurance policy; you might not be covered here.
Scenic Drive DRIVING TOUR
Though not much of a drive-by park, the paved road continues almost 7 miles from the visitor center to Big Spring Canyon Overlook. Parking areas along the way access several short trails to sights, including arches, Pothole Point, Ancestral Puebloan ruins and petroglyphs. All trails listed are off this drive; use the park map you receive on entry to navigate.
Cave Spring Trail HIKING
Especially popular with kids, the Cave Spring Trail (0.6-mile loop, easy to moderate) leads up ladders and over slickrock to an abandoned cowboy camp. The handprint pictographs on the last cave's walls are haunting.
Slickrock Trail HIKING
Scamper across slickrock to fabulous views of the canyon; on the return route, you face the district's needles and spires in the distance (2.4-mile loop, moderate).
Chesler Park/Joint Trail Loop HIKING
Get among the namesake needles formations. An awesome 11-mile route loops across desert grasslands, past towering red-and-white-striped pinnacles and between deep, narrow slot canyons, some only 2ft across. Elevation changes are mild, but the distance makes it an advanced day hike.
Elephant Canyon Trail HIKING
For gorgeous scenery, the Elephant Canyon Trail (11-mile loop) to Druid Arch is hard to beat. The _National Geographic Trails Illustrated_ Canyonlands map should suffice, but if you're inclined to wander, pick up a 7.5-minute quadrangle USGS map at the visitor center.
Elephant Hill MOUNTAIN BIKING, FOUR-WHEEL DRIVING
This 32-mile round-trip is the most well-known and technically challenging route in the state, with steep grades and tight turns (smell the burning brakes and clutches). If you've always wanted to rock climb on wheels, you've found the right trail. Don't try this as your first 4WD or mountain-bike adventure.
Colorado River Overlook MOUNTAIN BIKING, DRIVING TOUR
The route to the Colorado River Overlook is easy in a vehicle and moderately easy on a mountain bike. Park and walk the final, steep 1.5-mile descent to the overlook.
Salt Creek Canyon Trail MOUNTAIN BIKING, DRIVING TOUR
Following the district's main drainage, archaeology junkies love the rock art along this 27-mile loop; moderately easy for vehicles and moderate for bikes.
### INDIAN CREEK
About 16.5 miles along Hwy 211, driving into the Needles District, look up. Even if you don't rock climb, it's fascinating to watch the experts scaling the narrow cliffside fissures near Indian Creek (www.friendsofindiancreek.org). There's a small parking lot from where you can cross the freely accessible Nature Conservancy and BLM grazing land.
#### Sleeping & Eating
Backcountry camping, in prescribed areas only, is quite popular, so it's hard to secure an overnight permit (Click here) without advance reservation. Monticello (34 miles) and Moab (75 miles) are the nearest full-service towns.
Squaw Flat Campground CAMPGROUND $
(www.nps.gov/cany; tent & RV sites $15) This first-come, first-served, 27-site campground 3 miles west of the visitor center fills up every day – spring to fall. It has flush toilets and running water, but no showers, and no hookups. Opt for side A, where many sites (12 and 14, for example) are shaded by juniper trees and cliffs. Maximum allowable RV length is 28ft.
Needles Outpost CAMPGROUND $
( 435-979-4007; www.canyonlandsneedlesoutpost.com; Hwy 211; tent & RV sites $15; Apr-Nov) If Squaw Flat is full, the dusty private campground at Needles Outpost is an alternative. Shower facilities are $3 for campers, $7 for noncampers. An on-site store sells limited camping supplies, gasoline and propane. The lunch counter and grill (open 8:30am to 4:30pm) serves sandwiches and burgers.
### 127 HOURS: BETWEEN A ROCK AND A HARD PLACE
What started out as a day's adventure turned into a harrowing ordeal for one outdoorsman exploring some spectacular slots near Canyonlands National Park in the spring of 2003. Canyoneering southeast of the remote Horseshoe Canyon section in Bluejohn Canyon, Aron Ralston became trapped when a crashing boulder pinned his hand and wrist. The story of how he cut himself out of the situation (literally, he cut off his arm with a pocketknife) was first turned into a compelling book, and then the 2010 Oscar-nominated movie _127 Hours_. The film showcases both the amazing beauty of Utah's canyonlands, and the brutal reality of its risks.
#### Information
Needles Visitor Center (www.nps.gov/cany/needles; Hwy 211; 8am-6pm Mar-Oct, 9am-4:30pm Nov-Feb) Smaller, but has similar books and guidance to Islands in the Sky.
##### CANYONLANDS – HORSESHOE CANYON
Way far west of Island in the Sky, Horseshoe Canyon (admission free) shelters one of the most impressive collections of millennia-old rock art in the Southwest. The centerpiece is the Great Gallery and its haunting Barrier Canyon-style pictographs from between 2000 BC and AD 500. The heroic, bigger-than-life-size figures are magnificent. Artifacts recovered here date back as far as 9000 BC. That said, it's not easy to get to. The gallery lies at the end of a 6.5-mile round-trip hiking trail descending 750ft from a dirt road. Plan on six hours. Rangers lead hikes here on Saturday and Sunday from April through October; contact the Hans Flat Ranger Station ( 435-259-2652; www.nps.gov/cany/horseshoe; Hwy 24; 9am-4:30pm) for times.
You can camp on BLM land at the trailhead, though it's really a parking lot. There is a single vault toilet, but no water. From Moab the trip is about 120 miles/2¾ hours. Take Hwy 191 north to I-70 west, then Hwy 24 south. About 25 miles south of I-70, past the turnoff for Goblin Valley State Park, turn east and follow the gravel road 30 miles. Hanksville is 45 miles/1½ hours.
##### CANYONLANDS – THE MAZE
A 30-sq-mile jumble of high-walled canyons, the Maze (admission free) is a rare preserve of true wilderness for hardy backcountry veterans. The colorful canyons are rugged, deep and sometimes completely inaccessible. Many of them look alike and it's easy to get turned around – hence the district's name. (Think topographic maps and GPS.) Rocky roads absolutely necessitate reliable, high-clearance 4WD vehicles. Plan on spending at least three days, though a week is ideal. If you're at all inexperienced with four-wheel driving, stay away. Be prepared to repair your jeep and, at times, the road. There may not be enough money on the planet to get you towed out of here. Most wreckers won't even try.
Predeparture, always contact the Hans Flat Ranger Station ( 435-259-2652; www.nps.gov/cany/maze; 9am-4:30pm) for conditions and advice. The station is 136 miles (3½ hours) from Moab, and has a few books and maps, but no other services. Take Hwy 191 north, I-70 west, and then Hwy 24 south. Hans Flat is 16 miles south of Horseshoe Canyon. The few roads into the district are poor and often closed with rain or snow; bring tire chains from October to April.
### Around Canyonlands
The BLM Canyon Rims Recreation Area (www.blm.gov/utah/moab; Needles Overlook Rd; admission free) to the east of the national park has two interesting overlooks, undeveloped hiking and backcountry driving. Turn west off Hwy 191 (32 miles south of Moab, 27 miles north of Monticello); a paved road leads 22 miles to Needles Overlook and a panorama of the park. Two-thirds of the way to the overlook, the gravel Anticline Overlook Rd stretches 16 miles north to a promontory with awesome views of the Colorado River.
Three miles after the Hwy 191 turnoff is Windwhistle Campground (tent & RV sites $12; Mar-Oct). The 20 well-spaced, first-served sites have fire rings and scenic vistas. Pit toilets; water available May through September.
### Dead Horse Point State Park
The views at Dead Horse Point (www.stateparks.utah.gov; off Hwy 313; day-use per vehicle $10; 6am-10pm) pack a wallop, extending 2000ft down to the winding Colorado River, up to La Sal Mountains' 12,700ft peaks and out 100 miles across Canyonlands' mesmerizing stair-step landscape. (You might remember it from the final scene of _Thelma & Louise_, where they drove off into the abyss.) If you thrive on rare, epic views, you're gonna love Dead Horse.
Drive Hwy 313 south from Hwy 191, 30 miles northwest of Moab, following the road as it turns left into the park (if you go straight you'll reach Island in the Sky). Toward the end of the drive, the road traverses a narrow ridge just 90ft across. Around the turn of the 20th century, cowboys used the mesa top as a sort of natural corral by driving wild horses onto it and blocking the ridge. The story goes that ranch hands forgot to release the horses they didn't cull, and the stranded equines supposedly died with a great view of the Colorado River...
The visitor center ( 8am-6pm mid-Mar–mid-Oct, 9am-5pm mid-Oct–mid-Mar) has exhibits, shows on-demand videos and sells books and maps. Rangers lead walks and talks in summer. To escape the small (but sometimes chatty) crowds, take a walk around the mesa rim. Visit at dawn or dusk for the best lighting. South of the vistor center, the 21-site Kayenta Campground ( 800-322-3770; www.stateparks.utah.gov; tent & RV sites $20) provides limited water and a dump station, but no hookups. Reservations are accepted from March to October, but you can often secure same-day sites by arriving early. Fill RVs with water in Moab.
### Moab
An island of civilization in a sea of stunning wilderness, Moab serves as a terrific base camp for area excursions. Hike in Arches or Canyonlands National Parks during the day, then come back to a comfy bed, a hot tub and your selection of surprisingly good restaurants at night. Here you can browse the shelves at an indie bookstore, shop for groceries till midnight, sit down for dinner at 9pm and still find several places open for a beer afterward. There's a distinct sense of fun here in 'Utah's Recreation Capital'. Dozens of rafting and riding outfitters (mountain bike, jeep, ATV, horse...) based here take forays into national parks and onto public lands.
It was miners in search of 'radioactive gold', ie uranium, starting in the 1950s that blazed a network of back roads, laying the groundwork for Moab to become a 4WD mecca. But neither mining nor the hundreds of Hollywood films shot here had as much influence on the character of Moab as the influx of youth-culture, fat-tire, mountain-bike enthusiasts. Development does come at a price though: chain motels, fast-food joints and T-shirt shops line the main drag. The town gets overrun March through October, and the impact of all those feet, bikes and 4WDs on the fragile desert is a serious concern (use existing trails). People here love the land, even if they don't always agree about how to protect it. If the traffic irritates you, just remember – you can disappear into the vast desert in no time.
#### Sights
Between breakfast and dinner there's not much going on in Moab; most people get out of town for activities.
Museum of Moab MUSEUM
(www.moabmuseum.org; 118 E Center St; adult/child $5/free; 10am-5pm Mon-Sat, noon-5pm Sun Mar-Oct; noon-5pm Mon-Sat Nov-Apr) On a rainy day you might want to check out the regional exhibits – on everything from paleontology and geology to uranium mining and Native American art.
Red Cliffs Adventure Lodge MUSEUM
(Mile 14, Hwy 128; 8am-10pm) This lodge, 15 miles northeast of town, hosts the Moab Museum of Film & Western Heritage, showing Hollywood memorabilia and posters from all the films shot in the area. There's also a tasting and sales room for its on-site winery.
### WATER REFILLING STATIONS
In addition to the water stations at area national park visitor centers, you can refill your jugs for free at Gear Heads (471 S Main St; 7am-9pm May-Oct, off-season hours vary) outdoor store. Alternatively go to the natural, outdoor tap at Matrimony Springs (Hwy 128, 100yd east of Hwy 191 on the right).
Spanish Valley Winery WINERY
(www.moab-utah.com/spanishvalleywinery; Zimmerman Lane, off Stocks Dr; noon-7pm Mon-Sat Mar-Oct) For some no-frills wine tasting, visit the surprisingly good Spanish Valley Winery, 6 miles south of Moab on Hwy 191.
Moab
Sights
1Museum of Moab C3
Activities, Courses & Tours
2Adrift Adventures B1
3Canyon Voyages Adventure Co B2
4Cliffhanger Jeep Rental B4
5Desert Highlights B4
6Farabee's Outlaw Tours B6
7Gear Heads Outdoor Store C7
8High Point Hummer & ATV Tours B1
9Moab Adventure Center B5
10Moab Cliffs & Canyons B2
11Moab Cyclery B6
12Navtec Expeditions B1
13Rim Cyclery B3
Sleeping
14Best Western Canyonlands Inn B4
15Big Horn Lodge B7
16Bowen Motel B2
17Cali Cochitta C4
18Canyonlands Campground C7
19Gonzo Inn A5
20Redstone Inn C7
21Sunflower Hill D2
22Up the Creek Campground C6
Eating
23City Market & Pharmacy C6
24Eddie McStiff's C4
25EklectiCafé B1
26Jailhouse Café B3
27Jeffrey's Steakhouse B2
28Love Muffin B2
29Miguel's Baja Grill B3
30Moonflower Market C3
31Peace Tree Café B4
32Sabuku Sushi C4
33Singha Thai C4
34Zax B4
Drinking
Ghost Bar (see 27)
35Red Rock Bakery & Cafe B4
36Wake & Bake C4
37Woody's Tavern B4
Entertainment
38Moab Arts & Recreation Center C3
Shopping
39Arches Book Company & Back of Beyond B3
40Desert Thread C3
#### Activities
The visitor center has a helpful collection of free brochures highlighting near-town rock art, movie locations, driving tours, and 4WD and hiking trails. Moab abounds in outfitters for mountain biking, white-water rafting, hiking, and backcountry ATV and jeep tours. Can't choose just one activity? No worries. Many operators, such as Moab Adventure Company and CanyonVoyages Adventure Co, will help you plan multisport or multiday adventures. The visitor center has a complete list of all outfitters, way too numerous to include here.
###### Mountain Biking
Moab's mountain biking is world-famous. Challenging trails ascend steep slickrock and wind through woods and up 4WD roads. People come from everywhere to ride the famous Slickrock Bike Trail and other challenging routes. If you're a die-hard, ask about trips to the Maze. Bike shop websites and www.discovermoab.com/biking.htm are good trail resources, or pick up _Above & Beyond Slickrock_, by Todd Campbell, and _Rider Mel's Mountain Bike Guide to Moab_. __ In recent years, the BLM has opened several new loops and temporarily closed others. Follow BLM guidelines, avoid all off-trail ridingand pack everything out (including cigarette butts). Spring and fall are the busiest seasons. In summer you'd better start by 7am, otherwise it gets too hot.
For rentals, be sure to reserve in advance. Road and full-suspension bikes run $40 to $65 per day. Shops are generally open from 8am to 7pm from March through October, and 9am to 6pm November through February. Full-day tours run from $115 to $225 per person including lunch and rental.
### TOP MOAB MOUNTAIN-BIKING TRAILS
Slickrock Trail Moab's legendary trail will kick your ass. The 12.7-mile round-trip, half-day route is for experts only (as is the practice loop).
White Rim Trail Canyonlands National Park's 70-mile, three- to four-day journey around a canyon mesa-top is epic.
Bar-M Loop Bring the kids on this easy 8-mile loop skirting the boundary of Arches, with great views and short slickrock stretches.
Gemini Bridges A moderate, full-day downhill ride past spectacular rock formations, this 13.5-mile one-way trail follows dirt, sand and slickrock.
Klondike Bluffs Trail Intermediates can learn to ride slickrock on this 15.6-mile round-trip trail, past dinosaur tracks to Arches National Park.
Moonlight Meadow Trail Beat the heat by ascending La Sal Mountains to 10,600ft on this moderate 10-mile loop among aspens and pines (take it easy; you _will_ get winded).
Park to Park Trail A new paved-road bike path travels one-way from Moab into Arches National Park (30 miles), or you can turn off and follow the Hwy 313 bike lane to the end of Canyonlands' Island in the Sky park (35 miles).
Rim Cyclery MOUNTAIN BIKING
( 435-259-5333; www.rimcyclery.com; 94 W 100 N) Moab's longest-running family-owned bike shop not only does rentals and repairs, it also has a museum of mountain-bike technology.
Poison Spider Bicycles MOUNTAIN BIKING
( 435-259-7882, 800-635-1792; www.poisonspiderbicycles.com; 497 N Main St) Friendly staff are always busy helping wheel jockeys map out their routes. Well-maintained road and suspension rigs for rent; private guided trips organized in conjunction with Magpie Adventures.
Rim Tours TOUR
( 435-259-5223, 800-626-7335; www.rimtours.com; 1233 S Hwy 191) Well-organized multiday trips cover territory all across southern Utah; day tours are available for top local trails, including Canyonlands. The 18-mile downhill sunrise ride is all adrenaline.
Moab Cyclery MOUNTAIN BIKING
( 435-259-7423, 800-451-1133; www.moabcyclery.com; 391 S Main St) Good half-, full-,multiday – and multisport – tours. Rental and sales; biker shuttles available.
Chile Pepper Bike Shop MOUNTAIN BIKING
( 435-259-4688, 888-677-4688; www.chilebikes.com; 720 S Main St) Rentals and repairs, plus helpful trail maps. Used bikes for sale.
Western Spirit Cycling Adventures TOUR
( 435-259-8732, 800-845-2453; www.westernspirit.com; 478 Mill Creek Dr) Canyonlands White Rim, Utah and nationwide multiday tours.
###### White-Water Rafting
Whatever your interest, be it bashing through rapids or gentle floats studying canyon geology, rafting may prove the highlight of your vacation. Rafting season runs from April to September; jet-boating season lasts longer. Water levels crest in May and June.
Most local rafting is on the Colorado River, northeast of town, including the Class III to IV rapids of Westwater Canyon, near Colorado; the wildlife-rich 7-mile Class I float from Dewey Bridge to Hittle Bottom (no permit required); and the Class I to II Moab Daily, the most popular stretch near town (no permit required; expect a short stretch of Class III rapids).
Rafters also launch north of Moab to get to the legendary Class V rapids of Cataract Canyon (NPS permit required). This Colorado River canyon south of town and the Confluence is one of North America's most intense stretches of white water. If you book anything less than a five-day outfitter trip to get here, know that some of the time downstream will be spent in a powered boat. Advanced do-it-yourself rafters wanting to run it will have to book a jet-boat shuttle or flight return.
North of Moab is a Class I float along the Green River that's ideal for canoes. From there you can follow John Wesley Powell's 1869 route. (Note that additional outfitters operate out of the town of Green River itself.)
Full-day float trips cost $65 to $90; white-water trips start at $155. Multiday excursions run $350 to $800, while jet-boat trips cost about $70. Day trips are often available on short notice, but book overnight trips well ahead. Know the boat you want: an oar rig is a rubber raft that a guide rows; a paddleboat is steered by the guide and paddled by passengers; motor rigs are large boats driven by a guide (such as jet boats). For more on rapids classification, see Click here.
Do-it-yourselfers can rent canoes, inflatable kayaks or rafts. Canoes and kayaks run $35 to $45 per day, rafts $65 to $130 per day, depending on size. Without permits, you'll be restricted to mellow stretches of the Colorado and Green Rivers; if you want to run Westwater Canyon or enter Canyonlands on either river, you'll need a permit. Contact the BLM ( 435-259-2100; www.blm.gov/utah/moab) or NPS ( 435-259-4351; www.nps.gov/cany/permits.htm), respectively. Reserve equipment,permits (Click here) and shuttles way in advance.
Sheri Griffith Expeditions RAFTING
( 435-259-8229, 800-332-2439; www.griffithexp.com; 2231 S Hwy 191) Operating since 1971, this rafting specialist has a great selection of river trips on the Colorado, Green and San Juan Rivers – from family floats to Cataract Canyonrapids, from a couple hours to a couple weeks.
Canyon Voyages Adventure Co RAFTING
( 435-259-6007, 800-733-6007; www.canyonvoyages.com; 211 N Main St) In addition to half- to five-day mild white-water and kayaking trips, Canyon organizes multisport excursions that include options like hiking, biking and canyoneering. Kayak, canoe and outdoor equipment rental available.
Tex's Riverways KAYAKING
( 435-259-5101; www.texsriverways.com; 691 N 500West) Full-service independent adventure support: Tex's rents complete kayak and canoe outfits (with required portable toilets), offers land-transport boat shuttles and jet-boat hiker shuttles, and provides thorough advice.
Tag-A-Long Expeditions ADVENTURE SPORTS
( 435-259-8946, 800-453-3292; www.tagalong.com; 452 N Main St) This rafting outfitter offers a little of everything: flat-water jet boat rides, white-water rafting, land safaris, horseback riding, scenic flights, skydiving, Nordic skiing and more. Ask about jet boat return support for Cataract Canyon trips.
Canyonlands by Night and Day BOAT TOUR
( 435-259-2628, 800-394-9978; www.canyonlandsbynight.com; 1861 N Hwy 191) Daytime and sunset group jet boat tours are the primary attraction at this riverfront operator, but they also offer packages that include dinner, scenic flights and land tours.
Moab Rafting & Canoe Co KAYAKING
( 435-259-7722, 800-753-8216; www.moab-rafting.com; 805 N Main St) Small company with guided and self-guided canoe and raft trips.
Navtec Expeditions ADVENTURE SPORTS
( 435-259-7983, 800-833-1278; www.navtec.com; 321 N Main St) Comprehensive rafting excursions, combo hiking and 4WD trips.
Adrift Adventures ADVENTURE SPORTS
( 435-259-8594, 800-874-4483; www.adrift.net; 378 N Main St) Rafting, jet boat rides, sport boat rides, 4WD land excursions and multisport packages, plus Arches National Park bus tours.
Slickrock Air Guides SCENIC FLIGHTS
( 435-259-6216, 866-259-1626; www.slickrockairguides.com) Air shuttles for Cataract Canyon trips.
Splore RAFTING
( 801-484-4128; www.splore.org) If traveling with someone with a physical or mental disability book a raft trip with this operator, based in Salt Lake City.
###### Hiking
Don't limit yourself to the national parks, there's hiking on surrounding public lands as well.
Corona Arch Trail HIKING
(trailhead 6 miles north, Potash Rd) To see petroglyphs and two spectacular arches, hike the moderately easy 3-mile, two-hour walk. You may recognize Corona from a well-known photograph showing an airplane flying through it – this is one big arch.
Negro Bill Canyon Trail HIKING
(trailhead 3 miles north of Moab, Hwy 128) The moderately easy trail includes a 2.5-mile walk along a stream. (The totally politically incorrect canyon name refers to a prospector who grazed his cows here in the 1800s.) Scoot down a shaded side canyon to find petroglyphs, then continue to the 243ft-wide Morning Glory Natural Bridge, at a box canyon. Plan on three to four hours.
La Sal Mountains HIKING
(www.fs.usda.gov; La Sal Mountain Loop) To escape summer's heat, head up Hwy 128 to the Manti–La Sal National Forest lands in the mountains east of Moab and hike through white-barked aspens and ponderosa pines.
Canyonlands Field Institute TOUR
( 435-259-7750, 800-860-5262; http://canyonlandsfieldinst.org; 1320 S Hwy 191) All-ages interpretive hikes and canoe trips – a wonderful introduction to the parks and the area.
Deep Desert Expeditions HIKING
( 435-260-1696; www.deepdesert.com; full-day $175-220) Archaeological hikes, photo treks, multiday guided backpacking, catered camping and Fiery Furnace walks – in winter, too!
###### Four-Wheel Driving
The area's primitive backroads are made for 4WD enthusiasts. But if you don't bring or rent ($150 to $200 per day) your own Jeep, you still have options. Several outfitters offer group 4WD tours, or 'land safaris', in multipassenger-modified, six to eight person Humvee-like vehicles (two hours from $65 to $90). Note that rafting companies may have combination land/river trips. You can also bring your own ATV, or rent off-road utility vehicles like Rhinos and Mules (seating two to four), or four-wheelers (straddled like a bicycle), from $129 to $169 per day. Personal 4WD vehicles and ATVs require an off-highway vehicle (OHV) permit, available at the visitor center. Outfitter hours are generally 7:30am to 7pm March through October, 8am to 5pm November through February.
Moab Information Center has tons of free route info, as well as _Moab Utah Backroads & 4WD Trails_ by Charles Wells, and other books for sale. Canyonlands National Park also has some epic 4WD tracks. If you go four-wheeling, stay on established routes. The desert looks barren, but it's a fragile landscape of complex ecosystems. Biological soil crusts (see Click here) may take a century to regenerate after one tire track (really).
Hell's Revenge FOUR-WHEEL DRIVING
(www.discovermoab.com/sandflats.htm; Sand Flats Recreation Area, Sand Flats Rd) For experienced drivers only, the best-known 4WD road in Moab is in the BLM-administered area east of town, which follows an 8.2-mile route up and down shockingly steep slickrock.
Moab Adventure Center ADVENTURE SPORTS
( 435-259-7019, 866-904-1163; www.moabadventurecenter.com; 225 S Main St) The open-air, canopy-topped land safaris offered here are popular. This megacenter also arranges, alone or in combination, rafting trips, Jeep rental, horseback riding, rock climbing, guided hikes, scenic flights and even Arches National Park bus tours.
High Point Hummer
& ATV Tours ADVENTURE SPORTS
( 435-259-2972, 877-486-6833; www.highpointhummer.com; 281 N Main St) Take a two- to four-hour thrill ride up the slickrock on a group Hummer tour, follow a guide as you drive yourself on a four-wheeler or utility vehicle tour, or rent an ATV yourself.
Dan Mick's Jeep Tours DRIVING TOUR
( 435-259-4567; www.danmick.com) Private Jeeptours and guided drive-your-own-4WD trips with good ol' boy Dan Mick.
Elite Motorcycle Tours DRIVING TOUR
( 435-259-7621, 888-778-0358; www.elitemotorcycletours.com; 1310 Murphy Lane) Dirt bike and street-legal motorcycle rental and tours.
Farabee's Outlaw Jeep Tours DRIVING TOUR
( 435-259-7494; www.farabeesjeeprentals.com; 35 Grand St) Customized Jeep rental and off-road ride-along or guide-led tours.
Cliffhanger Jeep Rental DRIVING TOUR
( 435-259-0889; www.cliffhangerjeeprental.com; 40 W Center St) TeraFlex suspension Jeeps, Rhino two-seaters and four-wheelers for rent.
Coyote Land Tours DRIVING TOUR
( 435-259-6649; www.coyotelandtours.com) Dailytours in a bright-yellow Mercedes Benz Unimog off-road vehicle (seats 12); call ahead.
###### Rock Climbing & Canyoneering
Climb up cliffsides, rappel into rivers and hike through slot canyons. Half-day canyoneering or climbing adventures run from around $99 to $165 per person.
Wall Street ROCK CLIMBING
(Potash Rd) Rock climbers in town gravitate toward Wall Street; it's Moab's El Capitan, so it gets crowded.
### SEGO CANYON
It's rare to see the rock art of three different ancient cultures on display all in one canyon, but that's precisely what you can do at Sego. The canyon itself is 4 miles north of I-70 at Thompson Springs (41 miles north of Moab, 26 miles east of Green River). On the south-facing wall, the Barrier Culture pictographs are the oldest (at least 2000 years old); the wide-eyed anthropomorphic creatures take on a haunted, ghostlike appearance to modern eyes. The Fremont petroglyphs were carved about 1000 years ago. Many of the line-art figures are wearing chunky ornamentation and headdresses (or is it antennae?). The third panel is from the 19th-century Native American Ute tribe; look for the horses and buffalo.
If you drive half a mile further north up the canyon, you come to a little ghost town. The few buildings here were deserted when a mining camp was abandoned in the 1950s.
Gear Heads Outdoor Store ADVENTURE SPORTS
( 435-259-4327; www.gearheadsoutdoorstore.com; 471 S Main St; 7am-9pm) Stock up on all the outdoor gear you need, including climbing ropes, route guides, books and water-jug refills. The knowledgeable staff are quite helpful.
Moab Desert Adventures ADVENTURE SPORTS
( 435-260-2404, 877-765-6622; www.moabdesertadventures.com; 415 N Main St) Top-notch climbing tours scale area towers and walls; the 140ft arch rappel is especially exciting. Canyoneering and multisport packages available.
Desert Highlights ADVENTURE SPORTS
( 435-259-4433, 800-747-1342; www.deserthighlights.com; 50 E Center St) Canyoneering and combo raft trips here are big on personal attention. Regulations are being reviewed, but in the past they've had canyoneering permission for Fiery Furnace and other Arches National Park trips.
Moab Cliffs & Canyons ADVENTURE SPORTS
( 435-259-3317, 877-641-5271; www.cliffsandcanyons.com; 231 N Main St) Canyoneering, climbing and scenic hiking trips. Ask about Fiery Furnace hikes.
Windgate Adventures ADVENTURE SPORTS
( 435-260-9802; www.windgateadventures.com) Private guide Eric Odenthal leads guided climbing, canyoneering, arch-rappelling and photo trips.
###### Air Adventures
Moab's airport is 16 miles north of town on Hwy 191. Small-plane scenic flights run about $150 per hour.
Redtail Aviation SCENIC FLIGHTS
( 435-259-7421; www.redtailaviation.com) Fly high above Arches, Canyonlands, Lake Powell, San Rafael Swell, Monument Valley and more.
Slickrock Air Guides SCENIC FLIGHTS
( 435-259-6216; www.slickrockairguides.com) 'Flightseeing' over Canyonlands National Park and around greater southern Utah.
Skydive Moab EXTREME SPORTS
( 435-259-5867; www.skydivemoab.com; tandem jump $189-229) Skydiving and base-jumping.
Canyonlands Ballooning BALLOONING
( 435-655-1389, 877-478-3544; www.canyonlandsballooning.com; 4 hours $250) Soar over canyon country and Manti–La Sal Mountains.
###### Skiing & Snowshoeing
It's a local secret that La Sal Mountains, which lord over Moab off Hwy 128, receive tons of powder, just perfect for cross-country skiing – and there's a hut-to-hut ski system ($35 per person, per night).
Tag-A-Long Expeditions SKIING
( 435-259-8946, 800-453-3292; www.tagalong.com; 452 N Main St) Book self-guided cross-country ski packages, snowmobile transfers and hut lodging here.
Rim Cyclery SKIING
( 435-259-5333; www.rimcyclery.com; 94 W 100 N) Rents skis and provides trail maps.
Gear Heads Outdoor Store SNOW SPORTS
( 435-259-4327, 888-740-4327; www.gearheadsoutdoorstore.com; 471 S Main St) Rents snowshoes and provides trail maps.
### UTAH, YOU OUGHTA BE IN PICTURES
The movie industry has known about the rugged wilds of southern Utah since the early days – in the 1920s, film adaptations of Zane Grey novels were shot here. All told, more than 700 films (and many TV shows) have been shot on location across the state. Iconic movies with Utah cameos include:
» _Thelma & Louise_ – Remember where they drive off the cliff? That was outside Canyonlands National Park at Dead Horse Point (Click here). Scenes were also filmed in Arches National Park (Click here).
»Forrest Gump stopped his cross-country run in front of Monument Valley (Click here), which straddles the Utah-Arizona line _. Easy Rider_ motorcycled through, too; _2001: A Space Odyssey_ used the monoliths to represent outer space.
» _Con Air_ and _Independence Day_ both have landing scenes shot on the super-smooth Bonneville Salt Flats (Click here).
»In _High School Musical,_ Zac Efron danced his way through East High School in Salt Lake City (Click here), just like Kevin Bacon had done at Payson High School, south of Provo (Click here) in _Footloose_.
»Kanab (Click here) was the shooting location for heaps of Western movies, with stars such as John Wayne and Clint Eastwood.
###### Other Activities
Red Cliffs Lodge HORSEBACK RIDING
( 435-259-2002, 866-812-2002; www.redcliffslodge.com; Mile 14, Hwy 128; half-day $100) In Castle Valley, 14 miles north of town, Red Cliffs Lodge provides the only area horseback trail rides (March to November). If you book a multisport rafting trip that includes horseback riding, you'll still be coming here.
Matheson Wetlands Preserve BIRDWATCHING
( 435-259-4629; www.nature.org; 934 W Kane Creek Blvd; admission free; dawn-dusk) The Nature Conservancy oversees the 890-acre preserve just west of town. At the time of research, a wildfire had closed sections of the park indefinitely. Check for updates before heading out with your binoculars.
Moab Photo Tours PHOTOGRAPHY
( 435-259-4700; www.moabphototours.com) Areaphoto workshops and tours by local photographers.
#### Festivals & Events
Moab loves a party, and throws them regularly. For a full calendar, log onto www.discovermoab.com.
Skinny Tire Festival SPORTS
(www.skinnytirefestival.com) Road cycling festival; first weekend in March.
Jeep Safari SPORTS
(www.rr4w.com) The week before Easter, about 2000 Jeeps (and thousands more people) overrun the town in the year's biggest event. Register early; trails are assigned.
Moab Fat Tire Festival SPORTS
(www.moabfattirefest.com) One of Utah's biggest mountain-biking events, with tours, workshops, lessons, competitions and plenty of music; in October.
Moab Folk Festival MUSIC
(www.moabfolkfestival.com) Folk music and environmental consciousness combine. This November festival is 100% wind powered, venues are easily walkable and recycling is encouraged.
#### Sleeping
Rates given here are for March to October; prices drop by as much as 50% outside those months. Some smaller places close November through March. Most lodgings have hot tubs for aching muscles and mini-refrigerators to store snacks; motels have laundry facilities to clean up the trail dirt. Cyclists should ask whether a property provides _secure_ bike storage, not just an unlocked closet.
Though Moab has a huge number of motels, there's often no room at the inn. Reserve as far ahead as possible in season. For a full town lodging list, see www.discovermoab.com.
In addition to local campgrounds listedbelow, there's also camping in nearby national and state parks. Rafting outfitter Canyon Voyages rents tents and sleeping bags.
Sorrel River Ranch LODGE $$$
( 435-259-4642, 877-359-2715; www.sorrelriver.com; Mile 17, Hwy 128; r $340-530; ) Southeast Utah's only full-service luxury resort and gourmet restaurant was originally an 1803 homestead. The lodge and log cabinssit on 240 acres along the banks of the Colorado River. Ride horses past the alfalfa fields, or just soak in the fabulous spa with river views.
Cali Cochitta B&B $$
( 435-259-4961, 888-429-8112; www.moabdreaminn.com; 110 S 200 East; cottages incl breakfast $125-160; ) Make yourself at home in one of the charming brick cottages a short walk from downtown. A long wooden table on the patio provides a welcome setting for community breakfasts. The vibe is warm but the innkeepers live off-site, giving you your privacy.
Up the Creek Campground CAMPGROUND $
( 435-260-1888; www.moabupthecreek.com; 210 E 300 South; tent sites 1/2 people $25/25; Mar-Oct) There's something about this shady, tent-only grove that fosters a sense of community, and it's a plus that the 20 sites are within walking distance of downtown. Showers are included, but are also available to nonguests for $6; no fires.
Castle Valley Inn B&B $$
( 435-259-6012; www.castlevalleyinn.com; 424 Amber Ln, off La Sal Mountain Loop; r & cabins incl breakfast $135-225; ) For tranquility – or cycling – it's hard to beat this Castle Valley location, 15 miles north of Moab. Rooms (in the main house, or new cabins with kitchens) sit amid orchards of apples, plums and apricots. Cozy quilts add to the warm welcome and there's an outdoor hot tub.
Red Cliffs Lodge LODGE $$-$$$
( 435-259-2002, 866-812-2002; www.redcliffslodge.com; Mile 14, Hwy 128; ste $159-319; ) Part dude ranch, part luxury motel, Red Cliffs has comfy suites with vaulted ceilings, kitchenettes and private-if-cramped patios (some overlook the river). Taste the wines made at the on-site winery, go for a trail ride or arrange a rafting trip or ATV rental with the activities desk.
Redstone Inn MOTEL $
( 435-259-3500, 800-772-1972; www.moabredstone.com; 535 S Main St; r $75-99; ) You get a lot for your budget buck here: simple,pine-paneled rooms with refrigerators, microwaves, coffee makers and free wired internet access. There's a bike wash area and storage, guest laundry, on-site hot tub and pool privileges across the street. Thin walls, though.
Aarchway Inn MOTEL $$
( 435-259-2599, 800-341-9359; www.aarchwayinn.com; 1151 N Hwy 191; r incl breakfast $129-169; ) Space sets this 75-room motel apart. You could have a conga line in the giant standard bedrooms and family suites. Aarchway has the town's biggest swimming pool and there's a humongous parking lot next door for your all-terrain toys. Hike nature trails directly from here, at the northern end of town.
Goose Island Campground CAMPGROUND $
(www.blm.gov/utah/moab; Hwy 128; campsites $12) Ten no-reservation riverside BLM campgrounds lie along a 28-mile stretch of Hwy 128 that parallels the Colorado River northwest of town. The 18-site Goose Island, just 1.4 miles from Moab, is the closest. Pit toilets, no water.
Big Horn Lodge MOTEL $-$$
( 435-259-6171, 800-325-6171; www.moabbighorn.com; 550 S Main St; r $79-119; ) OK, so the exterior is kitschy Southwestern Indian-style, c 1970, but the knotty-pine paneled interiors are cozy, service is taken seriously and there are loads of extras (including heated swimming pool and hot tub, refrigerators and coffee makers).
Adventure Inn MOTEL $
( 435-259-6122, 866-662-2466; www.adventureinnmoab.com; 512 N Main St; s/d incl breakfast $65/80; Mar-Oct; ) A great little indie motel, the Adventure Inn has spotless rooms (some with refrigerators) and decent linens, as well as laundry facilities. There's a picnic area on site; no hot tub.
Inca Inn MOTEL $
( 435-259-7261, 866-462-2466; www.incainn.com; 570 N Main St; r incl breakfast $59-99; Feb-Nov; ) Who expects a pool at these prices? This small mom-and-pop motel has older but spick-and-span rooms, plus a place to take a dip. Breakfast is light and snacky.
Gonzo Inn MOTEL $$
( 435-259-2515, 800-791-4044; www.gonzoinn.com; 100 W 200 South; r $159, ste $205-339, both incl breakfast Apr-Oct; ) Brushed metal-and-wood headboards, concrete shower stalls and '50s retro patio furniture spruce up this standard motel. Bicycle wash-and-repair station on site.
Sunflower Hill INN $$
( 435-259-2974, 800-662-2786; www.sunflowerhill.com; 185 N 300 East; r incl breakfast $165-225; ) Kick back in an Adirondack chair amid the manicured gardens of two inviting buildings: a rambling 100-year-old farmhouse and an early 20th-century home. All 12 guest quarters have a sophisticated country sensibility.
Desert Hills B&B $$
( 435-259-3568; www.deserthillsbnb.com; 1989 S Desert Hills Ln; r incl breakfast $119-138; ) Get away from the traffic in town at this homey B&B in a suburban neighborhood. The four simple rooms have log beds, pillow-top mattresses and minifridges – and come with friendly, personal service.
Pack Creek Ranch LODGE $$-$$$
( 888-879-6622; www.packcreekranch.com; off La Sal Mountain Loop; cabins $175-275; ) Stay in one of 11 log cabins on a working ranch in the mountains, 2000ft above – but only 15 miles south – of Moab. No TVs; two-night minimum.
Mayor's House B&B $$
( 435-259-6015, 888-791-2345; www.mayorshouse.com; 505 Rose Tree Ln; r incl breakfast $100-140; ) A modern brick house with spacious, quiet rooms; near downtown. Has a heated pool and hot tub.
Bowen Motel MOTEL $
( 435-259-7132, 800-874-5439; www.bowenmotel.com; 169 N Main St; r incl breakfast $79-89; ) Basic motel steps from shops and restaurants. The two-story building has been updated; the single-story is scheduled to be.
Best Western Canyonlands Inn MOTEL $$
( 435-259-2300, 800-649-5191; www.canyonlandsinn.com; 16 S Main St; r $150-190; ) A comfortable, chain choice at the central crossroads of downtown. Features a fitness room, laundry, playground and outdoor pool.
Holiday Inn Express HOTEL $$
( 435-259-1150, 800-465-4229; www.hiexpress.com/moabut; 1653 Hwy 191 N; r $141-169; ) Some of the newest, upper midrange rooms in town.
Lazy Lizard Hostel HOSTEL $
( 435-259-6057; www.lazylizardhostel.com; 1213 S Hwy 191; dm/s/d $9/24/28, cabins $32-42; ) Hippie hangout with frayed couches, worn bunks and small kitchen.
Canyonlands Campground CAMPGROUND $
( 435-259-6848; www.canyonlandsrv.com; 555 S Main St; tent sites $25-29, RV sites with hookups $35-39, camping cabins $58; ) Old-growth tree-shaded sites, right in town but still quiet. Includes showers, laundry, store, small pool and playground.
Portal RV Resort CAMPGROUND $
( 435-259-6108; www.portalrvresort.com; 1261 N Hwy 191; tent sites $21, RV sites with hookups $30-55; ) The best place for luxury RVers, with long pull-throughs. Has showers, spa, laundry, store and dog run.
Slickrock Campground CAMPGROUND $
( 435-259-7660, 800-448-8873; www.slickrockcampground.com; 1301 1/2 N Hwy 191; tent sites $23-29, RV sites with hookups $31-38, cabins $49; Mar-Nov; ) North of town. Tent sites have canopies; RV sites have 30-amp hookups only. Nonguest showers $3; also has hot tubs, heated pool and a store.
Sand Flats Recreation Area CAMPGROUND $
(www.discovermoab.com/sandflats.htm; Sand FlatsRd; tent & RV sites $10) At the Slickrock Bike trailhead, this mountain-biker special has 120 nonreservable sites, fire rings and pit toilets, but no water and no hookups.
#### Eating
There's no shortage of places to fuel up in Moab, from backpacker coffeehouses to gourmet dining rooms. Pick up the _Moab Menu Guide_ (www.moabmenuguide.com) at area lodgings. Some restaurants close earlier, or on variable days, from December through March.
Love Muffin CAFE $
(139 N Main St; mains $6-8; 7am-2pm; ) Early-rising locals buy up many of the daily muffins – like the 'breakfast' with bacon and blueberries. Not to worry, the largely organic menu at this vibrant cafe also includes creative sandwiches, breakfast burritos and inventive egg dishes like 'verde', with brisket and slow-roasted salsa.
Jeffrey's Steakhouse STEAKHOUSE $$$
( 435-259-3588; 218 N 100 West; mains $22-40; 5-10pm) A historic sandstone building serves as home to one of the latest stars on the local dining scene. Jeffrey's is serious about beef, which comes grain-fed, wagyu-style and in generous cuts. If the night is too good to end, head upstairs to the upscale Ghost Bar. Reservations advised.
### HOLE 'N THE ROCK
An unabashed tourist trap 12 miles south of Moab, Hole 'n the Rock (www.moab-utah.com/holeintherock; 11037 S Hwy 191; adult/child $5/3; 9am-5pm; ) is a 5000-sq-ft home-cum-cave carved into sandstone and decorated in knockout 1950s kitsch. What _weren't_ owners Albert and Gladys Christensen into? He was a barber, a painter, an amateur engineer and a taxidermist; she was a cook (the cave once housed a restaurant) and lapidary jeweler, and they lived in the blasted-out home until 1974. The hodgepodge of metal art, old signs, small petting zoo and stores make it worth the stop, but you have to tour the surprisingly light-filled home to believe it.
Moab Brewery AMERICAN $$
(686 S Main St; mains $8-18; 11:30am-10pm Mon-Thu, 11:30am-11pm Fri & Sat) A good bet for a group with diverse tastes. Choosing from the list of microbrews made in the vats just behind the bar area may be easier than deciding what to eat off the vast and varied menu.
Milt's BURGERS $
(356 Mill Creek Dr; mains $3-6; 11am-8pm Mon-Sat) Pull up one of only a handful of stools at this tiny 1954 burger stand, or order through the screen window and eat under the tree. Locals love the chili cheeseburgers,hand-cut fries and oh-so-thick milkshakes (try butterscotch-banana).
Buck's Grill House MODERN SOUTHWESTERN $$-$$$
(1394 N Hwy 191; mains $15-36; 5:30-9:30pm) Contemporary Southwestern specialties, such as duck tamales with adobo and elk stew with horseradish cream, are what Buck's does best (there are veggie options, too). Opt for white tablecloth service in the restaurant, or a more casual evening in the bar.
EklectiCafé ORGANIC $
(352 N Main St; breakfast & sandwiches $5-7; 7am-2:30pm Mon-Sat, to 1pm Sun; ) Soy-ginger-seaweed scrambled eggs anyone? This wonderfully quirky cafe lives up to its eclectic name in food choice and decor. Come for organic coffee, curried wraps and vegetarian salads. Dinner served some weekend evenings.
Sorrel River Grill MODERN AMERICAN $$$
( 435-259-4642; Sorrel River Ranch, Mile 17, Hwy 128; breakfast $10-12, lunch $12-15, dinner $24-40; 7am-3pm & 5-10pm Mar-Oct, 8-10am & 5:30-7:30pm Nov-Feb) For romance, it's hard to beat the wraparound verandah overlooking red-rock canyons outside Moab. The New American menu changes seasonally, but expect seared steaks, succulent rack of lamb and the freshest seafood flown in.
Desert Bistro MODERN SOUTHWESTERN $$$
( 435-259-0756; 1266 N Hwy 191; mains $20-50; 5:30-10pm Mar-Oct) Stylized preparations of game and seafood are the specialty at this welcoming white-tablecloth restaurant inside an old house. Everything is made on site, from freshly baked bread to delicious pastries. Great wine list, too
Miguel's Baja Grill MEXICAN $$
(51 N Main St; mains $12-20; 5-10pm) Dine on Baja fish tacos and margaritas in the sky-lit breezeway patio lined with brightly painted walls. Fajitas, _chile rellenos_ (stuffed peppers) and seafood mains are all ample sized.
Singha Thai THAI $$
(92 E Center St; mains $13-18; 11am-9:30pm Mon-Sat, 5-9pm Sun) Ethnic food is rare as rain in these parts, so locals pile into this authentic Thai cafe for curries and organic basil chicken. No bar.
Sabuku Sushi FUSION $$
(101 N Main St; breakfast $7-15; 11am-2pm & 5-10pm) Newcomer Sabuku impresses with fresh sushi, inventive vegetarian rolls and small plates such as elk _tataki_ (like carpaccio, with an Asian twist).
Paradox Pizza PIZZERIA $$
( 435-259-9999; 729 S Main St; pizzas $12-22; shop 11am-10pm, delivery 4-10pm) You may want to order your scrumptious locally-sourced and organically-oriented pizzas to go; the dining area is kinda small and generic. Our favorite? The 'fun guy', with whole-milk mozzarella and ricotta, plus portabellas.
Eddie McStiff's AMERICAN $$
(59 S Main St; mains $10-20; 11:30am-midnight, until 1am Fri & Sat) Though it's as much microbrewery-bar as restaurant, the burgers and pizzas (gluten-free available) are almost as popular as the beer here.
Zax AMERICAN $-$$
(96 S Main St; breakfast $5-9, sandwiches $8-10, mains $16-22; 7am-10pm) Dining out in Moab can get expensive, so locals load up at the all-you-can-devour soup, pizza and salad bar ($12) in this semi-generic American eatery.
Jailhouse Café BREAKFAST $$
(101 N Main St; breakfast $11-14; 11am-noon Mar-Oct) The eggs benedict here is hard to beat but it ain't cheap. You're paying for the cute former-jailhouse and patio setting.
Peace Tree Café AMERICAN $
(20 S Main St; wraps $4-8, mains $16-24; 8am-6pm Nov-Feb, 8am-8pm Mar-Oct) Fresh fruit smoothies, sandwich wraps and healthy mains to take out or eat in.
Moonflower Market HEALTH FOOD $
(39 E 100 N; 9am-8pm Mon-Sat, 10am-3pm Sun) Nonprofit health food store with loads of community info.
Moab Farmers Market MARKET $
(400 N 100 West; 8am-noon Sat May-Oct) Local farms vend their summer produce in Swanny City Park.
City Market & Pharmacy MARKET $
(425 S Main St; 6am-midnight) Moab's largest grocery store, with sandwiches and salad bar to go.
#### Drinking
The two local brewpub restaurants, Moab Brewery and Eddie McStiff's, are good places to drink as well as eat, and the latter often has live music.
Wake & Bake CAFE
(McStiffs Plaza, 59 S Main St; 7am-7pm; ) Great vibe at this groovy cafe next to a bookstore; ice cream and sandwiches available.
Dave's Corner Market COFFEE SHOP
(401 Mill Creek Dr; 6am-10pm) Sip shade-grown espresso with locals at the corner convenience store.
Woody's Tavern BAR
(221 S Main St) Full bar with great outdoor patio; live music Friday and Saturday in season.
Ghost Bar BAR
(218 N 100 West; 7-11pm) A loungey, dime-sized jazz nook serving wine and a full list of cocktails; upstairs at Jeffrey's Steakhouse.
Red Rock Bakery & Cafe CAFE
(74 Main St; internet per ½hr $2; 7am-6pm; ) This tiny coffeehouse has tasty baked goods - and three internet terminals for web surfing.
#### Entertainment
Bar-M Chuckwagon DINNER SHOW
( 435-259-2276, 800-214-2085; www.barmchuckwagon.com; Hwy 191; adult/child $25/12.50; Apr-Oct; ) Reserve ahead for a night of unapologetic tourist fun, 7 miles north of Moab. The evening starts with a gunfight in a faux Western town, followed by a cowboy Dutch-oven dinner and Western music show.
Canyonlands by Night & Day DINNER SHOW
( 435-259-5261, 800-394-9978; www.canyonlandsbynight.com; 1861 N Hwy 191; adult/child $65/55; Apr-Oct; ) Start with dinner riverside, then take an after-dark boat ride on the Colorado with an old-fashioned light show complete with historical narration.
Moab Arts & Recreation Center CONCERT VENUE
(www.moabcity.state.ut.us/marc; 111 E 100 N) The rec center hosts everything from yoga classes to contra dance parties and poetry gatherings.
#### Shopping
Every few feet along downtown's Main St, there's a shop selling T-shirts and Native American-esque knickknacks, but there are good galleries among the mix. Every second Saturday in spring and fall there's an evening artwalk that includes artist's receptions; contact the Moab Arts Council (www.moabartscouncil.org) for more information. Note that from March to October most stores stay open until 9pm.
Desert Thread ARTS & CRAFTS
(29 E Center St) Pick up a gorgeous hand-knitted scarf or bag, or buy supplies to do it yourself.
Arches Book Company & Back of Beyond BOOKS
(83 N Main St; ) Excellent, adjacent indie bookstores with extensive regional selection. Coffee shop on site.
#### Information
###### Emergency
Cell phones work in town, but not in canyons or the parks.
Grand County Emergency Coordinator ( 435-259-8115) Search and rescue.
Police ( 911)
###### Medical Services
Moab Regional Hospital ( 435-259-7191; 719 W 400 N) For 24-hour emergency medical care.
###### Tourist Information
BLM ( 435-259-2100; www.blm.gov/utah/moab) Phone and internet info only.
Moab Information Center (cnr Main & Center Sts; 8am-8pm) Excellent source of information on area parks, trails, activities, camping and weather. Extensive bookstore and knowledgeable staff. Walk-in only.
###### Websites
Moab Area Travel Council (www.discovermoab.com) Comprehensive online resource.
Moab Happenings __ (www.moabhappenings.com) Events listings.
#### Getting There & Around
Moab is 235 miles southeast of Salt Lake City, 150 miles northeast of Capitol Reef National Park, and 115 miles southwest of Grand Junction, CO.
Great Lakes Airlines ( 800-554-5111; www.flygreatlakes.com) has regularly scheduled flights from Canyonlands Airport (CNY; www.moabairport.com; off Hwy 191), 16 miles north of town, to Denver, CO, Las Vegas, NV, and Page, AZ. Major car-rental agencies have representatives at the airport. Roadrunner Shuttle ( 435-259-9402; www.roadrunnershuttle.com) and Coyote Shuttle ( 435-260-2097; www.coyoteshuttle.com) offer on-demand Canyonland Airport, hiker-biker and river shuttles.
Moab Luxury Coach ( 435-940-4212; www.moabluxurycoach.com) operates a scheduled van service to and from SLC (4¾ hours, $149 one-way) and Green River (one hour, $119 one-way).
A private vehicle is pretty much a requirement to get around Moab and the parks. But on weekday evenings and weekends, Moab Pedicab Company ( 435-210-1382) runs a luxury bike taxi – hail it on the street or call dispatch.
### Arches National Park
Giant sweeping arcs of chunky sandstone frame snowy peaks and desert landscapes at Arches National Park, 5 miles north of Moab. The park boasts the highest density of rock arches anywhere on Earth: more than 2500 in a 116-sq-mile area. You'll lose all perspective on size at some, such as the thin and graceful Landscape Arch, which stretches more than 290ft across (one of the largest in the world). Others are tiny, the smallest only 3ft across. Once you train your eye, you'll spot them everywhere (like a giant game of _Where's Waldo?_ ). An easy drive makes the spectacular arches accessible to all. Fiery Furnace is a not-to-be-missed area of the park, though a guided tour is required to reach it.
#### Sights & Activities
The park (admission 7-day, per vehicle $10) has many short hikes; the most popular stops lie closest to the visitor center. Crowds are often unavoidable, and parking areas overflow on weekends, spring to fall. In summer arrive by 9am, when crowds are sparse and temperatures bearable, or visit after 7pm and enjoy a moonlight stroll. July highs average 100°F (38°C); carry at least one gallon of water per person if hiking. Two rugged backroads lead into semi-solitude, but 4WD is recommended – ask at the visitor center.
Rock climbing is allowed only on unnamed features. Routes require advanced techniques. No permits are necessary, but ask rangers about current regulations and route closures. For guided canyoneering into the Fiery Furnace, contact an outfitter in Moab.
There are also some fairly easy hikes here, too. Many quick walks lead to named formations, such as Sand Dune Arch (0.4-mile round-trip) and Broken Arch (1-mile round-trip).
### SHOWERING ESSENTIALS
Area BLM, national and state park campgrounds do not have showers. You can wash up at several in in-town campgrounds, and at biking outfitter Poison Spider Bicycles, for a small fee ($3 to $6).
Scenic Drive DRIVING TOUR
The park's one main road snakes up ancient Navajo sandstone, past many trailheads and incredible formations, such as Park Avenue, a mile-long trail past a giant fin of rock reminiscent of a New York skyline, and Balanced Rock, a 3577-ton boulder sitting atop a spindly pedestal, like a fist shooting out of the earth. Don't miss the two small spur roads that veer off to the west (43 miles round-trip total). Sights listed here are all along this drive; use the park map received on entry to navigate.
Delicate Arch HIKING
You've seen this arch before: it's the unofficial state symbol and is pictured on what seems like every piece of Utah tourist literature ever printed. The best way to experience the arch is from beneath it. Park near Wolfe Ranch, a well-preserved 1908 pioneer cabin. From there a footbridge crosses Salt Wash (near Native American rock art) and marks the beginning of the moderate-to-strenuous, 3-mile round-trip trail to the arch itself. The trail ascends slickrock, culminating in a wall-hugging ledge before reaching the arch. Tip: ditch the crowds by passing beneath the arch and continuing down the rock by several yards to where there's a great view, but fewer folks (bring a picnic). If instead you drive past the ranch to the end of the spur road, there's a 50yd paved path (wheelchair accessible) to the Lower Delicate Arch Viewpoint.
Windows Trail HIKING
Tight on time? Do part or all of the easy 1-mile round-trip, which brings you up to North Window, where you can look out to the canyon beyond. Continue on to South Window and castle-like Turret Arch. Don't forget to see Double Arch, just across the parking lot.
Fiery Furnace HIKING
Advance reservation is usually necessary for the three-hour ranger-led Fiery Furnace hikes (adult/child $10/5; Mar-Oct) that explore the maze of spectacularly narrow canyons and giant fins. This is no walk in the park. (Well, it is, but...) Be prepared to scramble up and over boulders, chimney down between rocks and navigate narrow ledges. The effort is rewarded with a surprising view – an incredibly thin arch or soaring slot – around every turn. The ranger stops plenty of times to talk (and let hikers rest).
If you're an accomplished route-finder and want to go it alone, you must pay a fee, watch a video and discuss with rangers how to negotiate this confusing jumble of canyons before they'll grant you a permit. A few outfitters in Moab have permits to lead hikes here as well.
Devils Garden Trail HIKING
At the end of the paved road, 19 miles from the visitor center, Devils Garden trailhead marks the beginning of a 2- to 7.7-mile round-trip hike that passes at least eight arches. Most people only go the relatively easy 1.3 miles to Landscape Arch, a gravity-defying 290ft-long behemoth. Further along the trail gets less crowded, and grows rougher and steeper toward Double O Arch and Dark Angel Spire. The optional, difficult Devils Garden Primitive Loop has narrow-ledge walking and serious slickrock hiking. Ask rangers about conditions before attempting.
#### Sleeping & Eating
Devils Garden Campground CAMPGROUND $
( 877-444-6777; www.recreation.gov; tent & RV sites $20) Don't expect much shade, just red rock and scrubby piñon trees at the park's only campground, 19 miles from the visitor center. A few of the sites at the top have La Sal Mountain views. From March to October only, half the sites are available by reservation. Otherwise, it's first-come, first-served.For same-day availability check at the visitor center, not the campground. Facilities include drinking water, picnic tables, grills and toilets, but no showers (available in Moab). RVs up to 30ft are welcome, but generator hours are limited; no hookups.
No food is available in the park. Again, Moab is the place to stock up or dine out.
#### Information
Cell phones do not work in most of the park.
Canyonlands Natural History Association (www.cnha.org) Sells area-interest books and maps online, and at national park visitor centers.
Grand County Emergency Coordinator ( 435-259-8115) Search and rescue coordinator.
Visitor center (www.nps.gov/arch; 7-day per vehicle $10; 24hr, visitor center 7:30am-6:30pm Apr-Oct, 8am-4:30pm Nov-Mar) Watch the informative video, check ranger-led activityschedules and pick up your Fiery Furnace tickets here.
#### Getting There & Around
One may be instituted eventually, but as yet the park has no shuttle system and no public buses. So you pretty much need your own wheels. Several outfitters in Moab run motorized park tours: Moab Adventure Center and Adrift Adventures have scenic drive van tours; Tag-A-Long Expeditions ventures into the backcountry.
### ROCK FORMATIONS 101
The magnificent formations you see throughout southern Utah are created by the varying erosion of sandstone, mudstone, limestone and other sedimentary layers. When water freezes and expands in cracks it forms fins: thin, soaring, wall-like features like those in the Fiery Furnace at Arches. When portions of the rock break away underneath, an arch results. A bridge forms when water passes beneath sandstone, causing its erosion. But rivers dry up or change course, so it can sometimes become difficult to tell a bridge from an arch. Hoodoos are freestanding pinnacles that have developed from side-eroding fins; layers disintegrate at different rates, creating an irregular profile (often likened to a totem-pole shape). Though they look stable, rock formations are forever in flux, and eventually they all break and disappear. As you stroll beneath these monuments to nature's power, listen carefully, especially in winter, and you may hear spontaneous popping noises in distant rocks – it's the sound of the future forming. (If you hear popping noises _overhead,_ however, run like heck!)
### Green River
This laid-back little town is primarily useful as a base for river running on – guess where? The Green River, go figure. The Colorado and Green Rivers were first explored in 1869 and 1871 by the legendary one-armed Civil War veteran, geologist and ethnologist John Wesley Powell. The town was settled in 1878, and now mainly relies on the limited tourism for income. Accommodations may be slightly cheaper here than in Moab, 53 miles southeast, but there are far fewer services. If you're passing through the third weekend in September, be sure to attend the Melon Days festival; this is, after all, the 'world's watermelon capital'.
#### Sights
Outside of town there is an unpredictable geyser, and fossil track sites; ask at the visitor center for directions.
John Wesley Powell River History Museum MUSEUM
(www.jwprhm.com; 885 E Main St; adult/child $3/1; 8am-7pm Apr-Oct, 9am-5pm Tue-Sat Nov-Mar) Learn about John Wesley Powell's amazing travels at this comprehensive museum, with a 20-minute film based on his diaries. It has good exhibits on the Fremont Indians, geology and local history.
Green River State Park PARK
(www.stateparks.utah.gov; Green River Blvd; per car $5; 7am-10pm Mar-Oct, 8am-5pm Nov-Feb) Shady Green River State Park has picnic tables, a boat launch and a nine-hole golf course, but no trails.
#### Activities
White-water rafting trips are the most popular, but the Green River is flat between the town and the confluence of the Colorado River, making it good for floats anddo-it-yourself canoeing. But the current is deceptively strong – swim only with a life jacket.
Moki Mac River Expeditions RAFTING
( 435-564-3361, 800-284-7280; www.mokimac.com; 220 E 700 South) Rent a canoe ($25 per day), take an easy day-float (per adult/child $69/55), or book a single- to multiday white-water raft (from $100 per person, per day).
Holiday Expeditions RAFTING
( 435-564-3273, 800-624-6323; www.holidayexpeditions.com; 10 Holiday River St) Multiday rafting tours; themed trips (naturalist, women-only, mountain biking) available.
Colorado River & Trail RAFTING
( 801-261-1789, 800-253-7328; www.crateinc.com) Though based in Salt Lake City, this outfitter offers several Green River-launched rafting trips.
#### Sleeping
Midrange chain motels are surprisingly well represented along Business 70 (Main St).
Green River State Park CAMPGROUND $
( 800-322-3770; http://utahstateparks.reserveamerica.com; tent & RV sites $16) Though the 42 green and shady campsites in this riverfront park are open year-round, the restrooms are closed December through February. Water, showers and boat launch on site; no hookups.
Robbers Roost Motel MOTEL $
( 435-564-3452; www.rrmotel.com; 325 W Main St; s $31-38, d $40-45; ) What a great mini motorcourt motel. Staff are super accommodating and small-and-simple budget rooms are well cared for.
River Terrace Inn MOTEL $$
( 435-564-3401, 877-564-3401; www.river-terrace.com; 1880 E Main St; r incl breakfast $110-106; ) Ask for a riverfront room, with a terrace overlooking the water. There's a full-service restaurant, and the free breakfast bar includes omelets.
Shady Acres RV Park CAMPGROUND $
( 435-564-8290, 800-537-8674; www.shadyacresrv.com; 350 E Main St; tent sites $20-27, RV sites $33-36, camping cabins $42; ) 16-acre campground with lots of facilities: playground, dog run, associated laundromat, internet cafe and sandwich shop.
#### Eating & Drinking
Roadside stands sell fresh watermelons in summer.
Ray's Tavern BURGERS $$
(25 S Broadway; mains $8-26; 11am-10pm) Residents and rafters alike flock to this local beer joint for the best hamburgers and fresh-cut French fries around. The steaks aren't bad either. Pass the time reading the displayed T-shirts donated by river runners from around the world, or have a game of pool with a Utah microbrew in hand.
Green River Coffee Co CAFE $
(115 W Main St; breakfast & lunch sandwiches $5-8; 7am-5pm; ) As the sign says, 'We're open when we're here.' Drop in and discuss politics with the local coffee circle, grab a sandwich or catch up on your used-book reading at this super-relaxed coffeehouse.
Desert Flavors ICE CREAM $
(cnr Main St & Broadway; treats $2-6; 8am-4pm Apr-Oct) Homemade ice cream flavors may include watermelon or 'Green River mud', their own version of rocky road.
Melon Vine Food Store MARKET $
(76 S Broadway; 8am-7pm Mon-Sat) Grocery store; deli sandwiches available.
#### Information
Emery County Visitor Center ( 435-564-3600, 888-564-3600; www.emerycounty.com/travel; 885 E Main St; 8am-8pm Mar-Oct, 8am-4pm Tue-Sun Nov-Feb) Attached to the local museum, pick up info and river guide books and maps here.
#### Getting There & Around
Green River is 182 miles southeast of SLC and 53 miles northwest of Moab. It is the only town of note along I-70 between Salina, UT (108 miles west), and Grand Junction, CO (102 miles east) –so fuel up.
Amtrak ( 800-872-7245; www.amtrak.com; 250 S Broadway) Green River is the only stop on the daily California Zephyr train run in southeastern Utah. Next stop east is Denver, CO ($85, 10¾ hours).
Greyhound ( 435-564-3421, 800-231-2222; www.greyhound.com; Rodeway Inn, 525 E Main St) Buses go to Grand Junction, CO ($36, one hour and 40 minutes).
Moab Luxury Coach ( 435-940-4212; www.moabluxurycoach.com; Rodeway Inn, 525 E Main St) Operates a scheduled van service to and from SLC ($149 one-way, 3½ hours) and Moab ($119 one-way, one hour).
### Goblin Valley State Park & Around
A Salvador Dali-esque melted-rock fantasy,a valley of giant stone mushrooms, an otherworldly alien landscape or the results of an acid trip the creator went on? No matter what you think the stadium-like valley of stunted hoodoos resembles, one thing's for sure: the 3654-acre Goblin Valley State Park (www.stateparks.utah.gov; Goblin Valley Rd, off Hwy 24; per car $7; park 6am-10pm, visitor center 8am-5pm) is just plain fun. A few trails lead down from the overlooks to the valley floor, but after that there's no path to follow. You can climb down, around and even over the evocative 'goblins' (2ft to 20ft-tall formations). Kids, photographers and Lonely Planet writers especially love it. The park is 46 miles southwest of Green River.
A 19-site campground ( 800-322-3770; http://utahstateparks.reserveamerica.com; tent & RV sites $16) has little shade; nevertheless it books up on most weekends. Water and showers, but no hookups. West of the park off Goblin Valley Rd is BLM land – free dispersed camping, no services (stay on designated roads).
Twenty miles further south on Hwy 24 is Hanksville (population 350, elevation 4300ft). If you don't need gas, there's little reason to stop. It's better to stay in Green River, Torrey or at Lake Powell, depending on where you're headed. The BLM Field Office ( 435-542-3461; 380 S 100 West; 8:30am-4:30pm Mon-Fri) has maps and information for surrounding lands, particularly the Henry Mountains. If you have to stay, Whispering Sands Motel ( 435-542-3238; www.whisperingsandsmotel.com; 90 S Hwy 95; r $70-90; ) is the town's nicest lodging, though that's not saying much. Before continuing south, fill up your car and carry your own food and water. There are no more services until you get to Bullfrog Marina (70 miles) or Mexican Hat (130 miles).
### HENRY MOUNTAINS
Southwest of Hanksville, the majestic Henry Mountains (11,500ft) was the last range to be named and explored in the lower 48. It's so remote that the area was famous as a hiding place for outlaws such as Butch Cassidy. The range is home to one of the country's remaining free-roaming (and elusive) wild bison herds; you can expect pronghorn antelopes, mule deer and bighorn sheep as well. Exploring here is for serious adventurers only.
There are two main access roads: from Hanksville, follow 1100 East Street to the south, which becomes Sawmill Basin Rd; from Hwy 95, about 20 miles south of Hanksville, follow the Bull Mountain Scenic Backway west. Both are very rough and rocky dirt roads; flat tires are common and 4WD vehicles are highly recommended. Rangers patrol infrequently. Contact the BLM Field Office in Hanksville for more information.
### Glen Canyon National Recreation Area & Lake Powell
In the 1960s construction of a massive dam flooded Glen Canyon, forming Lake Powell, a recreational playground. Almost 50 years later this is still an environmental hot-buttontopic, but generations of Western families have grown up boating here. Water laps against stunning, multihued cliffs that rise hundreds of feet; narrow channels and tributary canyons twist off in every direction.
Lake Powell stretches for more than 185 miles, surrounded by millions of acres of desert incorporated into the Glen Canyon National Recreation Area (7-day per vehicle $15). Most of the watery way lies within Utah. However, Glen Canyon Dam itself, the main Glen Canyon National Recreation Area visitor center, the largest and most developed marina (Wahweap) and the biggest town on the lake (Page) are all in Arizona. For more on services, and sights such as Rainbow Bridge, see Click here.
In Utah, primary access is 70 miles south of Hanksville; check in at the Bullfrog Visitor Center ( 435-684-7423; 9am-5pm Mar-Oct) for general info. At the end of the road, Bullfrog Marina ( 435-684-3000; www.lakepowell.com; Hwy 276; 9am-4pm Mar-Oct) rents out boats – 19ft runabouts ($400) and personal watercraft ($335) – by the day, but houseboats are its big business. You can rent a 46ft boat that sleeps 12 for between $2500 and $4000 per week. Invest in the waterproof _Lake Powell Photomap_ ($11) so you can pilot your craft to some great canyon hikes.
Landlubbers can spend the night at the marina's waterfront Defiance House Lodge ( 435-684-3000; www.lakepowell.com; Hwy 276; r $140-175; Mar-Oct) and eat at Anasazi Restaurant (Hwy 276; breakfast $8-12, mains $10-28; 7am-10pm Mar-Oct). The restaurant serves pretty standard all-American fare, but it does try to use local produce and sustainable practices. Also on site: a small convenience store, marine fuel and trailer parking. The 24-space campground ( 435-684-3000; www.lakepowell.com; Hwy 276; tent & RV sites $34-38; Mar-Oct; ), with showers, is just up the road. The pavement is wide (50ft pull-throughs), but there's little ground cover.
Inland, 12 miles or so from the marina, there are a couple of marine-service/gas-station/convenience-store/deli complexes. Ticaboo Lodge ( 435-788-2110; www.ticaboo.com; Hwy 276; r $70-90; May-Sep; ) is a sleeping alternative with a three-meal-a-day restaurant and bar attached.
To continue south along Hwy 276 you have to take the ferry ( 435- 684-3088; www.lakepowell.com; per car $25; closed Dec-Feb) to Hall's Crossing. The trip takes about 30 minutes. There are four crossings a day between 9am and 4pm, June to August; only two boats run between 9am and 2pm, March through May and between 10am and 3pm September through November.
The Hall's Crossing ( 435-684-7000; www.lakepowell.com; 8am-4pm Mar-Oct) marina has a store, boat launch, great kid's playground and campground (tent & RV sites $34-38; Mar-Oct; ). At the time of writing Hite Marina remained closed due to low water levels.
## ZION & SOUTHWESTERN UTAH
Wonder at the deep-crimson canyons of Zion National Park, hike among the delicate pink-and-orange minarets at Bryce Canyon, drive past the swirling grey-white-and-purple mounds of Capitol Reef. Southwestern Utah is so spectacular that the vast majority of the territory has been preserved as national park or forest, state park or BLM wilderness. Rugged and remote Grand Staircase-Escalante National Monument (GSENM) is larger than Rhode Island and Delaware put together. The whole area is ripe for outdoor exploration, with narrow slot canyons to shoulder through, pink sand dunes to scale and wavelike sandstone formations to seek out.
Several small towns, including artsy Springdale, service these parks. But do note that getting to some of the most noteworthy sites can be quite an uphill hike. Elevation changes in the region – mountainous highs to desert lows – pose an additional weather challenge. In the end, any effort you make usually more than pays off with a stunning view of our eroding and ever-changing Earth.
(Note that you'll average no more than 35mph to 50mph on scenic highways in the area.)
### Capitol Reef National Park
Native Americans once called this colorful landscape of tilted buttes, jumbled rocks and sedimentary canyons the Land of the Sleeping Rainbow. The park's centerpiece is Waterpocket Fold, a 100-mile-long monocline (a buckle in the Earth's crust) that blocked explorers' westward migration like a reef blocks a ship's passage. Known also for its enormous domes – one of which kinda sorta resembles Washington DC's Capitol Dome – Capitol Reef harbors fantastic hiking trails, rugged 4WD roads and 1000-year-old Fremont petroglyph panels. At the park's heart grow the shady orchards of Fruita, a Mormon settlement dating back to the 1870s.
The narrow park runs north-south following the Waterpocket Fold. A little over 100 miles southwest of Green River, Hwy 24 traverses the park. Capitol Reef's central region is the Fruita Historic District. To the far north lies Cathedral Valley, the least-visited section, and toward the south you can cross over into Grand Staircase-Escalante National Monument on the Burr Trail Rd. Most services, including food, gas and medical aid, are in the town of Torrey, 11 miles west.
### MESA FARM MARKET
About 23 miles east of Capitol Reef's visitor center, near Mile 102, is Mesa Farm Market ( 435-487-9711; Hwy 24, Caineville; 7am-7pm Mar-Oct). Stop here for straight-from-the-garden organic salads, freshly baked artisan bread and cinnamon rolls, homemade cheeses, homegrown organic coffee and fresh-squeezed juices. Note that hours do vary.
#### Sights & Activities
There's no fee to enter or traverse the park in general, but the Scenic Drive has an admission fee. Remember that Capitol Reef has little shade. Drink at least one quart of water for every two hours of hiking and wear a hat. Distances listed for hiking are one-way. For backcountry hikes, ask for the information pamphlets at the visitor center or check online. Ranger Rick Stinchfield's _Capitol Reef National Park: The Complete Hiking and Touring Guide_ is also a great reference.
Technical rock climbing is allowed without permits. Note that Wingate Sandstone can flake unpredictably. Follow clean-climbing guidelines, and take all safety precautions. For details, check with rangers or see www.nps.gov/care.
Petroglyphs ARCHAEOLOGICAL SITE
Just east of the visitor center on Hwy 24, look for the parking lot for freely accessible petroglyphs; these are the rock-art carvings that convinced archaeologists the Fremont Indians were a group distinct from the Ancestral Puebloan. Follow the roadside boardwalk to see several panels.
Panorama Point & Gooseneck Overlook LOOKOUT
Two miles west of the visitor center off Hwy 24, a short unpaved road heads to Panorama Point and Gooseneck Overlook. The dizzying 800ft-high viewpoints above serpentine Sulphur Creek are worth a stop. Afternoon light is best for photography.
Fruita Historic District HISTORIC SITE
Fruita ( _froo_ -tuh) is a cool green oasis, where shade-giving cottonwoods and fruit-bearing trees line the Fremont River's banks. The first Mormon homesteaders arrived here in 1880; Fruita's final resident left in 1969. Among the historic buildings, the NPS maintains 2700 cherry, apricot, peach, pear and apple trees planted by early settlers. Visit between June and October and pluck ripe fruit from the trees, for free, from any unlocked orchard. For availability, ask rangers or call the fruit hotline ( 435-425-3791). Pick only mature fruit; leave the rest to ripen. Near the orchards is a wonderful picnic area, with roaming deer and birds in the trees – a desert rarity.
Across the road from the blacksmith shop (just a shed with period equipment) is the Ripple Rock Nature Center ( noon-5pm daily Jun, 10am-3pm Tue-Sat Jul-Aug; ), a family-oriented learning center. The Gifford Homestead ( 8am-5pm Mar-Oct) is an old homestead museum where you can also buy fruit-filled minipies and jams.
Scenic Dr SCENIC DRIVE
(per week, per vehicle $7; 24hr) Pay admission at the visitor center or self-service kiosk to go beyond Fruita Campground on the 9-mile-long, paved Scenic Dr. Numbered roadside markers correspond to an interpretive driving tour available at the visitor center or online. The best part is the last 2 miles between the narrow sandstone walls of Capitol Gorge – it'll knock your socks off. To continue south past Pleasant Creek, a 4WD vehicle is advised.
Capitol Gorge Trail HIKING
At the end of Scenic Dr is Capitol Gorge Trail (1 mile, easy), which leads past petroglyphs. Spur trails lead to Pioneer Register, where names carved in the rock date back to 1871, and the Tanks, giant water pockets. Look for the spur to the Golden Throne formation off Capitol Gorge Trail (another mile).
Grand Wash Trail HIKING
Also along Scenic Dr, a good dirt road leads to Grand Wash Trail (2.25 miles, easy), a flat hike between canyon walls that, at one point, tower 80 stories high but are only 15ft apart. You can follow an offshoot to Cassidy Arch (2 miles).
Hickman Bridge Trail HIKING
This popular walk (1 mile, moderate) includes a canyon stretch, a stunning natural bridge and wildflowers in spring. Mornings are coolest; it starts about 2 miles east of the visitor center off Hwy 24.
Notom-Bullfrog Rd SCENIC DRIVE
This is a rough, rough road that heads south from Hwy 24 (5 miles east of the visitor center) paralleling Waterpocket Fold. Thirty-two miles south, you can turn west toward Hwy 12 and Burr Trail Rd (Click here) in Grand Staircase-Escalante National Monument. Along the way, Strike Valley Overlook has one of the best comprehensive views of the Waterpocket Fold itself. If you instead continue south, you're on the way to Lake Powell and Bullfrog Marina in Glen Canyon National Recreation Area, another 35 miles away.
Cathedral Valley Loop MOUNTAIN BIKING, SCENIC DRIVE
(Caineville Wash Rd) Long-distance mountain bikers and 4WDers love this 58-mile route through Cathedral Valley, starting 18.6 miles east of the visitor center. The bumpy, roughshod backcountry road explores the remote northern area of the park and its alien desert landscapes, pierced by giant sandstone monoliths eroded into fantastic shapes. Before starting, check conditions at the visitor center and purchase an interpretive route guide.
Capitol Reef National Park
Sights
1Cassidy Arch B2
2Fruita Historic District B2
Gifford Homestead (see 2)
3Golden Throne B3
4Panorama Point B2
5Petroglyphs B2
6Pioneer Register B3
Ripple Rock Nature Center (see 2)
7Tanks C3
Activities, Courses & Tours
8Hickman Bridge Trail B2
Sleeping
9Cathedral Valley Campground A1
10Cedar Mesa Campground C4
11Fruita Campground B2
#### Sleeping & Eating
The nearest motel lodging and dining are, again, in Torrey.
Fruita Campground CAMPGROUND $
(Scenic Dr; campsites $10) The terrific71-site Fruita Campground sits under maturecottonwood trees alongside the Fremont River, surrounded by orchards. First-come, first-served sites have access to water, but no showers. Spring through fall, sites fill up early.
Free primitive camping is possible year round at Cathedral Valley Campground at the end of River Ford Rd, and at Cedar Mesa Campground, about 23 miles south along Notom-Bullfrog Rd.
#### Information
Occasional summer thunderstorms pose a serious risk of flash flooding. Always check weather with rangers at the visitor center. Bugs bite in May and June. Summer temperatures can exceed 100°F (38°C) at the visitor center (5400ft), but it's cooler than Moab. If it's too hot, ascend to Torrey (10°F, or 6°C, cooler) or Boulder Mountain (30°F, or 17°C, cooler).
Visitor center ( 435-425-3791; www.nps.gov/care; cnr Hwy 24 & Scenic Dr; 8am-6pm Jun-Aug, 8am-4:30pm Sep-May) Inquire about ranger-led programs, watch the short film, then ooh and aah over the 64-sq-ft park relief map, carved with dental instruments. The bookstore sells several interpretive trail and driving tour maps (50¢-$2) as well as area-interest books and guides.
#### Getting Around
Capitol Reef has no public transportation system. Aside from Hwy 24 and Scenic Dr, park routes are dirt roads bladed only a few times a year. In summer you may be able to drive Notom-Bullfrog Rd and the Burr Trail in a regular passenger car. Remote regions like Cathedral Valley will likely require a high-clearance 4WD vehicle. Check weather and road conditions with rangers before heading out.
Bicycles are allowed on all park roads but not trails. Cyclists and hikers can arrange drop-off/pick-up shuttle services (from $25) with Hondoo Rivers & Trails ( 435-425-3519, 800-332-2696; www.hondoo.com; 90 E Main St, Torrey).
### Torrey
Old pioneer homestead buildings line the main street of this quiet town and, in the distance, stunning red-rock cliffs and mountains catch the light. Torrey's primary industry has long since shifted from logging and ranching to outdoor tourism. Capitol Reef National Park is only 11 miles east, Grand Staircase-Escalante National Monument is 40 miles south and national forests surround the town. In summer there's a whiff of countercultural sophistication in the air –and great dining – but from November to February the town shuts down.
#### Sights & Activities
Capitol Reef is the major area attraction, but there are other freely-accessible public lands nearby. Many of the main street lodgings have Native American arts and crafts for sale in their 'trading posts'.
Fishlake National Forest PARK
More than 300 miles of trails cover the mountainous forest; four-wheel drive roads lead north of town around Thousand Lake Mountain (11,306ft). Hwy 72, 17 miles west of town in Loa, is a paved route through the same area. Fish Lake, a giant trout fishery, is 21 miles northwest of Loa, off Hwy 25. Check with the Fremont River/Loa Ranger District Office ( 435-836-2811; www.fs.fed.us/r4/fishlake; 138 S Main St, Loa; 9am-5pm Mon-Fri) for info.
Dixie National Forest PARK
(www.fs.fed.us/dxnf) The expansive Dixie National Forest contains Boulder Mountain (11,317ft) to the south of Torrey. Nearby are numerous fishable lakes and streams, as well as campgrounds, hiking, biking and ATV trails. Teasdale Ranger Station ( 435-425-3702; 138 E Main St, Teasdale; 9am-5pm Mon-Fri), 4 miles southwest, is the nearest source of information.
#### Tours & Outfitters
Guides and outfitters cover the surrounding area well (Capitol Reef, national forest lands, Grand Staircase-Escalante National Monument and beyond). A half-day excursion runs from $90 to $225 per person.
Hondoo Rivers & Trails ADVENTURE SPORTS
( 435-425-3519, 800-332-2696; www.hondoo.com)One of southern Utah's longest-operating backcountry guides has half- and full-day hiking and driving tours that cover slot canyons and rock art, multiday horseback trail rides, and raft-and-ride combo trips.
Capitol Reef Backcountry Outfitters ADVENTURE SPORTS
( 435-425-2010, 866-747-3972; www.backcountryoutfitters.com; 875 E Hwy) In addition to 4WD and hiking packages, Backcountry Outfitters also rents bicycles ($40 per day) and ATVs ($150 per day). Shuttles and guided bike, ATV and horseback rides available, too.
Thousand Lakes RV Park FOUR-WHEEL DRIVING
( 435-425-3500, 800-355-8995; www.thousandlakesrvpark.com; 1110 W Hwy 24) Rents 4WD vehicles from $95 per day.
### HWY 12
Arguably Utah's most diverse and stunning route, Hwy 12 Scenic Byway (http://scenicbyway12.com) winds through rugged canyonland, linking several national parks on a 124-mile journey from near Capitol Reef southeast past Bryce Canyon. See how quickly and dramatically the land changes from wooded plateau to red-rock canyon, from slickrock desert to alpine forest, as it climbs over an 11,000ft mountain. Many consider the best section of the road to be the switchbacks and petrified sand dunes between Torrey and Boulder. Then again, the razor-thin Hogback Ridge between Escalante and Boulder is pretty stunning, too.
Pretty much everything in this chapter between Torrey and Panguitch is on or near Hwy 12. Highlights include foodie-oriented eateries in tiny tot Boulder, Lower Calf Creek Falls recreation area for a picnic, a hike in GSENM, and an incredible drive through arches and technicolor red rock in Red Canyon. Take time to stop at the many viewpoints and pullouts, especially at Mile 70, where the Aquarius Plateau lords over giant mesas, towering domes, deep canyons and undulating slickrock, all unfurling in an explosion of color.
Boulder Mountain Adventures &
Alpine Angler's Flyshop FISHING
( 435-425-3660; www.alpineadventuresutah.com; 310 W Main St) Guided fishing trips and multiday excursions that include both horseback riding and fishing.
#### Festivals
If you're here on the third weekend in July, don't miss the Bicknell International Film Festival (www.thebiff.org), just a couple miles up Hwy 24 in Bicknell. This wacky B-movie spoof on Sundance includes films, parties, a swap meet and the 'fastest parade in America'.
#### Sleeping
Camping is available in Capitol Reef National Park and in Dixie and Fishlake National Forests.
Torrey Schoolhouse B&B B&B $$
( 435-633-4643; www.torreyschoolhouse.com; 150N Center St; r incl breakfast $110-140; Apr-Oct; ) Ty Markham has done an exquisite job of bringing a spacious, 1914 schoolhouse back to life as a B&B. Dressed-down in country elegance, each airy room has light colors, high ceilings and well-chosen antiques. After consuming the full gourmet breakfast you might need to laze in the garden a while before you head out hiking.
Austin's Chuckwagon Motel MOTEL $
( 435-425-3335; www.austinschuckwagonmotel.com; 12 W Main St; r $75-85, cabins $135; Mar-Oct; ) Rustic wood buildings ring the pool and shady grounds here at the town center. Good value-for-money motel rooms have sturdy, basic furnishings; cabins also have kitchens. The on-site general store, deli and laundromat are a bonus.
Thousand Lakes RV Park CAMPGROUND $
( 435-425-3500, 800-355-8995; www.thousandlakesrvpark.com; Hwy 24; tent/RV sites $18/28, camping cabins $35-95; Apr-Oct; ) Twenty-two acres filled with facilities and services, including a heated swimming pool, playground, trading post gift shop, 4WD rental and evening cook-out dinners ($15 to $23). Morning muffins and hot coffee included.
Lodge at Red River Ranch INN $$-$$$
( 435-425-3322, 800-205-6343; www.redriverranch.com; 2900 W Hwy 24, Teasdale; r incl breakfast $160-245; ) In the grand old tradition of Western ranches, the great room here has a three-story open-beam ceiling, timber walls and Navajo rugs. Details are flawless – from the country quilts on high-thread-count sheets to the cowboy bric-a-brac decorating the lodge's fine-dining room. Wander the more than 2000 private acres, or enjoy the star-filled sky from the outdoor hot tub. No room TVs.
Rim Rock Inn MOTEL $
( 435-425-3398, 888-447-4676; www.therimrock.net; 2523 E Hwy 24; r $69-89; Mar-Nov; ) Among the red-rock cliffs east of town near Capitol Reef, this family-owned hilltop place offers basic, standard-issue motel rooms – with superb sunset vistas. Two good on-site restaurants share the views.
Muley Twist Inn B&B B&B $$
( 435-425-3640, 800-530-1038; www.muleytwistinn.com; 249 W 125 South Teasdale; r incl breakfast $99-140; Apr-Oct; ) Set against a towering red sandstone dome in a Teasdale neighborhood, the big wooden farmhouse with a wraparound verandah looks small. It isn't. Casual rooms at the down-to-earth inn are spacious and bright.
Pine Shadows Cabins BUNGALOW $$
( 435-425-3939, 800-708-1223; www.pineshadowcabins.net; 195 W 125 South, Teasdale; cabins $76-99; ) Spacious, modern cabins (two beds and kitchenette) sheltered among piñon pines at the end of the road, near trails.
Sandcreek RV Park CAMPGROUND $
( 435-425-3577; www.sandcreekrv.com; 540 Hwy 24; tent sites/RV sites/cabins $15/23/30; ) Friendly little campground with horseshoe pit, horse pasture ($5 per night) and laundry. Nonguest showers $3.
Torrey Trading Post MOTEL $
( 435-425-3716; www.torreytradingpost.com; 75 W Main St; cabins $35) Bare-bones but dirt-cheap cabins with shared bathroom.
Best Western Capitol Reef Resort MOTEL $$
( 435-425-3761, 888-610-9600; www.bestwesternutah.com; 2600 E Hwy 24; r $76-129; ) Plain-Jane chain, with stunning red-cliff balcony views.
Skyridge Inn MOTEL $
( 435-425-3222, 877-824-1508; www.skyridgeinn.com; 950 E Hwy 24; r incl breakfast $109-142; ) Country farmhouse B&B near town.
#### Eating & Drinking
The nearest supermarket is 16 miles west, in Loa.
Café Diablo MODERN SOUTHWESTERN $$$
( 435-425-3070; 599 W Main St; mains $25-40; 11:30am-10pm mid-Apr–Oct; ) One of southern Utah's best, Café Diablo serves outstanding, highly stylized Southwestern cooking – including succulent vegetarian dishes – bursting with flavor and towering on the plate. Think turkey _chimole_ (a spicy stew), __ Mayan tamales and fire-roasted pork tenderloin on a cilantro waffle. Book ahead, you don't want to miss this one.
### ON BUTCH CASSIDY'S TRAIL
Nearly every town in southern Utah claims a connection to Butch Cassidy (1866-?), the Old West's most famous bank and train robber. As part of the Wild Bunch, Cassidy (né Robert LeRoy Parker) pulled 19 heists from 1896 to 1901. Accounts usually describe him with a breathless romanticism, likening him to a kind of Robin Hood. Bring up the subject in these parts and you'll likely be surprised at how many folks' grandfathers had encounters. The robber may even have attended a dance in the old Torrey Schoolhouse (Click here), now a B&B. And many a dilapidated shack or a canyon, just over yonder, served as his hideout. The most credible claim for the location of the famous Robbers' Roost hideout is in the Henry Mountains (Click here).
In the wee town of Circleville, located 28 miles north of Panguitch, stands the honest-to-goodness boyhood home of the gun-slingin' bandit. The cabin is partially renovated but uninhabited, and is situated 2 miles south of town on the west side of Hwy 89. When reporters arrived after the release of the film _Butch Cassidy and the Sundance Kid_ (1969), they met the outlaw's youngest sister, who claimed that Butch did in fact not die in South America in 1908, but returned for a visit after that. Writers have been digging for the truth to no avail ever since. You can see where they filmed Robert Redford's famous bicycle scene at the Grafton ghost town (Click here), outside Rockville.
Local lore holds that Cassidy didn't steal much in Utah because this is where his bread was buttered. Whatever the reason, the Wild Bunch's only big heist in the state was in April 1897, when the gang stole more than $8000 from Pleasant Valley Coal Company in Castle Gate, 4 miles north of Helper on Hwy 191. The little Western Mining & Railroad Museum (296 S Main St, Helper; adult/child $2/1; 10am-5pm Mon-Sat May-Aug, 11am-4pm Tue-Sat Sep-Apr), 8 miles north of Price, has exhibits on the outlaws, including photos, in the basement. For more, check out _The Outlaw Trail_ , by Charles Kelly.
Slacker's Burger Joint BURGERS $
(165 E Main St; burgers $6-8; 11am-9pm Fri & Sat, 11am-8pm Mon-Thu, 11am-5pm Sun Mar-Oct) Orderan old-fashioned burger (beef, chicken,pastrami or veggie), hand-cut fries (the sweet-potato version is delish) and thick milkshake (in a rainbow of cool flavors like cherry cordial), then enjoy – inside, or out at the picnic tables.
Rim Rock Patio PIZZERIA $
(2523 E Hwy 24; mains $6-10; lunch & dinner Apr-Oct, dinner Nov-Mar) The best place in Torrey to drink beer also serves up good pizzas, salads, sandwiches and ice cream. Families and friends play darts or disc golf, listen to live bands and hangout.
Rim Rock Restaurant AMERICAN $$-$$$
(2523 E Hwy 24; mains $18-29; 5-9:30pm Mar-Dec) Grilled steaks, pastas and fish come with a million-dollar view of red-rock cliffs. Arrive before sunset for the best show. Full bar.
Robber's Roost Books & Beverages CAFE $
(185 W Main St; baked goods $1.50-3; 8am-4pm Mon-Sat, 1-4pm Sun May-Oct; ) Linger over a latte and a scone on comfy couches by the fire at this peaceful cafe-bookstore with bohemian bonhomie. Sells local-interest books and maps; also has three computer terminals (internet access per hour $5) and free wi-fi.
Castle Rock Coffee & Candy CAFE $
(cnr Hwys 12 & 24; breakfast & sandwiches $4-8; 7am-5pm Mar-Oct; ) The coffeehouse that serves Utah-roast brews, bakes its own candy and banana bread, and blends up fruit smoothies, now also serves breakfast and lunch. Try the Reuben sandwich.
Austin's Chuckwagon General Store MARKET $
(12 W Main St; 7am-10pm Apr-Oct) Sells camping supplies, groceries, beer and deli sandwiches to go.
### KIVA KOFFEEHOUSE
Just past the Aquarius Plateau at Mile 73 on Hwy 12, you reach the singular Kiva Koffeehouse ( 435-826-4550; www.kivakoffeehouse.com; soups & pastries $2-6; 8am-4:30pm Wed-Mon Apr-Nov). This round structure was built directly into the cliffside. Floor-to-ceiling glass windows, separated by giant timber beams, overlook the expansive canyons beyond. Besides serving barista coffee and yummy baked goods, Kiva also rents two cushy hideaway cottage rooms (r $170; ) with whirlpool tubs, fireplaces – and the same stellar views.
#### Entertainment
Support the local arts scene by attending an Entrada Institute (www.entradainstitute.org; Sat Jun-Aug) event, such as an author reading or evening of cowboy music and poetry, at Robber's Roost Books & Beverages.
#### Information
Austin's Chuckwagon General Store has an ATM.
Sevier Valley Hospital ( 435-896-8271; 1000 N Main St, Richfield) The closest full hospital is 60 miles west on I-70.
Wayne County Travel Council ( 435-425-3365, 800-858-7951; www.capitolreef.org; cnr Hwys 24 & 12; noon-7pm Apr-Oct) Friendly source of area-wide information.
#### Getting There & Around
Rural and remote, Torrey has no public transportation. Activity outfitters can provide hiker shuttles to the national park.
### Boulder
Though the tiny town of Boulder is only 32 miles south of Torrey on Hwy 12, you have to traverse 11,317ft-high Boulder Mountain to get there. Until 1940, this isolated outpost received its mail by mule. It's still so remote that the federal government classifies it as a 'frontier community'. Nevertheless, Boulder has a diverse population of down-to-earth folks that range from artists and ecologists to farmers and cowboys. It's a great little place, and well worth a stop. Stay longer and use it as a base to explore surrounding public lands. Note that pretty much all services shut down November through March.
#### Sights & Activities
Hikes in the northern area of Grand Staircase-Escalante National Monument are near here, but the national forest and BLM lands in the area are also good for hiking and backcountry driving. Burr Trail Rd (Click here) is the most scenic drive, but Hell's Backbone (Click here) has its thrills, too.
Anasazi State Park Museum MUSEUM
(www.stateparks.utah.gov; Main St/Hwy 12; admission $5; 8am-6pm Jun-Aug, 9am-5pm Sep-May) The pieced-back-together jars and jugs on display are just a few of the thousands and thousands of pottery shards excavated. Today the petite museum protects the Coomb's Site, excavated in the 1950s and inhabited from AD 1130 to 1175. The minimal ruins aren't as evocative as some in southeastern Utah, but the museum is well worth seeing for the re-created six-room pueblo and excellent exhibits about the Ancestral Puebloan peoples. Inside, there's a seasonal information desk where you can talk to rangers and get backcountry road updates.
Box-Death Hollow Wilderness Area HIKING
(www.blm.gov) This ruggedly beautiful wilderness area surrounds Hell's Backbone Rd. A 16-mile backpack, Boulder Mail Trail follows the mule route the post used to take.
Dixie National Forest HIKING
(www.fs.fed.us/dxnf) North of Boulder, the Escalante District of this 2 million-square-acre forest has trails and campgrounds, including a few up on Boulder Mountain.
Earth Tours HIKING
( 435-691-1241; www.earth-tours.com; trips per person from $150; Mar-Oct; ) Founder, and main guide, PhD geologist Keith Watt has an enthusiasm for the area that is catching. Choose from among the numerous half- and full-day area hikes offered or take a 4WD trip into the backcountry.
Escalante Canyon Outfitters HIKING
(ECO; 435-691-3037, 888-326-4453; www.ecohike.com; 2520 S Lower Deer Creek Rd; Mar-Nov) Started by cofounder of the Southern Utah Wilderness Alliance Grant Johnson, ECO hikes has well-regarded multiday treks with canyonland or archaeological-site focus.
Hell's Backbone Ranch & Trails HORSEBACK RIDING
( 435-335-7581; www.bouldermountaintrails.com;off Hell's Backbone Rd; half-day $80-95) Head across the slickrock plateau, into Box-Death Hollow Wilderness or up the forested mountain on two-hour to full-day area horseback rides. Or maybe you prefer a multiday camping trip or cattle drive?
Red Rock 'n Llamas HIKING
( 435-616-7421, 877-955-2627; www.redrocknllamas.com) Yes, these multiday treks are actually Llama-supported (kids love it). Drop-camp service, camping gear rental and hiker shuttles also available.
#### Sleeping
Boulder Mountain Lodge LODGE $$
( 435-335-7460; www.boulder-utah.com; 20 N Hwy 12; r $110-175; ) Watch the birds flit by on the adjacent 15-acre wildlife sanctuary and stroll through the organic garden –Boulder Mountain Lodge has a strong eco-aesthetic. It's an ideal place for day-hikers who want to return to high-thread-count sheets, plush terry robes and an outdoor hot tub. Hell's Backbone Grill, on site, is a southern Utah must-eat.
Boulder Mountain Ranch LODGE $-$$
( 435-335-7480; http://bouldermountainguestranch.com; off Hell's Backbone Rd; r $70-105, cabins $95-115; ) Enjoy a peaceful 160-acre wilderness setting with outfitter-led hikes and activities available. Bunk and queen rooms in the giant log lodge enjoy a communal atmosphere; rustic out-cabins are more private. The dining room has chef-cooked meals at breakfast and dinner.
Pole's Place MOTEL $
( 435-335-7422, 800-730-7422; www.boulderutah.com/polesplace; r $50-75; Mar-Oct; ) Small and simple, this mom-and-pop motel is lovingly maintained. Limited TV.
#### Eating
Hell's Backbone Grill MODERN SOUTHWESTERN $$-$$$
( 435-335-7464; Boulder Mountain Lodge, 20 N Hwy 12; breakfast $8-10, dinner $16-34; 7am-11:30am & 5:30-9:30pm Mar-Oct) Soulful, earthy preparations of Southwestern dishes include locally-raised meats and organically grown produce from their garden. Zen Buddhist owners Jen Castle and Blake Spalding not only feed the stomach, they feed the community, training staff in mindfulness and inviting the whole town to a 4th of July ice cream social and talent show. Dinner reservations are a must. Save room for the Chimayo-chile ginger cake with butterscotch sauce.
Burr Trail Grill & Outpost MODERN SOUTHWESTERN $-$$
(cnr Hwy 12 & Burr Trail Rd; mains $7-18; grill 11am-2:30pm & 5-9:30pm, outpost 7:30am-8pm Mar-Oct; ) The organic vegetable tarts and eclectic burgers (plus scrumptious homemade cookies and cakes) at the Grill rival the more famous restaurant next door. We like the homey vibe here, where locals come to chat-and-chew or celebrate friends' birthdays. The Outpost is a wonderfully artsy gallery as much as it is gift shop and coffeehouse.
Hills & Hollows Country Store MARKET $
(Hwy 12; 9am-7pm, gas 24hr) Groceries and organic snacks available year-round, though hours may be limited November through February.
#### Information
The tiny town has no visitor center, but info is available online at www.boulderutah.com.
Boulder Interagency Desk ( 435-335-7382; Anasazi State Park Museum, Hwy 12; 9am-5pm mid-Mar–mid-Nov) BLM and other public-land trail and camping information.
### Escalante
With a population of just under one thousand, Escalante is the largest settlement on the north side of the GSENM. Folks here are an interesting mix of ranchers, old-timers, artists and post-monument-creation outdoors lovers. The town itself doesn't have tons of character, but there are lodgings and restaurants. Numerous outfitters make this their base for hiking excursions, and you could too. Lying at the head of several park backroads, not far from the most popular GSENM hikes, the location is good. Escalante is 28 miles south of Boulder, roughly halfway between Capitol Reef (76 miles) and Bryce Canyon (50 miles).
#### Sights & Activities
The Monument provides most of the attraction for the area; hikes off Hwy 12 and Hole-in-the-Rock Rd are within 12 to 30 miles drive.
Escalante Petrified Forest State Park PARK
(www.stateparks.utah.gov; day use $6; day use 8am-10pm) Two miles west of town, the centerpiece of this state park is a 130-acre lake. Hike uphill about a mile on an interpretive route to see pieces of colorful millions-of-years-old petrified wood. Follow another short interpretive trail past further examples of the mineralized wood. The sites at the campground ( 800-322-3770; http://utahstateparks.reserveamerica.com; tent & RV sites with/without hookups $16/20; ) are reserveable; showers available.
Escalante Outfitters ADVENTURE SPORTS
( 435-826-4266; www.escalanteoutfitters.com; 310 W Main St; 8am-9pm Mar-Oct, 9am-6pm Tue-Sat Nov-Feb; ) A traveler's oasis: this store and cafe sells area books, topographic maps, camping and hiking gear, liquor, espresso, breakfasts and pizza. Guided fly-fishing trips and natural-history tours are available (from $45 per person). It also rents out tiny, rustic cabins ($45) and mountain bikes (from $35 per day).
Excursions of Escalante HIKING
( 800-839-7567; www.excursionsofescalante.com; 125 E Main St; full-day from $145) For area canyoneering and climbing trips, Excursions is the best; it does hiker shuttles and guided photo hikes, too. At the time of writing,its outfitter store and cafe was under reconstruction.
Escape Goats ADVENTURE SPORTS
( 435-826-4652; http://escapegoats.us; full-day $80-150) Take an evening tour or day-hike to dinosaur tracks, slot-canyons and ancient sites. Supplies for multiday catered pack-trips are carried by goats. Yes, goats.
Utah Canyons ADVENTURE SPORTS
( 435-826-4967; www.utahcanyons.com; 325 W Main St) Guided day hikes, multiday supported treks, hiker shuttles and a small outdoors store.
Escalante Jeep Rental ADVENTURE SPORTS
( 435-616-4144; www.escalantejeeprentals.com; 495 W Main St; 10am-5pm) Jeeps, ATVs and 4WD utility vehicles for rent; from $180 per day.
Gallery Escalante GALLERY
(http://galleryescalante.com; 425 W Main St; 9am-5pm) This artist-owned local art gallery with multiday Photoshop workshops sends students out into the field 'on assignment'.
#### Sleeping
For a full list of area motels, B&Bs and rentals, check out www.escalante-cc.com.
Canyons Bed & Breakfast B&B $$
( 435-826-4747, 866-526-9667; www.canyonsbnb.com; 120 E Main St; r incl breakfast $125-135; ) Upscale cabin-rooms with porches surround a shaded terrace and gardens where you can enjoy your gourmet breakfast each morning. Except for a small dining area, the wooden 1905 ranch house on-site is private.
Rainbow Country Bed & Breakfast B&B $-$$
( 435-826-4567, 800-252-8824; www.bnbescalante.com; 586 E 300 S; r incl breakfast $69-109; ) You couldn't ask for better trail advice than what you receive over big home-cooked breakfasts here. The split-level house on the edge of town is not flashy, just comfortable and homey – with a big TV lounge (no room TVs), guest refrigerator and outdoor hot tub.
Circle D Motel MOTEL $
( 435-826-4297; www.escalantecircledmotel.com; 475 W Main St; r $65-75; ) It's just an updated, older motel, but the friendly proprietor goes out of his way to accommodate guests. Room microwaves and minifridges are standard.
#### Eating
Esca-Latte Cafe & Pizza PIZZERIA $-$$
(310 W Main St; breakfast $3-6, pizza $10-18; 8am-9pm Mar-Oct; ) For granola and quiche at breakfast, and tasty homemade pizza and beer for lunch and dinner, visit Escalante Outfitters' eatery.
Cowboy Blues AMERICAN $$
(530 W Main St; sandwiches & mains $9-20; 11am-10pm) Family-friendly meals here include BBQ ribs, steaks and daily specials like burritos or meatloaf. Plus this is the only place in town with a full bar.
Circle D Eatery AMERICAN $$
(475 W Main St; breakfast & sandwiches $5-9, mains $9-16; 7am-9:30pm, limited hours Nov-Feb) Smoked meats, pastas, burgers and hearty breakfasts.
Griffin Grocery MARKET $
(30 W Main St; 8am-7pm Mon-Sat) The only grocery in town.
#### Information
There's no town visitor center; check out www.escalante-cc.com. The nearest hospital is 65 miles west in Panguitch.
Escalante Interagency Office ( 435-826-5499; www.ut.blm.gov/monument; 775 W Main St; 7am-5:30pm mid-Mar–mid-Nov, 8am-4:30pm mid-Nov–mid-Mar) _The_ source for information about area public lands; jointly operated by the BLM, the USFS and NPS.
### Grand Staircase-Escalante National Monument
Nearly twice the size of Rhode Island, the 1.9-million-acre Grand Staircase-Escalante National Monument (GSENM) is the largest park in the Southwest and has some of the least visited yet most spectacular scenery. Its name refers to the 150-mile-long geological strata that begins at the bottom of the Grand Canyon and rises, in stair steps, 3500ft to Bryce Canyon and Escalante River Canyon. Together the layers of rock reveal 260 million years of history in a riot of colors. Sections of the GSENM have so much red rock that the reflected light casts a pink hue onto the bottom of clouds above.
Established amid some local controversy by President Bill Clinton in 1996, the monument is unique in that it allows some uses that would be banned in a national park (such as hunting and grazing, by permit), but allows fewer uses than other public lands to maintain its 'remote frontier' quality. Tourist infrastructure is minimal and limited to towns on the park's edges. Hwy 12 skirts the northern boundaries between Boulder, Escalante and Tropic. Hwy 89 arcs east of Kanab into the monument's southwestern reaches.
The park encompasses three major geological areas. The Grand Staircase is in the westernmost region, south of Bryce Canyon and west of Cottonwood Canyon Rd. The Kaiparowits Plateau runs north-south in the center of the monument, east of Cottonwood Canyon Rd and west of Smoky Mountain Rd. Canyons of the Escalante lie at the easternmost sections, east of Hole-in-the-Rock Rd and south of the Burr Trail, adjacent to Glen Canyon National Recreational Area.
#### Sights & Activities
The BLM puts out handy one-page summaries of the most-used day trails. GSENM is also filled with hard-core backcountry treks. Ask rangers about Coyote Gulch, off Hole-in-the-Rock Rd; Escalante River Canyon; Boulder Mail Trail; and the Gulch, off the Burr Trail. Falcon Guide's _Hiking Grand Staircase-Escalante_ is the most thorough park-hiking handbook, but we like the more opinionated _Hiking From Here to Wow: Utah Canyon Country_ – it has great details and snazzy color pics, too. The waterproof Trails Illustrated/National Geographic map _No 710 Canyons of the Escalante_ is good, but to hike the backcountry you'll need USGS 7.5-minute quadrangle maps. Pick these up at any visitor center.
Heading off-trail requires significant route-finding skills; GPS proficiency isn't enough. Know how to use a compass and a topographical map, or risk getting lost. Always check with rangers about weather and road conditions before driving or hiking. After heavy rain or snow roads may be impassable, even with a 4WD. Slot canyons and washes are flash-flood prone. If it starts to rain while you're driving, _stop_. Storms pass and roads dry quickly, sometimes even within 30 minutes. Never park in a wash. Carry a gallon of water per person, wear a hat and sunscreen, and carry food, maps and a compass. Help in case of an emergency will be hard to find. Avoid walking on biological soil crusts (Click here), the chunky black soil that looks like burnt hamburger meat; it fixes nitrogen into the ground, changing sand to soil.
There are no entrance fees for the 24-hour-accessible GSENM.
### READ ALL ABOUT IT
The otherworldly beauty of Utah has moved many to words almost as eloquent as the nature itself.
Edward Abbey (1927-89) Abbey became intimate with Arches National Monument when he worked there in the 1950s as a seasonal ranger, pre-national park. Environmentalist? Anarchist? It's hard to pin Abbey down. Many of his essay collections are set (in part) in Utah. Start with _Desert Solitaire: A Season in the Wilderness_.
Everett Ruess (1914-34) Artist, poet, writer and adventurer, Everett Ruess set out on his burro into the desert near the Escalante River Canyon at 20 years old, never to be seen again. He left behind scores of letters that paint a vivid portrait of life in canyon country before humans and machines. Pick up a copy of _Everett Ruess: A Vagabond for Beauty_ , which includes his letters and an afterword by Edward Abbey.
Craig Childs (1967-) You'll never see a slot canyon in the same light again after reading the heart-thumping account of flash floods in _Secret Knowledge of Water_ , a travelogue that follows naturalist Childs' Utah desert hikes. His _House of Rain_ explores ancient ruins in the Four Corners area.
Terry Tempest Williams (1955-) Born and raised in Utah, Tempest Williams has been both poet and political advocate for the wilderness she loves. In addition to _Red_ , an essay collection focused on southeastern Utah, check out _Refuge_ , a lyrical elegy for her mother and the Great Salt Lake.
Wallace Stegner (1909-93) A graduate of the University of Utah, Stegner became one of the classic writers of the American West. _Mormon Country_ provides an evocative account of the land the Mormons settled and their history; _Big Rock Candy Mountain_ is historical fiction that follows a couple's prosperity-seeking moves to Utah.
Tony Hillerman (1925-2008) Many of Hillerman's whodunits take place on Navajo tribal lands similar to those in Utah and New Mexico around Monument Valley. Landscape and lore are always woven into his mysteries.
Devils Garden HIKING
(Mile 12, Hole-in-the-Rock Rd; ) Easy hikes are scarce in the monument – the closest thing is a foray into Devils Garden, where rock fists, orbs, spires and fingers rise 40ft above the desert floor. A short walk from the car leads to giant sandstone swirls and slabs. From there you have to either walk in the sand or over, among and under the sandstone – like in a giant natural playground.
Lower Calf Creek Falls Trail HIKING
(Mile 75, Hwy 12; admission $2) The most popular and accessible hike lies halfway between Torrey and Boulder. This sandy, 6-mile round-trip track skirts a year-round running creek through a spectacular canyon before arriving at a 126ft waterfall – a joy on a hot day. Pick up the interpretive brochure to help spot ancient granary ruins and pioneer relics.
Escalante Natural Bridge Trail HIKING
(15 miles east of Escalante, Hwy 12) Be ready to get your feet wet. You'll crisscross a stream seven times before reaching a 130ft-high, 100ft-long natural bridge and arch beyond (4.4 miles round-trip).
Upper Calf Creek Falls Trail HIKING
(btwn Mile 81 & 82, Hwy 12) A short (2.2 miles round-trip) but steep and strenuous trail leads down slickrock, through a desert moonscape, to two sets of pools and waterfalls that appear like a mirage at hike's end.
Dry Fork Slot Canyons HIKING
(Mile 26, Hole-in-the-Rock Rd) A remote but popular Hole-in-the-Rock Rd hike leads to four different slot canyons, complete with serpentine walls, incredible narrows and bouldering obstacles. Dry Fork is often overlooked as not tight or physically challenging enough, but it's our favorite. You can walk for miles between undulating orange walls, with only a few small boulder step-ups. To get into dramatic Peekaboo, you have to climb up a 12ft handhold-carved wall (much easier if you're tall or not alone). Even narrower Spooky Gulch may be too small for some hikers. The farthest, Brimstone Gulch, is also the least interesting. Ask rangers for directions and always return the way you came. Climbing up and out of slots, then jumping down the other side, may trap you below the smooth face you've descended.
Cottonwood Canyon Rd SCENIC DRIVE
(off Hwys 12 & 89) This 46-mile scenic backway heads east, then south, from Kodachrome Basin State Park, emerging at Hwy 89 near Paria Canyon-Vermilion Cliffs Wilderness Area. It's the closest entry into GSENM from Bryce and an easy though sometimes rough drive, passable for 2WD vehicles (RVs not recommended). Twenty miles south of Hwy 12 you'll reach Grosvenor Arch, a yellow-limestone double arch, with picnic tables and restrooms.
The road continues south along the west side of the Cockscomb, a long, narrow monocline in the Earth's crust. The Cockscomb divides the Grand Staircase from Kaiparowits Plateau to the east; there are superb views. The most scenic stretch lies between Grosvenor Arch and Lower Hackberry Canyon, good for hiking. The road then follows the desolate Paria River valley toward Hwy 89.
Hole-in-the-Rock Rd SCENIC DRIVE
(off Hwy 12) From 1879 to 1880, more than 200 pioneering Mormons followed this route on their way to settle southeastern Utah. When the precipitous walls of Glen Canyon on the Colorado River blocked their path, they blasted and hammered through the cliff, creating a hole wide enough to lower their 80 wagons through – a feat that is honored by the road's name today. The final part of their trail lies submerged beneath Lake Powell. History buffs should pick up Stewart Aitchison's _Hole-in-the-Rock Trail_ for a detailed account.
The history is often wilder than the scenery along much of this 57-mile, dusty washboard of a road, but it does have several sights and trailheads. The road is passable to ordinary passenger cars when dry, except for the last, extremely rugged 7 miles, which always require 4WD. The road stops short of the actual Hole-in-the-Rock, but hikers can trek out and scramble down past the 'hole' to Lake Powell in less than an hour. Sorry, no elevators for the climb back up.
Skutumpah & Johnson Canyon Rds SCENIC DRIVE
The most westerly route through the monument, the unpaved Skutumpah Rd ( _scoot-em-paw_ ) heads southwest from Cottonwood Canyon Rd near Kodachrome Basin State Park. First views are of the southern end of Bryce Canyon's Pink Cliffs. A great little slot-canyon hike, accessible to young and old, is 6.5 miles south of the turnoff at Willis Creek. After 35 miles (two hours), Skutumpah Rd intersects with the 16-mile paved Johnson Canyon Rd, and passes the White Cliffs and Vermilion Cliffs areas en route to Hwy 89 and Kanab. Four-wheel drive is recommended; ask GSENM rangers about conditions
### BURR TRAIL RD
The region's most immediately gratifying, dramatic backcountry drive is a comprehensive introduction to southern Utah's geology. You pass cliffs, canyons, buttes, mesas and monoliths – in colors from sandy white to deep coral red. Sweeping curves and steep up-and-downs add to the attraction. Just past the Deer Creek trailhead look for the towering vertical red-rock slabs of Long Canyon. Stop at the crest for views of the sheer Circle Cliffs, which hang like curtains above the undulating valley floor. Still snowcapped in summer, the Henry Mountains rise above 11,000ft on the horizon.
After 30 paved miles (1½ hours), the road becomes loose gravel as it reaches Capitol Reef National Park and the giant, angled buttes of hundred-mile-long Waterpocket Fold. The dramatic Burr Trail Switchbacks follow an original wagon route through this monocline. Be sure to see the switchbacks before returning to Boulder. Another option is to turn onto Notom-Bullfrog Rd and continue north to Hwy 24 (32 miles) near Torrey, or south to Glen Canyon and Lake Powell (35 miles). Note that this part of the route is rough, and not generally suited to 2WD.
#### Tours & Outfitters
Outfitters and guide services that operate in GSENM are based in Boulder, Escalante, Torrey and Kanab.
#### Sleeping & Eating
Most sleeping and eating is done in Escalante, Boulder or Kanab. The GSENM website (www.ut.blm.gov/monument) lists suggested areas for free dispersed camping. Pick up the required permit at a visitor center. Remember: water sources must be treated or boiled, campfires are permitted only in certain areas (use a stove instead), and biting insects are a problem in spring and early summer. Watch for scorpions and rattlesnakes.
There are two developed campgrounds in the northern part of the monument:
Calf Creek Campground CAMPGROUND $
(www.ut.blm.gov; Hwy 12; tent & RV sites $7) Beside a year-round creek, Calf Creek Campground is surrounded by red-rock canyons (hot in summer) and has 14 incredibly popular, nonreserveable sites and drinking water available; no hookups. The campground is near the trailhead to Lower Calf Creek Falls, 15 miles east of Escalante.
Deer Creek Campground CAMPGROUND $
(www.ut.blm.gov; Burr Trail Rd; tent & RV sites $5; mid-May–mid-Sep) This campground, 6 miles southeast of Boulder, has few sites and no water, but sits beside a year-round creek beneath tall trees.
#### Information
Food, gas, lodging and other services are available in Boulder, Escalante, Torrey and Kanab.
Big Water Visitor Center ( 435-675-3200; 100 Upper Revolution Way, Big Water; 9am-6pm Apr-Oct, 8am-5pm Nov-Mar) Near Lake Powell.
Cannonville Visitor Center ( 435-826-5640; 10 Center St, Cannonville; 8am-4:30pm Apr-Oct) Five miles east of Tropic.
Escalante Interagency Office ( 435-826-5499; 775 W Main St, Escalante; 7am-5:30pm mid-Mar–mid-Nov, 8am-4:30pm mid-Nov–mid-Mar)
Grand Staircase-Escalante National Monument ( 435-826-5499; www.ut.blm.gov/monument; PO Box 225, Escalante, UT 84726) For advance information.
Grand Staircase-Escalante Partners (http://gsenm.org) Volunteer opportunities.
Kanab Visitor Center ( 435-644-4680; 745 E Hwy 89, Kanab; 7:30am-5:30pm) Southwestern section; park headquarters.
#### Getting Around
There is no public transportation in the park. High-clearance 4WD vehicles allow you the most access, since many roads are unpaved and only occasionally bladed. (Most off-the-lot SUVs and light trucks are _not_ high-clearance vehicles.) Heed all warnings about road conditions. Remember to buy gasoline whenever you see it.
Some outfitters in towns around the park have hiker shuttles or 4WD rentals. However, if you plan to do a lot of backroad exploring and are arriving via Las Vegas, it may be cheaper overall to rent from there.
### Kodachrome Basin State Park
Petrified geysers and dozens of red, pink and white sandstone chimneys – some nearly 170ft tall – resemble everything from a sphinx to a snowmobile at Kodachrome Basin ( 435-679-8562; www.stateparks.utah.gov; per vehicle $6; day use 6am-10pm) The park lies off Hwy 12, 9 miles south of Cannonville and 26 miles southeast of Bryce Canyon National Park. Visit in the morning or afternoon, when shadows play on the red rock. Most sights are along hiking and mountain-biking trails. The moderately easy, 3-mile round-trip Panorama Trail gives the best overview. Be sure to take the side trails to Indian Cave, where you can check out the handprints on the wall (cowboys' or Indians'?), and Secret Passage, a short hike through a narrow slot canyon. Angel Palace Trail (1-mile loop, moderate) has great desert views from on high.
Red Canyon Trail Rides ( 435-834-5441, 800-892-7923; www.redcanyontrailrides.com; 1-hr ride $30; Mar-Nov), based near Bryce, offers horseback rides here in the state park.
The 26 well-spaced sites at the reservable park service campground ( 800-322-3770; http://utahstateparks.reserveamerica.com; tent/RV sites with hookups $16/20) get some shade from juniper trees. Big showers, too.
The four Red Stone Cabins ( 435-679-8536; www.redstonecabins.com; Kodachrome Basin State Park; cabin $90; Mar-Nov, by prearrangement Dec-Feb; ) are simple, but cozy, with all the essentials (linens, microwave, minifridge and coffee maker) and either a king bed or two queens. The same family runs a little camp store ( 8am-6:30pm Sun-Thu, to 8pm Fri & Sat Apr-Oct).
### Bryce Canyon National Park & Around
The sorbet-colored, sandcastle-like spires and hoodoos of Bryce Canyon look like something straight out of Dr Seuss' imagination. Though the smallest of southern Utah's national parks, this is perhaps the most immediately visually stunning, particularly at sunrise and sunset when an orange wash sets the otherworldly rock formations ablaze. Steep trails descend from the rim into the 1000ft amphitheaters of pastel daggers, then continue through a maze of fragrant juniper and undulating high-mountain desert. The location, 77 miles east of Zion and 39 miles west of Escalante, helps make this a must-stop on any southern Utah park itinerary.
Shaped somewhat like a seahorse, the narrow, 56-mile-long park is an extension of the sloping Paunsaugunt Plateau which rises from 7894ft at the visitor center to 9115ft at Rainbow Point, the plateau's southernmost tip. The high altitude means cooler temperatures here than at other Utah parks (80°F, or 27°C, average in July). Crowds arrive in force from May to September, clogging the park's main road (shuttle optional). For solitude, explore trails on the canyon floor. Weatherwise, June and September are ideal; in July and August be prepared for thunderstorms and mosquitoes. In winter, snow blankets the park, but the snowcaps on formations are stunning. Most roads are plowed; others are designated for cross-country skiing and snowshoeing.
You can't enter the park without passing through the townlike sleep-shop-eat-outfit complex, Ruby's Inn, immediately north. The motel has been part of the landscape since 1919 when it was located at the canyon's rim. After the area was declared a national monument in 1923, owner Rueben Syrett moved his business north to his ranch, its current location. In 2007 the 2300-acre resort was officially incorporated as Bryce Canyon City.
#### Sights & Activities
Park admission is $25 per week, per car. TheNPS newspaper, _Hoodoo_ , lists hikes, activities and ranger-led programs. The views fromthe overlooks are amazing, but the best thing about Bryce is that you can also experience the weirdly eroding hoodoos up close. Descents and ascents can be long and steep, and the altitude makes them extra strenuous. Take your time; most trails skirt exposed drop-offs.
Additional activities, including mountain-biking trails, are available nearby in Red Canyon, 13 miles west, and Kodachrome Basin State Park, 22 miles east, on Hwy 12.
Rim Road Scenic Drive SCENIC DRIVE
The lookout views along along the park's 18-mile-long main road are amazing; navigate using the park brochure you receive at the entrance. Bryce Amphitheater – where hoodoos stand like melting sandcastles in shades of coral, magenta, ocher and white, set against a deep-green pine forest – stretches from Sunrise Point to Bryce Point. For full effect, be sure to walk all the way out to the end of any of the viewpoints; a shaft of sunlight suddenlybreaking through clouds as you watch can transform the scene from grand to breathtaking.
Note that the scenic overlooks lie on the road's east side. You can avoid left turns on the very busy road by driving all the way south to Rainbow Point, then turning around and working your way back, stopping at the pullouts on your right. From late May to early September a free bus shuttle goes as far as Bryce Amphitheater, the most congested area. You can hop off and back on at viewpoints. The free Rainbow Point bus tour hits the highlights daily at 9am and 1pm; inquire at the visitor center.
Rim Trail HIKING
The easiest hike, this 0.5- to 5.5-mile-long (one-way) trail outlines Bryce Amphitheater from Fairyland Point to Bryce Point. Several sections are paved and wheelchair accessible, the most level being the half mile between Sunrise and Sunset Points. In the summer, you could easily take the shuttle to any one point and return from another instead of backtracking to a car.
Navajo Loop HIKING
Many moderate trails descend below the rim, but this is one of the most popular. The 1.4-mile trail descends 521ft from Sunset Point and passes through the famous narrow canyon Wall Street. Combine part of the Navajo with the Queen's Garden Trail for an easier ascent. Once you hike the 320ft to Sunrise Point, follow the Rim Trail back to your car (2.9-mile round-trip).
Fairyland Loop HIKING
With a trailhead at Fairyland Point north of the visitor center, the 8-mile round-trip makes for a good half-day hike (four to five hours). The tall hoodoos and bridges unfold best if you go in a clockwise direction. On the trail there's a 700ft elevation change, plus many additional ups and downs.
Bristlecone Loop HIKING
The 1-mile Bristlecone Loop, at road's end near Rainbow Point, is an easy walk past 1600-year-old bristlecone pines, with 100-mile vistas.
Mossy Cave Trail HIKING
Outside main park boundaries (east of the entrance), off Hwy 12 at Mile 17, take the easy half-mile one-way walk to the year-round waterfall off Mossy Cave Trail, a summertime treat and frozen winter spectacle.
Peekaboo Trail HIKING
The fairly level 7-mile-long Peekaboo Trail, which leaves from Bryce Point, allows dogs and horses. Not recommended in high summer – it doesn't always smell the best.
Ranger-Led Activities HIKING
During summer and early fall, rangers lead canyon-rim walks, hoodoo hikes, geology lectures, campfire programs and kids' ecology walks. If you're here when skies are clear and the moon's full, don't miss the two-hour Moonlight Hike among the hoodoos. Register same-day at the visitor center , but do so early.
Backcountry Hikes HIKING
Only 1% of all visitors venture onto the backcountry hikes. You won't walk among many hoodoo formations here, but you will pass through forest and meadows with distant views of rock formations. And oh, the quiet. The 23-mile Under-the-Rim Trail, south of Bryce Amphitheater, can be broken into several athletic day hikes. The 11-mile stretch between Bryce Point and Swamp Canyon is one of the hardest and best. Get backcountry permits ($5 to $15) and trail info from rangers at the visitor center.
Bryce Museum MUSEUM
(www.brycewildlifeadventure.com; 1945 W Hwy 12; admission $8; 9am-7pm Apr-Oct) Visit this barnlike natural history museum – with more than 400 taxidermied animals, butterflies, and Native American artifacts – then feed the feral deer and other animals in the yards surrounding. West of the park.
#### Tours & Outfitters
Canyon Trail Rides HORSEBACK RIDING
( 435-679-8665; www.canyonrides.com; Bryce Canyon Lodge) The national park's only licensed outfitter operates out of the park lodge. You can take a short, two-hour trip to the canyon floor ($50) or giddy-up for a half day ($75) through the dramatic hoodoos on Peekaboo Trail.
Ruby's Inn ADVENTURE SPORTS
( 435-834-5341, 866-866-6616; www.rubysinn.com; 1000 S Hwy 63) Just outside the park, Ruby's offers guided horseback rides (half-day $75), ATV tours (three hours $100) and mountain-bike rental (half-day $35) – not to mention the rodeo performances, helicopter rides and snowmobiling. Inquire at the inn.
Red Canyon Trail Rides HORSEBACK RIDING
( 435-834-5441, 800-892-7923; www.redcanyontrailrides.com; Bryce Canyon Pines, Hwy 12; half-day $65; Mar-Nov) Ride for as little as a half hour or as long as a whole day on private and public lands outside the park, including Red Canyon.
Bryce Wildlife Adventures ADVENTURE SPORTS
( 435-834-5555; www.brycewildlifeadventure.com; Bryce Museum, 1945 W Hwy 12; 9am-7pm Apr-Oct) ATV (from $105 for three hours) and mountain-bike ($12.50 per hour) rentals, near public land trails outside the park.
Mecham Outfitters HORSEBACK RIDING
( 435-679-8823; www.mechamoutfitters.com; half-day $75) Based in Tropic, leads half- and full-day rides in nearby Dixie National Forest and on GSENM lands.
###### Cycling
Several companies lead four- to six-day, Bryce to Zion road cycling tours:
Rim Tours CYCLING
( 435-259-5223, 800-626-7335; www.rimtours.com)
Western Spirit Cyclery CYCLING
( 435-259-8732, 800-845-2453; www.westernspirit.com)
Backroads Bicycle Adventures CYCLING
( 800-462-2848; www.backroads.com)
#### Festivals & Events
The park doesn't host any events, but Ruby's Inn does.
Bryce Canyon Winterfest SPORTS
In early February; includes everything from cross-country skiing and snowmobiling to archery and snow sculpting.
Bryce Canyon Rim Run SPORTS
Held in August, the run follows a 6-mile course partially along the Bryce Canyon rim outside the park.
### SCENIC DRIVES: SOUTHERN UTAH
People come from around the world to drive in southern Utah, and Hwy 12 (Click here) and Burr Trail (Click here) may be the biggest draws. But from paved desert highways for RV-cruisers to rugged backcountry trails for Jeepsters, there are drives for every taste.
Comb Wash Rd (near Bluff) Straddling Comb Ridge, Comb Wash Rd (or CR 235) is a dirt track that runs for about 20 miles between Hwys 163 and 95 (parallel to Hwy 191) west of Blanding and Bluff. Views are fantastic (bring binoculars) and the ridge contains numerous ancient cliff dwellings. High-clearance 4WD vehicles recommended; in wet weather, this road is impassable.
Colorado River Byway (near Moab) Hwy 128 follows the river northeast to Cisco, 44 miles away just off I-70. Highlights are Castle Rock, the 900ft-tall Fisher Towers, the 1916 Dewey Bridge (one of the first across the Colorado) and sightings of white-water rafters.
La Sal Mountain Loop Rd (near Moab) This road heads south into the Manti–La Sal forest from 15 miles north of Moab, ascending switchbacks (long RVs not recommended) into the refreshingly cool forest, with fantastic views. Connects with Hwy 191, 8 miles south of Moab. The 67-mile (three to four hour) paved loop closes in winter.
Loop-the-Fold (near Torrey) This 100-mile loop links several top drives; roughly half is on dirt roads generally accessible to 2WD passenger vehicles. Pick up a driving guide ($2) at the Capitol Reef National Park visitor center. West of the park, there are the rocky valleys of Hwy 12. It only gets better after turning east along Burr Trail Rd to Strike Valley Overlook. Then take the rough Notom-Bullfrog Rd north to finish the loop at Hwy 24.
Caineville Wash Rd (near Torrey) Just west of Capitol Reef National Park, turn north off Hwy 24 to the otherworldly monoliths like Temple of the Sun and Temple of the Moon on Caineville Wash Rd. Continue on into the northern part of the park and Glass Mountain, a 20ft mound of fused selenite. Two-wheel drive is usually fine for the first 15.5 miles. With a 4WD you can make this a 58-mile Cathedral Valley loop along Hartnet Rd, which fords the Fremont River just before rejoining Hwy 24.
Hell's Backbone Rd (near Boulder) The gravel-strewn 48 miles from Hwy 12 along Hell's Backbone Rd to Torrey is far from a shortcut. You'll twist, you'll turn, you'll ascend and descend hills, but the highlight is a single-lane bridge atop an impossibly narrow ridge called Hell's Backbone.
Hwy 14 (near Cedar City) This paved scenic route leads 42 miles over the Markagunt Plateau, ending in Long Valley Junction at Hwy 89. The road rises to 10,000ft, with splendid views of Zion National Park to the south. Make sure you detour at Cedar Breaks National Monument.
#### Sleeping
The park has one lodge and two campgrounds. Most travelers stay just north of the park in Bryce Canyon City, near the Hwy 12/63 junction or 11 miles east in Tropic. Other lodgings are available along Hwy 12, and 24 miles west in Panguitch. Red Canyon and Kodachrome Basin State Park also have campgrounds.
##### INSIDE THE PARK
Trailers are allowed only as far as Sunset Campground, 3 miles south of the entrance. Backcountry camping permits ($5) are available at the visitor center.
Bryce Canyon Lodge LODGE $$-$$$
( 435-834-8700, 877-386-4383; www.brycecanyonforever.com; Hwy 63; r & cabins $130-175; Apr-Oct; ) Built in the 1920s, the main lodge exudes rustic mountain charm, with a large stone fireplace and exposed roof timbers. Most rooms are in two-story wooden satellite buildings with private balconies. A variety of older and newer cabins all have inherent charm, with creaky porches and woodsy settings. Be warned: the walls prove thin if the neighbors decide to get noisy. Furnishings are decidedly dated througout. No TVs.
North Campground CAMPGROUND $
( 877-444-6777; www.recreation.gov; Bryce Canyon Rd; tent & RV sites $15) The 100-plus NPS campground near the visitor center has a camp store, laundry, showers, flush toilets and water. Loop C is the closest to the rim (sites 59 and 60 have great views, but little privacy). Reservations are accepted early May through late September. No hookups.
Sunset Campground CAMPGROUND $
( 877-444-6777; www.recreation.gov; Bryce Canyon Rd; tent & RV sites $15; Apr-Sep) Though more wooded than North Campground, Sunset has few amenities beyond flush toilets and water available. (For laundry, showers and groceries, visit North.) Twenty of the tent sites are reservable early May to late August.
##### OUTSIDE THE PARK
A full list of area motels is available at www.brycecanyoncountry.com.
Best Western Ruby's Inn MOTEL $-$$$
( 435-834-5341, 866-866-6616; www.rubysinn.com; 1000 S Hwy 63; r $135-180; ) Watch a rodeo, admire Western art, buy cowboy souvenirs, wash laundry, seriously grocery shop, fill up with gas, log on to the internet, dine at restaurants and then post a letter about it all. At Ruby's complex you can even buy bottles of wine and spirits – maybe the rarest service of all. The main inn motel rooms are thoroughly up-to-date. Subsidiary Bryce View Lodge ( 435-834-5180, 888-279-2304; www.bryceviewlodge.com; r $70-110; Apr-Oct) has smaller, less spiffy rooms, geared toward budget travelers. Best Western Plus Bryce Grand Canyon Lodge ( 435-834-5700, 866-866-6634; www.brycecanyongrand.com; r $135-199; Apr-Oct; ) is the newest of the options, with cushy rooms, lodgey decor and additional guest-only amenities, such as a private pool, laundry and fitness center.
Stone Canyon Inn INN $$-$$$
( 435-679-8611, 866-489-4680; www.stonecanyoninn.com; 1220 Stone Canyon Lane, Tropic; r incl breakfast $135-190, cabins $330; ) Backed by natural hills and technicolor sunsets adjoining backcountry parklands, this stately stone-and-wood inn offers adventure out the back door. New cabins are spacious and luxuriantly private, though they're trumped by the charm of the main house rooms, with hot breakfasts with homemade pastries and breads included.
Bryce Country Cabins BUNGALOW $-$$
( 435-679-8643, 888-679-8643; www.brycecountrycabins.com; 320 N Main St, Tropic; cabins $75-195; Feb-Oct; ) Knotty-pine walls and log beds add lots of charm to the roomy one- and two-bedroom cabins here; some with kitchens, some with microwaves and minifridges. Though the cabins line the main street, rear-facing swings have great views of farm fields and far-off cliffs.
Bullberry Inn B&B $$
( 435-679-8820, 800-249-8126; www.bullberryinn.com; 412 S Hwy 12, Tropic; r incl breakfast $95-125) Built in 1998 this purpose-built, farmhouse-style B&B at the far edge of town has spacious, spotless rooms. The welcoming owners make the bullberry jam served with home-baked goodies at the full country breakfast.
Bryce Canyon Resort MOTEL $$
( 435-834-5351, 800-834-0043; www.brycecanyonresort.com; cnr Hwys 12 & 63; r $99-189, cabins $159-210; ) Four miles from the park, this is the less-chaotic alternative to Ruby's Inn. Deluxe rooms include newer furnishings and extra amenities; cabins and cottages have kitchenettes and sleep up to six. Outfitter packages and smoking rooms available.
Bryce Canyon Pines MOTEL $-$$
( 435-834-5441, 800-892-7923; www.brycecanyonmotel.com; Hwy 12; tent/RV sites $20/30, r & cottages $75-130; Apr-Nov; ) This old, rambling white clapboard motel has been in the same family for ages. Cottages have the most character; dated standard rooms have simple beds with simple spreads. There's is a homey restaurant, horseback riding and basic campground on site, 8 miles northwest of the park entrance.
Ruby's RV Park & Campground CAMPGROUND $
( 435-834-5301, 866-866-6616; www.rubysinn.com; 1000 S Hwy 63; tent sites $24, tipis $34-46, RV sites with partial/full hookups $35/42, cabins $55-59; Apr-Oct; ) The 200 sites, camping cabins (no linens) and tipis (bring your own sleeping bag and cot) adjacent to all those services at Ruby's Inn are in a fairly forestlike, if commercial, setting.
Buffalo Sage B&B B&B $-$$
( 435-679-8443, 866-232-5711; www.buffalosage.com; 980 N Hwy 12, Tropic; r incl breakfast $80-110; ) Up on a bluff west of town, three exterior-access rooms lead out to an expansive, upper-level deck or ground-level patio with great views. The owner's background in art is evident in the decor. Do note that the communal living area is shared by cats and dog.
#### Eating & Entertainment
Nobody comes to Bryce for the cuisine. Expect so-so Western fare, such as grilled pork chops and chicken-fried steaks. If you're vegetarian, BYOV or subsist on salad and fries.
##### INSIDE THE PARK
Bryce Canyon Lodge MODERN AMERICAN $$$
( 435-834-5361; Bryce Canyon Rd; breakfast & sandwiches $8-15, dinner $26-42; 7am-10pm Apr-Oct) By far the best, and priciest, place to eat. Meats are perfectly grilled and sauces caringly prepared. Though upscale, the rustic, white tablecloth-clad dining room is more family-friendly than romantically refined – or quiet, even.
Bryce Canyon General Store & Snack Bar MARKET $
(Bryce Canyon Rd, nr Sunrise Point; dishes $3-7; noon-10pm) Sells basic supplies, sandwiches and pizza in season.
##### OUTSIDE THE PARK
Most of the area motels have so-so eateries on site.
Pizza Place PIZZERIA $$
(21 N Main St, Tropic; pizzas & sandwiches $5-18; noon-9pm Apr-Oct, 5-8:30pm Thu-Sat Nov-Mar) Think wood-fired flatbread piled high with fresh ingredients. When locals eat out, they come to this family-owned joint. Serves pizzas, salads and sandwiches.
Ebenezer's Bar & Grill DINNER SHOW $$$
( 800-468-8660; www.rubysinn.com; 1000 S Hwy 63; dinner show $26-32; 7pm nightly mid-May–Sep) Kitschy but good-natured fun, an evening at Ebenezer's includes live country-and-western music served up beside a big BBQ dinner: steak, pulled pork, chicken or salmon. It's probably the best meal served at the Ruby's complex and is wildly popular, so book ahead.
Bryce Canyon Pines AMERICAN $-$$
( 435-834-5441; Bryce Canyon Pines, Hwy 12; breakfast & lunch $5-12, dinner $10-19; 6:30am-9:30pm Apr-Nov) A classic, rural Utah, meat-and-potatoes kind of place. Homemade pies baked here are so good, they're also served in Tropic.
Clarke's Restaurant AMERICAN $$
(121 N Main St, Tropic; breakfast & lunch $4-15, dinner $12-22; 7:30am-9pm Mon-Sat, variably shortened hours Nov-Mar; ) Beer and wine are available at this full-service, three-meal-a-day option.
Clarke's Grocery MARKET $
(121 N Main St, Tropic; sandwiches $4-6; 7:30am-7pm Mon-Sat) Tropic's only grocery store has a deli sandwich counter and homemade baked goods.
#### Information
Some services are just north of the park boundaries on Hwy 63. The nearest town is Tropic, 11 miles northeast on Hwy 12; the nearest hospital is 25 miles northwest in Panguitch.
Bryce Canyon National Park Visitor Center ( 435-834-5322; www.nps.gov/brca; Hwy 63; 8am-8pm May-Sep, to 6pm Oct & Apr, to 4:30pm Nov-Mar) Get information on weather, trails, ranger-led activities and campsite availability; the introductory film is worth seeing. Good selection of maps and books.
Bryce Canyon Natural History Association ( 435-834-4600; www.brycecanyon.org) Pre-trip online book shopping.
Garfield County Travel Council ( 435-676-1160, 800-444-6689; www.brycecanyoncountry.com) There's no town visitor center, so plan ahead online or by phone.
Ruby's Inn (www.rubysinn.com; 1000 S Hwy 63) Post office, grocery store, showers ($6), free wi-fi and computer terminals ($1 for five minutes).
#### Getting Around
A private vehicle is the only way around from fall through spring. If you're traveling in summer, ride the voluntary shuttle (ride free; 9am-6pm late May-Sep), lest you find yourself stuck without a parking spot. (Note: the park's visitor center parking lot fills up, too.) Leave your car at the Ruby's Inn or Ruby's Campground stops, and ride the bus into the park. The shuttle goes as far as Bryce Point; buses come roughly every 15 minutes, 8am to 8pm. A round-trip without exiting takes 50 minutes. Tune in to 1610AM as you approach Bryce to learn about current shuttle operations. The _Hoodoo_ newspaper shows routes.
No trailers are permitted south of Sunset Point. If you're towing, leave your load at your campsite or in the trailer turnaround lot at the visitor center.
### Red Canyon
Impressive, deep-ocher-red monoliths rise up roadside as you drive along Hwy 12, 10 miles west of the Hwy 63-Bryce Canyon turnoff. The aptly named Red Canyon (www.fs.fed.us/dxnf; Dixie National Forest) provides super-easy access to these eerie, intensely colored formations. In fact, you have to cross under two blasted-rock arches to continue on the highway. A network of trails leads hikers, bikers and horseback riders deeper into these national-forest-service lands.
Check out the excellent geologic displays and pick up trail maps at the visitor center ( 435-676-2676; Hwy 12; 9am-6pm Jun-Aug, 10am-4pm May & Sep). Several moderately easy hiking trails begin near the center: the 0.7-mile Arches Trail passes 15 arches as it winds through a canyon; the 1-mile Pink Ledges Trail winds through red rock formations. For a harder hike, try the 2.8-mile, two- to four-hour Golden Wall Trail. Legend has it that outlaw Butch Cassidy once rode here; a tough 8.9-mile hiking route, Cassidy Trail, bears his name.
There are also excellent mountain-biking trails in the area; the best is 7.8-mile Thunder Mountain Trail, which cuts through pine forest and red rock. Outfitters near Bryce Canyon National Park rent mountain bikes and offer horseback rides through Red Canyon.
Surrounded by limestone formations and ponderosa pines, the 37 no-reservation sites at Red Canyon Campground (www.fs.fed.us/dxnf; tent & RV sites $15; mid-May–Sep) are quite scenic. Quiet-use trails (no ATVs) lead off from here, making this a good alternative to Bryce Canyon National Park camping. There are showers and a dump station, but no hookups.
If you prefer a roof over your head, continue west. The rooms and log cabins at family-run Harold's Place ( 435-676-2350; www.haroldsplace.net; Hwy 12; r $55-70, cabins$65-75; Mar-Oct; ), just before the intersection of Hwys 12 and 89, are cozy andspotless. Locals recommend the above-average restaurant (breakfast $5-10, dinner $12-20; 7-11am & 5-10pm Mar-Nov) for favorites like balsamic chicken and pecan-crusted trout. More food and lodging choices are available in nearby Panguitch and Hatch.
### Panguitch
Founded in 1864, historically Panguitch was a profitable pioneer ranching and lumber community. Since the 1920s inception of the national park, the town has had a can't-live-with-or-without-it relationship with Bryce Canyon, 24 miles east. Lodging long ago became the number-one industry, as it's also used as an overnight stop halfway between Las Vegas (234 miles) and Salt Lake City (245 miles). Other than some interesting turn-of-the-20th-century brick homes and buildings, there aren't a lot of attractions in town. The small downtown main street has an antique store or two, but mostly people fill up with food and fuel, rest up, and then move on. In a pinch you could use it as a base for seeing Bryce, Zion and Cedar Breaks.
Panguitch is the seat of Garfield County and hosts numerous festivals. Two of the best are in June: the Quilt Walk Festival celebrates pioneer history and Chariots in the Sky is a huge hot-air balloon festival.
#### Sleeping
Red Brick Inn B&B $$
( 435-676-2141, 866-732-2745; www.redbrickinnutah.com; 11161 N 100 West; r incl breakfast $99-199; May-Oct; ) One of the town's beloved red-bricks, this 1920s Dutch colonial was once the town's hospital. Be sure to ask warm and welcoming proprietor Peggy to share some of its history. Comfy room styles here vary from country gingham and Victorian frill to a fun, faux-lakefront cabin room. Beverage center and outdoor hot tub on site.
Crum Cottage B&B $
( 435-676-2574; www.crumcottage.com; 259 E Center St; r incl breakfast $85; ) Nicely simple new B&B rooms in this renovated redbrick home are an excellent alternative to a motel. The price is more than right; friendly hosts provide a big breakfast and advice on area adventures.
Grandma's Cottage RENTAL $$
( 435-690-9495; www.aperfectplacetostay.net; 90 N 100 West; rentals $85-145; Mar-Nov; ) A renovated studio, cottage and home in central Panguitch now serve as vacation rentals; great for families.
Marianna Inn Motel MOTEL $-$$
( 435-676-8844, 800-598-9190; www.mariannainn.com; r $75-105; ) Rooms in the dollhouse-like, pink-and-lavender motelwith the large shaded swing deck are standard. But the newest additions – deluxe log-style rooms – are worth splurging on. BBQ grill available for guests.
Hitch-N-Post CAMPGROUND $
( 435-676-2436; www.hitchnpostrv.com; 420 N Main St; tent/RV sites with hookups $15/25; ) Small lawns and trees divide RV spaces; tent sites are in a grassy field, but still have barbecue grills. RV wash and heavy-duty laundry on site.
Canyon Lodge MOTEL $
( 435-676-8292, 800-440-8292; www.colorcountry.net/~cache; 210 N Main St; r $59-69; ) Thoroughly clean, older 10-room motel, with classic neon sign and helpful hosts. Hot tub on site.
Color Country Motel MOTEL $
( 435-676-2386, 800-225-6518; www.colorcountrymotel.com; 526 N Main St; r $50-80; ) An economical, standard motel with perks – a pool and outdoor hot tub. Smoking rooms available.
#### Eating & Drinking
Remember that eateries in Hatch, and Harold's Place in Red Canyon, are also close by.
Cowboy's Smokehouse BBQ BARBECUE $$
(95 N Main St; breakfast & lunch $5-12, dinner $15-28; 7am-9pm Mar-Oct) The best barbecue in Garfield County draws 'em in from all over, including Bryce. Good steaks, too. The old main street storefront is a perfect setting for live country music some summer weekends.
Henrie's Drive-in BURGERS $
(154 N Main St; burgers $3-6; 11am-9pm Mar-Oct) Craving a deliciously greasy burger and fries? Look no further. (Don't forget the milkshake.)
Joe's Main Street Market MARKET $
(10 S Main St) The town's main grocery store.
#### Information
Garfield County Travel Council ( 435-676-1102, 800-444-6689; www.brycecanyoncountry.com) Town and county information.
Garfield Memorial Hospital ( 435-676-8811; 224 N 400 East; 24hr)
Powell Ranger Station ( 435-676-9300; www.fs.fed.us/dxnf; 225 E Center St; 8am-4:30pm Mon-Fri) Dixie National Forest camping and hiking info.
### Hwy 89 – Panguitch To Kanab
Most people pass through this stretch of Hwy 89 as quickly as possible en route from Zion to Bryce national parks. All the better for you – the tiny old towns along the way have a few restaurant and lodging gems hidden within. (Note that businesses' seasonal closings change with weather and whim.) Remember when reading distances that you'll average between 35mph and 50mph along these roads.
Independent motels and a few eateries line Hwy 89 in Hatch, 25 miles southwest of Bryce Canyon and 15 miles south of Panguitch. Café Adobe (16 N Main St, Hatch; mains $7-15; 10:30am-7pm Mar–mid-Nov) has long been the residents' fave for gourmet hamburgers, creative sandwiches and tasty Mexican food. And 'locals' here live in Panguitch or Tropic. Don't pass up the homemade tortilla chips and chunky salsa.
A locally-retired Las Vegas developer and his family have single-handedly breathed new life into sleepy Hatch with several seasonal lodgings and eateries. Galaxy Diner (177 S Main St; mains $5-10; 6:30am-2pm mid-Mar–late Oct) is a pseudo-typical 1950s diner and ice cream parlor, next to a Harley Davidson shop. Hatch Station Dining Car (177 S Main St; mains $15-23; 5-9:30pm mid-Mar–late Oct) serves the best prime rib around, in fun, knickknacky surrounds. Next door, there's a convenience store and bargain rooms at Hatch Station Motel (177 S Main St; r $48-56; mid-Mar–late Oct; ). Even better are the Hatch Has Cabin Fever (177 S Main St; cabins $65; mid-Mar–late Oct; ) king and double-queen log cabins with lots of room, microwaves, little refrigerators and coffee makers.
If you're looking for more of an escape, turn off the highway and head toward Cottonwood Meadow Lodge ( 435-676-8950; www.panguitchanglers.com; Mile 123, Hwy 89; cabins & houses $205-360; ) on the Sevier River. The restored pioneer farmhouse has three bedrooms; 1860s log-and-mortar cabins evoke rustic romanticism; and upscale Western decor makes it hard to imagine that the one-bedroom building was ever a barn. Fly-fish on the property in the day, then hang out by the fire pit at night.
Further south, 50 miles from Bryce and 26 miles to Zion, Glendale is a historic little Mormon town founded in 1871. Today it's an access point for Grand Staircase-Escalante National Monument (Click here). From Hwy 89, turn onto 300 North at the faded sign for GSENM; from there it turns into Glendale Bench Rd, which leads to scenic Johnson Canyon and Skutumpah Rds.
The seven-room Historic Smith Hotel ( 435-648-2156, 800-528-3558; www.historicsmithhotel.com; 295 N Main St, Glendale; r incl breakfast $47-84; ) is more comfortable than a favorite old sweater. Don't let the small rooms turn you off. The proprietors are a great help in planning your day and the big breakfast tables are a perfect place to meet other intrepid travelers from around the globe. Great back decks and garden, too. Next door, Buffalo Bistro (305 N Main St; burgers & mains $8-24; 4-9:30pm Thu-Sun mid-Mar–mid-Oct) conjures a laid-back Western spirit with a breezy porch, sizzling grill and eclectic menu. Try buffalo steaks, wild boar ribs, rabbit and rattlesnake sausages – or pasta. The gregarious owner-chef has a great sense of humor; he sometimes hosts music and events, and sometimes closes early.
In Mt Carmel, the Thunderbird Foundation for the Arts ( 435-648-2653; www.thunderbirdfoundation.com; Mile 84, Hwy 89, Mt Carmel) runs exhibits and artist retreats in adjacent spaces. The beautiful Maynard Dixon Home & Studio (self-guided tour $10; 10am-5pm May-Oct) is where renowned Western painter Maynard Dixon (1875-1946) lived and worked in the 1930s and '40s. Look, too, for a couple other galleries, arts-and-crafts and rock shops along the way.
At the turnoff for Hwy 9, Mt Carmel Junction has two gas stations (one with a sandwich counter) and a couple of decent sleeping options about 15 slow-and-scenic miles from the east entrance of Zion and 18 miles north of Kanab. The Navajo lookout on the outside of the Best Western East Zion Thunderbird Lodge ( 435-648-2203, 800-780-7234; www.bestwesternutah.com; cnr Hwys 9 & 89, Mt Carmel Junction; r $85-109; ) is just a facade; the rooms within are standard Best Western.
The quilt-covered four-poster beds sure are comfy at Arrowhead Country Inn & Cabins ( 435-648-2569, 888-821-1670; www.arrowheadbb.com; 2155 S State St, Mt Carmel Junction; r $79-129, cabins $129-269, both incl breakfast; ). The east fork of the Virgin River meanders behind the inn and a trail leads from here to the base of the white cliffs.
### Kanab
Vast expanses of rugged desert extend in each direction from the remote outpost of Kanab. Don't be surprised if it all looks familiar: hundreds of Western movies were shot here. Founded by Mormon pioneers in 1874, John Wayne and other gun-slingin' celebs really put Kanab on the map in the 1940s and '50s. Just about every resident had something to do with the movies from the 1930s up until the '70s. You can still see a couple of movie sets in the area and hear old-timers talk about their roles. In August, the Western Legends Roundup celebrates 'Utah's little Hollywood'.
Kanab sits at a major crossroads: GSENM is 20 miles, Zion 40 miles, Bryce Canyon 80 miles, Grand Canyon's North Rim 81 miles and Lake Powell 74 miles. It makes a good base for exploring the southern side of GSENM and Paria Canyon-Vermilion Cliffs Wilderness formations such as the Wave. Coral Pink Sand Dunes State Park is a big rompin' playground to the northwest.
Note that local opening hours are often altered by mood and demand, especially off season.
#### Sights
Though the town itself isn't the main attraction, there are false-front facades and store names such as Denny's Wig Wam, so just looking around can be kitschy fun. The visitor center has an exhibit of area-made movie posters and knowledge about sites.
Best Friends Animal Sanctuary RESCUE CENTER
( 435-644-2001; www.bestfriends.org; Angel Canyon, Hwy 89; admission free; 9:30am-5:30pm; ) Kanab's most famous attraction is outside of town. Surrounded by more than 33,000 mostly private acres of red-rock desert 5.5 miles north of Kanab, Best Friends is the largest no-kill animal rescue center in the country. The center shows films and gives facility tours four times a day; call ahead for times and reservations. The 1½-hour tours let you meet some of the more than 1700 horses, pigs, dogs, cats, birds and other critters on site. Volunteers come from around the country to work here. Spending the night in one of eight one-bedroom cottages with kitchenettes ($140) or in a one-room cabin ($92) and volunteering for at least a half-day allows visitors to borrow a dog, cat or pot-bellied pig for the night.
The sanctuary is located in Angel Canyon (Kanab Canyon to locals) where scores of movies and TV shows were filmed during Kanab's Hollywood heyday. The cliff ridge about the sanctuary is where the Lone Ranger reared up and shouted 'Hi-yo Silver!' at the end of every episode.
Frontier Movie Town
& Trading Post FILM LOCATION
(297 W Center St; 7:30am-11pm Apr-Oct, 10am-5pm Nov-Mar) Wander through a bunkhouse, saloon and other buildings used in Western movies filmed locally, including _The Outlaw Josey Wales_ , and brush up on such tricks of the trade as short doorways (to make movie stars seem taller). This classic roadside attraction sells all the Western duds and doodads you could care to round up. Lists of movies shot here, and some of the DVDs of the films themselves, are available.
Parry Lodge HISTORIC SITE
(www.parrylodge.com; 89 E Center St; 8pm Sat Jun-Aug) Parry Lodge became movie central when it was built in the 1930s. Stars stayed here and owner Whit Parry provided horses, cattle and catering for the sets. There are nostalgic photos on lobby and dining room walls, and on summer Saturday nights the hotel shows the old Westerns in a barn out back.
Johnson Canyon DRIVING TOUR
Heading into GSENM, the paved scenic drive into Johnson Canyon is popular. More movies were filmed here, and 6 miles along you can see in the distance the Western set where the long-time TV classic _Bonanza_ was filmed (on private land). Turn north off Hwy 89, 9 miles east of Kanab.
Paria movie set DRIVING TOUR
The Paria movie set (pa- _ree_ -uh), where many Westerns were filmed, was burnt down during the 2007 Western Legends Roundup. A 5-mile dirt road leads to a picnic area and an interpretive sign that shows what the set looked like. A mile further north, on the other side of the river, it's a hike to look for the little that's left of Pahreah ghost town. Floods in the 1880s rang the death knell for the 130-strong farming community. Since then, time and fire have taken the buildings and all but the most rudimentary signs of settlement. But the valley is a pretty introduction to GSENM. The signed turnoff for Paria Valley is 33 miles from Kanab on Hwy 89.
Moqui Cave MUSEUM
(www.moquicave.com; adult/child $4/2; 9am-7pm Mon-Sat Mar-Nov) Another interesting tourist trap, Moqui Cave, 5 miles north of town, is an oddball collection of genuine dinosaur tracks, real cowboy and Indian artifacts, and other flotsam and jetsam that the football-star father of the owner collected in the 1950s – all inside a giant cave.
#### Tours & Outfitters
Half-day outfitter tours start at $120.
Paria Outpost ADVENTURE TOUR
( 928-691-1047; www.paria.com) Friendly, flexible and knowledgeable; 4WD tours and guided hikes through the rocks and sand of GSENM and Paria Canyon-Vermillion Cliffs.
Lit'l Bit Ranch HORSEBACK RIDING
( 435-899-9655; http://litlbitranch.org; 2550 E Hwy 89) Horseback rides (from $60 for two hours) and horse boarding by arrangement; lodging available also.
Windows of the West
Hummer Tours ADVENTURE TOUR
( 888-687-3006; www.wowhummertours.com) Personalizable backcountry excursions (two hours to full-day) to slot canyons, petroglyphs and spectacular red-rock country.
Terry's Camera PHOTO TOUR
( 435-644-5981; www.utahcameras.com) Customized area photo tours and workshops.
#### Festivals & Events
Western Legends Roundup FILM
( 800-733-5263; www.westernlegendsroundup.com) The town lives for the annual Western Legends Roundup in late August. There are concerts, gunfights, cowboy poetry, dances, quilt shows, a film festival and more. Take a bus tour to all the film sites, or sign up for a Dutch-oven cooking lesson.
#### Sleeping
Kanab has a proliferation of old, indie budget motels and some house rentals. For a full list, see www.kaneutah.com.
Quail Park Lodge MOTEL $$
( 435-215-1447; www.quailparklodge.com; 125 N 300 W; r $100-130; ) Schwinn Cruiser bicycles stand near vibrant beach balls bobbing in the postage-stamp-size pool and yellow clamshell chairs wait outside surprisingly plush rooms. A colorful retro style pervades all 13 rooms at the refurbished 1963 motel. Mod cons include free phone calls, microwaves, minifridges and complimentary gourmet coffee.
Purple Sage Inn B&B $$
( 435-644-5377, 877-644-5377; www.purplesageinn.com; r incl breakfast $120-150; ) From a cabinet-encased, fold-down bathtub to brass push-button light switches, the antique details are exquisite. In the 1880s this was a Mormon polygamist's home, then in the 1900s it became a hotel where Western author Zane Grey stayed. As a B&B, Zane's namesake room – with its quilt-covered wood bed, sitting room and balcony access –is our favorite.
Parry Lodge MOTEL $-$$
( 435-644-2601, 888-289-1722; www.parrylodge.com; 89 E Center St; r 70-125; ) The aura of Western movie-days gone by is more special than many of the rooms at the town's classic, rambling old motel. Some bear the names of movie stars who stayed here, like Gregory Peck or Lana Turner. If quality is your concern, opt for the L-shaped double queens, nicely refurbished in cottage decor.
Bob-Bon Inn Motel MOTEL $
( 435-644-3069, 800-644-5094; www.bobbon.com; 236 N 300 West; r $40-60; ) The small-but-spotless 16 log-cabin rooms here are a great deal. Owner Bonnie Riding knows a lot about local movies; every inch of every reception room wall is covered with old Western stars' autographed photos.
Victorian Charm Inn HOTEL $$
( 435-644-8660, 800-738-9643; www.kanabvictoriainn.com; 190 N 300 West; r incl hot breakfast $119-130; ) From the architecture to appointments, the inn is a modern-day interpretation of period Victoriana. Ethan Allen furnishings, gas fireplaces and jetted tubs grace every room.
Holiday Inn Express HOTEL $$
( 435-644-3100, 800-315-2621; www.hiexpress/kanabut.com; 217 S 100 E; r/ste $129/149; ) Newest and nicest chain property.
Treasure Trail Motel MOTEL $
( 435-577-2645, 800-603-2687; www.treasuretrailmotel.net; 150 W Center St; r $66-85; ) Friendly little independent motel; microwaves and mini-refrigerator standard.
Hitch'n Post Campground CAMPGROUND $
( 435-644-2142, 800-458-3516; www.hitchnpostrvpark.com; 196 E 300 South; tent/RV sites with hookups $16/27, camping cabins $28-32; ) Friendly 17-site campground near the town center; laundry and showers.
#### Eating & Drinking
Numerous themed restaurants, ice cream parlors and such line Center St.
Rocking V Café MODERN AMERICAN $$
(97 W Center St; mains $12-25; 5-10pm; ) Fresh ingredients star in dishes like hand-cut buffalo tenderloin and chargrilled zucchini with curried quinoa. Local artwork decorating the 1892 brick storefront is as creative as the food.
Houston's Trail's End Restaurant AMERICAN $$
( 435-644-2488; 32 E Center St; breakfast $5-10, mains $7-21; 7am-10pm) The food must be good if locals frequent a place where the waitresses wear cowboy boots and play six-shooters. Order up chicken-fried steak and gravy for down-home goodness. No alcohol.
Calvin T's Smoking Gun BARBECUE $$
(78 E Center St; mains $12-24; 11:30am-10pm; ) Excellent barbecue, including pulled pork and slabs of ribs, served cafeteria style. In the back courtyard there's a kitschy replica of an Old West movie backdrop, with a pioneer wagon, a saloon and a jail to play on.
Jakey Leighs CAFE $
(4 E Center St; sandwiches $4-8; 7am-10pm Tue-Sat, to 3pm Sun & Mon; ) Come here for tasty quiche and OK coffee on the pleasant patio, or grab a sandwich for the road.
Laid Back Larry's HEALTH FOOD $
(98 S 100 East; 7:30am-3pm, off-season hours vary; ) Pick up fresh smoothies, egg sandwiches on spelt English muffin or healthy lunch specials at this tiny stop. A few health-food and vegetarian goodies are for sale, too.
Luo's CHINESE $$
(365 S 100 E; mains $10-18; 11am-10pm) For a change. Surprisingly good Chinese food; great vegetable selection.
Honey's Marketplace MARKET $
(260 E 300 S; 7am-10pm) Full grocery store with deli; look for the 1950s truck inside.
#### Entertainment
Crescent Moon Theater THEATER
( 435-644-2350; www.crescentmoontheater.com;150 S 100 East; May-Sep) Cowboy poetry, bluegrass music and comedic plays are just some of what is staged here. Monday is $2 Western movie night.
#### Shopping
Western clothing and bric-a-brac are sold, along with Native American knickknacks, at shops all along Center St.
Willow Canyon Outdoor Co OUTDOOR EQUIPMENT
(263 S 100 East; 7:30am-8pm, off-season hours vary) It's easy to spend hours sipping espresso and perusing the eclectic books here. Before you leave, outfit yourself with field guides, camping gear, USGS maps and hiking clothes.
#### Information
As the biggest town around the GSENM, Kanab has several grocery stores, ATMs, banks and services.
BLM Kanab Field Office ( 435-644-4600; 318 N 100 East; 8am-4pm Mon-Fri) Provides information and, November 16 through March 14, issues permits for hiking the Wave in Paria Canyon-Vermilion Cliffs Wilderness Area.
GSENM Visitor Center ( 435-644-4680; www.ut.blm.gov/monument; 745 E Hwy 89; 7:30am-5:30pm) Provides road, trail and weather updates for the Monument.
Kane County Hospital ( 435-644-5811; 355 N Main St; 24hr)
Kane County Office of Tourism ( 435-644-5033, 800-733-5263; www.kaneutah.com; 78 S 100 East; 9am-7pm Mon-Fri, to 5pm Sat) The main source for area information; great old Western movie posters and artifacts on display.
Local police ( 435-644-5807; 140 E 100 South)
Visit Kanab (www.visitkanab.com)
#### Getting There & Around
There is no public transportation to or around Kanab.
Xpress Rent-a-Car ( 435-644-3408; www.xpressrentalcarofkanab.com; 1530 S Alt 89) Car and 4WD rental.
### Around Kanab
##### CORAL PINK SAND DUNES STATE PARK
Coral-colored sand is not especially strange in the southern half of GSENM, but seeing it gathered as giant dunes in a 3700-acre state park ( 435-648-2800; Sand Dunes Rd; day-use $6; day-use dawn-dusk, visitor center 9am-9pm Mar-Oct, to 4pm Nov-Feb) is quite novel. The pinkish hue results from the eroding red Navajo sandstone in the area. Note that 1200 acres of the park are devoted to off-highway vehicles, so it's not necessarily a peaceful experience unless you're here during quiet hours (10pm to 9am), though a 0.5-mile interpretive dune-hike does lead to a 265-acre, ATV-free conservation area.
The same winds that shift the dunes can make tent camping unpleasant at the 22-site campground ( 800-322-3770; http://utahstateparks.reserveamerica.com; tent & RV sites $16), with toilets and hot showers; no hookups. Reservations are essential on weekends when off-roaders come to play.
##### PARIA CANYON-VERMILION CLIFFS WILDERNESS AREA
With miles of weathered, swirling slickrock and slot-canyon systems that can be hiked for days without seeing a soul, it's no wonder that this wilderness area is such a popular destination for hearty trekkers, canyoneers and photographers. Day-hike permits cost $5 to $7 and several are very tough to get. General information and reservations are available at www.blm.gov/az/st/en/arolrsmain/paria/coyote_buttes.html. In-season info and permits are picked up at Paria Contact Station (www.blm.gov/az; Mile 21, Hwy 89; 8:30am-4pm Mar 15-Nov 15), 44 miles east of Kanab. Rangers at the BLM Kanab Field Office are in charge of permits from November 16 through March 14. Remember that summer is scorching; spring and fall are best – and busiest. Beware of flash floods.
Day hikers fight like dogs to get a North Coyote Buttes permit. This trail-less expanse of slickrock includes one of the Southwest's most famous formations – the Wave. The nearly magical sight of the slickrock that appears to be seething and swirling in waves is well worth the 6-mile, four- to five-hour round-trip hike. Go online to request advance permits four months ahead. Otherwise you can hope for one of the handful of next-day walk-in permits available. Line up for the lottery by 7am in spring and fall.
### OFF-THE-BEATEN-TRAIL, EAST ZION
East Zion has several little-traveled, up-country hikes that provide an entirely different perspective on the park, leading off from Zion Ponderosa Ranch. Cable Mountain and Deertrap Mountain have incredible views.
It feels deliciously like cheating to wander through open stands of tall ponderosa pines and then descend 500ft to Observation Point instead of hiking 2500ft uphill from Zion Canyon floor; East Mesa Trail (6.4 miles round-trip, moderate difficulty) does just that. It's less legwork because it's a hearty drive. Getting to the trailhead requires a 4WD for the last few miles, but Zion Ponderosa Ranch Resort, and outfitters in Springdale, can provide hiker shuttles. Ask rangers for details.
Note that at 6500ft, these trails may be closed due to snow November through March.
As an alternative, take the 3.4-mile round-trip hike starting at Wire Pass trailhead, a popular slot-canyon day-hike with self-service trailhead permits. The pass dead-ends where Buckskin Gulch narrows into some thrillingly slight slots. Another option is to start at the Buckskin Gulch trailhead and hike 3 miles one-way to its narrow section.
All trailheads listed lie along House Rock Valley Rd (4.7 miles west of the contact station); it's a dirt road that may require 4WD. Inquire with rangers.
Two miles south of the contact station along a different dirt road, you come to primitive White House Campground (tent sites $5). The five walk-in sites have pit toilets, but no water and few trees. Overnight backcountry camping permits are easier to get than day-hike ones, and can be reserved online and in person. Use of human-waste carryout bags is encouraged; the contact station provides them for free.
Paria Outpost & Outfitters ( 928-691-1047; www.paria.com; Mile 21, Hwy 89; r incl breakfast $65, tent/RV sites $16/20; ) has spare B&B rooms at its kicked-back lodge and campground (no hookups) between Kanab and the wilderness area. Outfitter trips and hiker shuttles available.
### East Zion
Eighteen miles north of Kanab, the turnoff for Hwy 9 leads about 15 miles to the east entrance of Zion National Park.
Families love activity-rich Zion Ponderosa Ranch Resort ( 435-648-2700, 800-293-5444; www.zionponderosa.com; N Fork Rd, off Hwy 9; tent & RV sites with hookups $10/47, cabins without bath/deluxe ste $65/159; ), occupying 4000 acres on Zion's eastern, up-country side. Several great backcountry trails lead from 4WD roads here into the national park. But you may never leave the property since you can hike, bike, canyoneer, climb, swim, play sports, ride four-wheelers and horses, and eat three meals a day here (packages available). Wi-fi-enabled camping sites and cabins (linens included), served by huge showers/bathrooms, are real bargains. The fancier cabin suites are the only lodgingswith air-con, but it's less essential up here above 6000ft. North Fork Rd is about 2.5 miles from the park's East Entrance; continue 5 miles north of Hwy 9 from there.
Closer to the highway, Zion Mountain Resort ( 435-688-1039, 866-648-2555; http://zionmountainresort.com; Hwy 9; cabins $159-199, ste $225-300; ) has a similar adventure and lodging set-up, though it's a bit fancier. Buffalo roam (and appear on the dinner menu) at this 6000-acre resort. Inseason it runs a restaurant, pizza place and primitive campground (sites $10) too. Registration is 2.5 miles east of the Zion park entrance.
### Zion National Park
The soaring red-and-white cliffs of Zion Canyon, one of southern Utah's most dramatic natural wonders, rise high over the Virgin River. Hiking downriver through the Narrows or peering beyond Angels Landing after a 1400ft ascent is indeed amazing. But, for all its awe-inspiring majesty, the park also holds more delicate beauties: weeping rocks, tiny grottoes, hanging gardens and meadows of mesa-top wildflowers. Lush vegetation and low elevation give the magnificent rock formations here a whole different feel from the barren parks in the east.
Most of the 2.7 million annual visitors enter the park along Zion Canyon floor; even the most challenging hikes become congested May through September (shuttle required). But you have other options. Up- country, on the mesa tops (7000ft), it's easy to escape the crowds – and the heat. And the Kolob Canyons section, 40 miles northwest by car, sees one-tenth of the visitors year-round.
Zion National Park
Sights
1Checkerboard Mesa D4
2Court of the Patriarchs C4
3Human History Museum C4
4Kolob Canyons Viewpoint A2
5Lava Point C2
6The Subway B3
Activities, Courses & Tours
7Angels Landing Trail C4
8Canyon Overlook Trail C4
9Canyon Trail Rides C4
10East Mesa Trail D3
11Emerald Pools Trails C4
Hidden Canyon Trail (see 17)
12Northgate Peaks Trail B3
Observation Point Trail(see 17)
13Pa'rus Trail C4
14Riverside Walk Trail C3
15Taylor Creek Trail A1
16Timber Creek Trail A2
17Weeping Rock Trail D4
18Wildcat Canyon Trailhead B3
Sleeping
19Lava Point Campground C2
20South Campground C4
21Watchman Campground C4
22Zion Lodge C4
23Zion Mountain Resort D4
24Zion Ponderosa Ranch Resort D4
Eating
Castle Dome Café (see 22)
Red Rock Grill (see 22)
Summers are hot (100°F, or 38°C, is common); summer nighttime temperatures drop into the 70s (low 20s in Celsius). Beware of sudden cloudbursts from July to September. Winter brings some snow, but daytime temperatures can reach up to 50°F (10°C). Wildflowers bloom in May, as do the bugs; bring repellant.
###### Fees & Permits
Park admission is $25 per week, per vehicle, and an annual Zion Pass is $50. Note that you have to pay to drive through the park on Hwy 9, whether you plan to stop or not. Keep your receipt, it's good for both the main and Kolob Canyons sections.
Backcountry permits ( 435-772-0170; www.nps.gov) are required for all overnight trips (including camping and rock climbs with bivouacs), all through-hikes of the Virgin River (including the Narrows top hike) and any canyoneering hikes requiring ropes for descent. Use limits are in effect on some routes to protect the environment Online permit reservations ($5 reservation fee) are available for many trips, up until 5pm the preceding day. For busy routes there may be a lottery. Twenty-five percent of available permits remain reserved for walk-in visitors the day before or day of a trip. Trying to get a next-day walk-in permit on a busy weekend is like trying to get tickets to a rock concert; lines form at the Backcountry Desk by 6am or earlier.
Permit fees (which are in addition to the reservation fee) are $10 for one to two hikers, $15 for three to seven hikers, and $20 for eight to twelve hikers.
#### Sights & Activities
The park occupies 147,000 acres. Driving in from east Zion, Hwy 9 undulates past yellow sandstone before getting to tighter turns and redder rock after the Zion-Mt Carmel Tunnel. Zion Canyon – with most of the trailheads and activities – lies on Hwy 9 near the south entrance, and the town of Springdale. No roads within the park directly connect this main section with the Kolob Canyons section in the northwest. Unless you hike, you'll have to drive the 40 miles (an hour) between the two, via Hwy 9, Rte 17 and I-15.
##### SCENIC DRIVES
Zion Canyon Scenic Dr SCENIC DRIVE
The premier drive in the park leads between towering cliffs of an incredible red-rock canyon and accesses all the major front-country trailheads. A shuttle bus ride is required April through October. If you've time for only one activity: this is it. Your first stop should be the Human History Museum ( 435-772-0168; admission free; 9am-7pm late May-early Sep, 10am-5pm early Mar-late May & early Sep-Nov, closed Dec-early Mar); the excellent exhibits and 22-minute film are a great introduction to the park. There are shuttle stops, and turn-outs, at viewpoints like the Court of the Patriarchs, at the Zion Lodge, and the end point, the Temple of Sinawava. Use the map you receive at the entrance to navigate. The shuttle takes 45 minutes round-trip; we'd suggest allowing at least two hours with stops.
Hwy 9 SCENIC DRIVE
East of the main park entrance, Hwy 9 rises in a series of six tight switchbacks before the 1.1-mile Zion-Mt Carmel Tunnel, an engineering marvel constructed in the late 1920s. It then leads quickly into dramatically different terrain – a landscape of etched multicolor slickrock, culminating at the mountainous Checkerboard Mesa.
Kolob Canyons Rd SCENIC DRIVE
The less-visited, higher-elevation alternative to Zion Canyon Scenic Dr. Sweeping vistas of cliffs, mountains and finger canyons dominate the stunning 5-mile overlook-rich red-rock route. The scenic road, off I-15, lies 40 miles from the main visitor center.
##### HIKING
Distances for hikes listed below are one-way. Trails can be slippery; check weather conditions before you depart. Flash floods occur year-round, particularly in July and August. Check weather and water conditions with rangers before hiking in river canyons. If you hear thunder, if water rises suddenly or goes muddy, or if you feel sudden wind accompanied by a roar, immediately seek higher ground. Climbing a few feet can save your life; if you can't, get behind a rock fin. There's no outrunning a flash flood.
### ANGELS LANDING TRAIL
Among harder trails, the 2.5-mile Angels Landing Trail (1490ft ascent) is the one everyone's heard of – and fears. At times the trail is no more than 5ft wide, with 1500ft drop-offs to the canyon floor on both sides. Follow the sandy flood plain until you start ascending sharply. After Walter's Wiggles, the set of 21 stonework zigzags that take you up a cleft in the rock, there's a wide area (with pit toilet) which offers vistas and a place to gather strength. Acrophobes may stop here, before the chain-assist rock climb and the 5ft-wide ridge – with 1000ft-plus drop-offs – that you have to cross. The final push to the top is even steeper, and requires some rock scrambling – but oh, the views from the top...
Zion Canyon HIKING
Spring to fall, the mandatory shuttle stops at all major trailheads along Zion Canyon Scenic Dr, allowing one-way hikes. In low season you can park at these stops, but you'll have to hike back to your car.
Of the easy-to-moderate trails, the paved, mile-long Riverside Walk (1 mile) at the end of the road is a good place to start. When the trail ends, you can continue along in the Virgin River for 5 miles to Big Springs; this is the bottom portion of the Narrows – a difficult backpacking trip. Yes, you'll be hiking in the water (June through October), so be prepared.
A steep, but paved, half-mile trail leads to the lower of the Emerald Pools. Here water tumbles from above a steep overhang, creating a desert varnish that resembles rock art. It's worth your while to hike a mile further up the gravel to the more secluded Upper Pool. Note: you will have to scramble up (and back down) some stairlike rocks. The quarter-mile-long Weeping Rock Trail climbs 100ft to hanging gardens.
Hidden Canyon Trail has sheer drop-offs and an 850ft elevation change in just over a mile before you reach the narrow, shady canyon. Think of it as an easier test of your fear of heights.
The most work (2150ft elevation change) is rewarded with the best views – at the top of Observation Point Trail (4 miles). From here you look down on Angels Landing – heck, the whole park really. A backcountry shortcut leads here with much less legwork –the East Mesa Trail, see Click here.
The paved Pa'rus Trail parallels the scenic drive from Watchman Campground to the main park junction (about 2 miles). It's the only trail that allows bicycles and dogs.
The only marked trail along Hwy 9 in east Zion is Canyon Overlook Trail, a moderately easy half-mile walk, yielding thrilling views 1000ft down into Zion Canyon. But you can also stop at Hwy 9 pullouts where there are some interesting narrow canyon hikes and slickrock scrabbles. In summer, locals park at one turnout, climb down, cross under the road and follow a wash to the river for a cool dip...happy searching. Just be aware of your surroundings, and stay in the wash or on the rock to avoid damaging the desert ecology.
Kolob Terrace Road HIKING
Fourteen miles west of Springdale, Kolob Terrace Rd takes off north from Hwy 9, weaving in and out of BLM and national park highlands. (The road is closed due to snow from at least November to March.) Wildcat Canyon Trailhead lies about 28 miles north, after a hairpin turn. From here, follow the Wildcat Canyon Trail till you get to the turnoff for Northgate Peaks Trail. You'll traipse through meadows, filled with wildflowers in spring, and pine forests before you descend to the viewpoint overlooking the peaks. It's a whole different – and much less visited – side of Zion. Wildcat Canyon to Northgate Peaks overlook is 2.2 miles one-way. About 5 miles north of Wildcat Canyon is the gravel road to Lava Point, where there's a lookout and a campground.
Kolob Canyons Road HIKING
In the northwestern section of the park, the easiest trail is at the end of the road: Timber Creek Trail (0.5 miles) follows a 100ft ascent to a small peak with great views. The main hike is the 2.7-mile-long Taylor Creek Trail, which passes pioneer ruins and crisscrosses the creek. The 7-mile one-way hike to Kolob Arch has a big payoff: this arch competes with Landscape Arch in Arches National Park in terms of being one of the biggest in the world. Fit hikers can manage it in a day, or continue on to make it a multiday backcountry trans-park connector.
Backcountry HIKING
Zion has hundreds of miles of backcountryhiking trails, wilderness camping and enough quiet to hear the whoosh of soaring ravens overhead. The most famous route is the unforgettable Narrows, a 16-mile journey into skinny canyons along the Virgin River's north fork (June through October). Plan on getting wet: at least 50% of the hike is in the river. The trip takes 12 hours; split it into two days, spending the night at one of the designated campsites you reserved or finish the hike in time to catch the last park shuttle. The trail ends among the throngs of day hikers on Riverside Walk at the north end of Zion Canyon. A trailhead shuttle is necessary for this and other one-way trips.
Ask rangers about weather conditions and other trails. If you hike the entirety of Zion, north to south, it's a four-day traverse of 50-plus miles. All backcountry hiking and camping requires a permit.
##### CYCLING
Zion Canyon Scenic Drive is a great road ride when cars are forbidden in shuttle season. You can even carry your bicycle up to the end of the road on the shuttle and cruise back down. Bikes are only allowed on the scenic drive and on the 2-mile Pa'rus Trail. Mountain biking is prohibited in the park, but there are other public land trails nearby. Rentals and advice are available in Springdale.
##### CLIMBING & CANYONEERING
If there's one sport that makes Zion special, it's canyoneering. Rappel over the lip of a sandstone bowl, swim icy pools, trace a slot canyon's curves – canyoneering is beautiful, dangerous and sublime all at once. Zion's slot canyons are the park's most sought-after backcountry experience; reserve far in advance.
Zion Canyon also has some of the most famous big-wall rock climbs in America. However, there's not much for beginners or those who like bolted routes. Permits are required for all canyoneering and climbing. Get information at the Backcountry Desk at the Zion Canyon Visitor Center, which also has route descriptions written by climbers.
Guided trips are prohibited in the park. Outfitters in Springdale hold courses outside Zion, after which students can try out their newfound skills in the park.
Subway CANYONEERING
This incredibly popular route (9.5 miles, 1850ft elevation change) has four or five rappels of 20ft or less, and the namesake tube-looking slickrock formation. Start at the Wildcat Canyon trailhead off Kolob Terrace Rd. Hiker shuttle required.
Mystery Canyon CANYONEERING
Mystery Canyon lets you be a rock star: the last rappel drops into the Virgin River before admiring crowds hiking the Narrows. It's accessed off Zion Ponderosa Ranch roads in East Zion; ask rangers for more information. Backcountry permit required; hiker shuttle necessary.
Pine Creek Canyon CANYONEERING
A popular route with moderate challenges and rappels of 50ft to 100ft, Pine Creek has easy access from near the Canyon Overlook Trail. A backcountry permit is required.
##### OTHER ACTIVITIES
Canyon Trail Rides HORSEBACK RIDING
( 435-679-8665, 435-772-3810; www.canyonrides.com; Mar-Nov) Zion's official horseback-riding concessionaire operates across from Zion Lodge. Take a one-hour ($40) or three-hour ($75) ride on the Sand Bench Trail along the Virgin River.
#### Tours & Outfitters
Cycling, rock-climbing, canyoneering and driving-tour outfitters from Springdale operate outside the park.
Zion Canyon Field Institute TOUR
( 435-772-3264, 800-635-3959; www.zionpark.org; half-day from $50) Explore Zion by moonlight, take a wildflower photography class, investigate Kolob Canyon's geology or help clean up the Narrows. All courses and tours include some hiking.
Ride Along With A Ranger DRIVING TOUR
( 435-772-3256; www.nps.gov/zion; Zion CanyonVisitor Center; May-Oct) Reservations are usually required for the entertaining 90-minute, ranger-led Zion Canyon shuttle tour that makes stops not on the regular route. It's a great non-hiking alternative for those with limited mobility.
Red Rock Shuttle & Tours DRIVING TOUR
( 435-635-9104; www.redrockshuttle.com) Private van tours of Zion, $100 per person for six hours.
#### Sleeping
Both of the park's large, established campgrounds are near the Zion Canyon Visitor Center. For wilderness camping at designated areas along the West Rim, La Verkin Creek, Hop Valley and the Narrows you'll need a permit (Click here). More lodging and camping is available in Springdale.
Zion Lodge LODGE $$-$$$
( 435-772-7700, 888-297-2757; www.zionlodge.com; Zion Canyon Scenic Dr; r $150-170, cabins $165-180, ste $185; ) Stunning red-rock cliffs surround you on all sides, and that coveted location in the middle of Zion Canyon (and the red permit that allows you to drive to the lodge in shuttle season) is what you're paying for. The lodge was first built in the 1920s, but it burnt down in 1966. The reconstructed lodge is not as grand as those in other states. Although they're in wooden buildings with balconies, the motel rooms are just motel rooms: nothing fancy. Carved headboards, wood floors and gas fireplaces do give 'Western cabins' more charm, but be warned that paper-thin walls separate you from neighbors. There are two eateries and a big lawn for lounging outside. No room TVs.
Watchman Campground CAMPGROUND $
( 435-772-3256, 877-444-6777 for reservations; www.recreation.gov; Hwy 9; tent sites $16, RV sites with hookups $18-20) Towering cottonwoods provide fairly good shade for the 165 well-spaced sites at Watchman (95 have electricity). Reservations are available May through October; book as far in advance as possible to request a riverside site. Fire grates, drinking water and flush toilets; no showers. Note that there is sometimes construction works happening during the winter season.
South Campground CAMPGROUND $
( 435-772-3256; Hwy 9; tent & RV sites $16; mid-Mar–Oct) The South Campground has very similar scenery and the same basic facilities as Watchman, except that here limited generator use is allowed because there are no hookups. The 116 first-come, first-served tent sites often fill up by 10am. Note that this ground sits beside the busy Pa'rus Trail.
Lava Point Campground CAMPGROUND $
(Lava Point Rd; Jun-Sep) Six first-come, first-served park sites 35 miles up Kolob Terrace Rd at 7900ft. Pit toilets, no water.
#### Eating
The lodge has the only in-park dining; otherwise head to Springdale.
Red Rock Grill AMERICAN $$-$$$
( 435-772-7760; Zion Lodge, Zion Canyon Scenic Dr; breakfast $6-11, lunch sandwiches $7-12, dinner $16-28; 6:30-10:30am, 11:30am-3pm & 5-10pm Mar-Oct, hours vary Nov-Feb) Settle into your log-replica chair and peer out of the window-lined dining room or relax on the big deck with magnificent canyon views. Though the dinner menu touts its sustainable-cuisine stance for dishes like roast pork loin and flatiron steak, the results are hit-or-miss. Dinner reservations recommended. Full bar.
Castle Dome Café CAFE $
(Zion Lodge, Zion Canyon Scenic Dr; mains $4-8; 11am-5pm Apr-Oct) This counter-service cafe serves sandwiches, pizza, salads, soups, Asian-ish rice bowls and ice cream.
#### Information
Visitor center hours vary slightly month to month. We list the minimums for each season.
Kolob Canyons Visitor Center ( 435-586-0895; Kolob Canyons Rd, off I-15; 8am-6pm May-Sep, 8am-4:30pm Oct-Apr) Small, secondary visitor center in the northwest section of the park.
Lonely Planet (www.lonelyplanet.com/usa/southwest/zion-national-park) Planning advice, author recommendations, traveler reviews and insider tips.
National Park Rangers Emergency ( 435-772-3322)
Zion Canyon Backcountry Desk ( 435-772-0170; www.nps.gov/zion/planyourvisit; Zion Canyon Visitor Center; 7am-6pm May-Sep, 8am-4:30pm Oct-Apr) Provides backcountry trail and camping information and permits. Some permits available online.
Zion Canyon Visitor Center ( 435-772-3256; www.nps.gov/zion; 8am-6pm May-Sep, 8am-4:30pm Oct-Apr) Several rangers are on hand to answer questions at the main visitor center; ask to see the picture binder of hikes to know what you're getting into. The large number of ranger-led activities are listed here.
Zion Lodge ( 435-772-3213; Zion Canyon Scenic Dr) Free wi-fi and two free internet terminals in the lobby.
Zion Natural History Association ( 435-772-3264, 800-635-3959; www.zionpark.org) Runs visitor center bookstores; great online book selection for advance planning.
#### Getting There & Around
###### Bus
There is no public transportation to the park.
St George Express ( 435-652-1100; www.stgeorgeexpress.com) Shared van service to St George ($75, one hour) and Las Vegas ($100, three hours).
###### Private Vehicle
Arriving from the east on Hwy 9, you have to pass through the free Zion-Mt Carmel Tunnel. If your RV or trailer is 7ft 10in wide or 11ft 4in high or larger, it must be escorted through, since vehicles this big need both lanes. Motorists requiring an escort pay $15 over the entrance fee, good for two trips. Between April and October, rangers are stationed at the tunnel from 8am to 8pm daily; at other times, ask at the entrance stations. Vehicles prohibited at all times include those more than 13ft 1in tall or more than 40ft long.
###### Park Shuttle
How you get around Zion depends on the season. Between April and October, passenger vehicles are not allowed on Zion Canyon Scenic Dr. The park operates two free, linked shuttle loops. The Zion Park Shuttle makes nine stops along the canyon, from the main visitor center to the Temple of Sinawava (a 45-minute round-trip). The Springdale Shuttle makes six regular stops and three flag stops along Hwy 9 between the park's south entrance and the Majestic View Lodge in Springdale, the hotel furthest from the park. You can ride the Springdale Shuttle to Zion Canyon Giant Screen Theatre and walk across a footbridge into the park. The visitor center and the first Zion shuttle stop lie on the other side of the kiosk.
The propane-burning park shuttle busses are wheelchair-accessible, can accommodate large backpacks and carry up to two bicycles or one baby stroller. Schedules change, but generally shuttles operate from at least 6:45am to 10pm, every 15 minutes on average.
HIKER SHUTTLE Outfitters that offer hiker shuttles (from $25 to $35 per person, two-person minimum, reservation required) to backcountry and canyoneering trailheads include:
Red Rock Shuttle & Tours ( 435-635-9104; www.redrockshuttle.com) Picks up from Zion Canyon Visitor Center.
Zion Adventure Company ( 435-772-1001; www.zionadventures.com)
Zion Rock & Mountain Guides ( 435-772-3303; www.zionrockguides.com)
### Springdale
Positioned at the entrance to Zion National Park, Springdale is a perfect little park town. Stunning red cliffs form the backdrop to eclectic cafes and restaurants big on local produce and organic ingredients. Galleries and shops line the long main drag, interspersed with indie motels and B&Bs. Many of the outdoorsy folk who live here moved from somewhere less beautiful, but you will occasionally run into a life-long local who thinks 'they're just rocks.'
#### Sights & Activities
Hiking trails in Zion are the area's biggest attraction. There are also some awesome single-track, slickrock mountain-bike trails as good as Moab's. Ask local outfitters about Gooseberry Mesa, Hurricane Cliffs and Rockville Bench.
The Virgin River is swift, rocky and only about knee-deep: more of a bumpy adventure ride than a leisurely float, but tubing (outside the park only) is popular in the summer. Note that from June to August, the water warms to only 55°F to 65°F (13°C to 18°C). Zion CanyonCampground and some other riverside lodgings have good water-play access.
Zion Adventure Company WATER SPORTS
( 435-772-1001; www.zionadventures.com; 36 Lion Blvd; tubing 10am-4pm May-Sep) River-tubing packages include tube and water-sock rental, drop-off and pick-up. The float stretches about 2.5 miles, and lasts from 90 minutes to two hours depending on waterflow. There's much faster, high-adventure tubing (including safety gear) on offer during spring run-off in May.
Deep Canyon Adventure Spa DAY SPA
( 435-772-3244; www.deepcanyonspa.com; Flanigan's Inn, 428 Zion Park Blvd; 1hr treatments from $89) After a hard day's hike, the river-stone massage will be your muscles' new best friend.
Zion Canyon Elk Ranch FARM
( 435-619-2424; 792 Zion Park Blvd; by donation; dawn to dusk; ) You can't miss this ranch right in the middle of town. It offers kids of all ages the chance to pet and feed the elk and buffalo. The property has been in the owner's family for more than 100 years.
#### Tours & Outfitters
The towns two main outfitters, Zion Rock & Mountain Guides and Zion Adventure Company, lead hiking, biking, climbing, rappelling and multisport trips on the every-bit-as-beautiful BLM lands near the park (half-days from $150). We highly recommend canyoneering as a quintessential area experience. Both outfitters are also one-stop shops for adventure needs: they sell ropes and maps, have classes, provide advice and suit you up with rental gear (harnesses, helmets, canyoneering shoes, dry suits, fleece layers, waterproof packs and more). The hiker shuttles and gear rental are especially handy for one-way slot-canyon routes and Narrows hikes. Both companies have excellent reputations and tons of experience around Zion.
Bike rentals range from $25 to $40 per half day.
Zion Rock & Mountain Guides ADVENTURE SPORTS
( 435-772-3303; www.zionrockguides.com; 1458 Zion Park Blvd; 8am-8pm Mar-Oct, hours vary Nov-Feb) More down-to-business than other outfitters, and especially good for sporty types. All classes and trips are private. Static rope line rental available.
Bike Zion MOUNTAIN BIKING
( 435-772-0320; www.bikingzion.com; Zion Rock & Mountain Guides) Zion Rock's on-site sister cycle shop; does rentals and tours. Showers available.
Zion Adventure Company ADVENTURE SPORTS
( 435-772-1001; www.zionadventures.com; 36 Lion Blvd; 8am-8pm Mar-Oct; 9am-noon & 4-7pm Nov-Feb) Slick videos and diagrams help put the tentative at ease; good for young families. Winter snowshoes and crampon rentals available.
Zion Cycles MOUNTAIN BIKING
( 435-772-0400; www.zioncycles.com; 868 ZionPark Blvd; 9am-7pm Feb-Nov) Tandem, road andmountain-bike rentals and sales. No tours.
Red Desert Adventures ADVENTURE SPORTS
( 435-668 2888; www.reddesertadventures.com) A small company; provides private guided hiking, biking and canyoneering.
Zion Outback Safaris ADVENTURE TOUR
( 866-946-6494; www.zionjeeptours.com; 3hr adult/child $64/46) Backroad 4WD tours in a 12-seat modified truck.
#### Festivals & Events
Springdale celebrates quite often, contact the Zion Canyon Visitor Bureau for specifics.
St Patrick's Day PARADE
St Patrick's Day (March 17) parade and celebration includes a green Jell-O sculpture competition.
Zion Canyon Music Festival MUSIC
(www.zioncanyonmusicfestival.com) Folk (and other music) filled weekend in late September.
#### Sleeping
Prices listed here are for March through October – rates plummet in the off-season. The lower the address number on Zion Park Blvd, the closer the park entrance; all lodgings are near shuttle stops. Look for slightly less expensive B&Bs around Zion, eg in Rockville.
Under the Eaves Inn B&B $$
( 435-772-3457, 866-261-2655; www.under-the-eaves.com; 980 Zion Park Blvd; r incl breakfast $95-125, ste $185; ) From colorful tractor reflectors to angel art, the owners' collections enliven every corner of this quaint 1930s bungalow. The fireplace suite is huge; other character-filled rooms are snug. Hang out in the arts-and-crafts living room or on Adirondack chairs and swings in the gorgeous gardens. Local restaurant coupon for breakfast.
Canyon Ranch Motel MOTEL $-$$
( 435-772-3357, 866-946-6276; www.canyonranchmotel.com; 668 Zion Park Blvd; r $89-119, apt $109-139; ) Small, cottage-like buildings surround a shaded lawn with redwood swings, picnic tables and a small pool at this 1930s motor-court motel. Inside, rooms are thoroughly modern; apartments have kitchenettes.
Driftwood Lodge LODGE $$-$$$
( 435-772-3262, 888-801-8811; www.driftwoodlodge.net; 1515 Zion Park Blvd; r $129-159, ste $199-299; ) Rich material and dark leathers define the upscale style of thoroughly remodeled rooms at this eco-minded lodging. Some of the contemporary suites have pastoral sunset views of field, river and mountain beyond. An expansive pool and the town's top restaurant, Parallel 88, are on the grounds.
Zion Canyon Campground
& RV Resort CAMPGROUND $
( 435-772-3237; www.zioncamp.com; 479 Zion Park Blvd; tent/RV sites with hookups $30/25; ) Water and tubing access at this 200-site campground are just across the Virgin River from the national park. Attached to the Quality Inn Motel, shared amenities include: heated pool, laundry, camp store, playground and restaurant. Not all sites have shade.
Cliffrose Lodge MOTEL $$-$$$
( 435-772-3234, 800-243-8824; www.cliffroselodge.com; 281 Zion Park Blvd; r $159-189; ) Kick back in a lounge chair or take a picnic lunch to enjoy on the five gorgeous acres of lawn and flower gardens leading down to the river. High-thread-count bedding and pillow-top mattresses are among upscale touches.
Canyon Vista Suites B&B B&B $$
( 435-772-3801; www.canyonvistabandb.com; 897 Zion Park Blvd; ste incl breakfast $129-159; ) All the homey comfort of a B&B, coupled with the privacy of a hotel. Individual entrances lead out from Southwestern or Old World-esque rooms onto a wooden porch or a sprawling patio and lawn with river access. Breakfast coupons; hot tub on-site.
Red Rock Inn B&B $$
( 435-772-3139; www.redrockinn.com; 998 Zion Park Blvd; cottages incl breakfast $127-132; ) Five romantic country-contemporary cottages spill down the desert hillside, backed by incredible red rock. Enjoy the full hot breakfast (egg dish and pastries) that appears at the door either on the hilltop terrace or your private patio.
Zion Canyon Bed & Breakfast B&B $$-$$$
( 435-772-9466; www.zioncanyonbandb.com; 101 Kokopelli Circle; r incl breakfast $135-185; ) Deep canyon colors – magenta, eggplant, burnt sienna – complement not only the scenery, but the rustic Southwestern styling. Everywhere you turn there's another gorgeous red-rock view framed perfectly in an oversized window. Full gourmet breakfasts.
Desert Pearl Inn HOTEL $$-$$$
( 435-772-8888, 888-828-0898; www.desertpearl.com; 707 Zion Park Blvd; r $158-188, ste $300; ) How naturally stylish: twig sculptures decorate the walls and molded metal headboards resemble art. Opt for a spacious riverside king suite to get a waterfront patio.
Novel House Inn B&B $$$
( 435-772-3650, 800-711-8400; www.novelhouse.com; 73 Paradise Rd; r $139-159; ) Incredible detail has gone into each of the author-themed rooms: Rudyard Kipling has animal prints and mosquito netting, and a pillow in the Victorian Dickens room reads 'Bah humbug'... Breakfast coupons; hot tub.
Pioneer Lodge MOTEL $$
( 435-772-3233, 888-772-3233; www.pioneerlodge.com; 838 Zion Park Blvd; r $134-149; ) In the absolute center of town; pine-bed rooms have a rustic feel.
Harvest House B&B $$
( 435-772-3880; www.harvesthouse.net; 29 Canyon View Dr; r incl breakfast $120-150; ) Modern B&B alternative with full breakfast.
Best Western Zion Park Inn MOTEL $$
( 435-772-3200, 800-934-7275; www.zionparkinn.com; 1215 Zion Park Blvd; r $115-119; ) Rambling lodge complex includes a great room, putting green, badminton court, two pools, two restaurants and a liquor store.
Terrace Brook Lodge MOTEL $
( 435-772-3932, 800-342-6779; 990 Zion Park Blvd; s & d $85-109; ) Bare-bones basic motel. The two-bed rooms are newer than the singles.
### LIKE A VIRGIN
Fourteen miles west of Springdale, you can't help but pass a Virgin. The town, named after the river (what else?), has an odd claim to fame – in 2000 the council passed a law requiring every resident to own a gun. Locals are fined $500 if they don't. Kolob Terrace Rd takes off north from here to Lava Point in Zion National Park. The huge store at the Virgin Trading Post (1000 W Hwy 9; 9am-7pm) sells homemade fudge, ice cream and every Western knickknack known to the world. But it's the hard-to-miss Old West Village (admission $1; ) that's the real reason to stop. Have your picture taken inside the 'Virgin Jail' or 'Wild Ass Saloon' before you feed the deer, donkey and llama in the petting zoo. It's pure, kitschy fun.
#### Eating
Note that many places in town limit hours variably – or close entirely – off season. Those listed as serving dinner have beer and wine only, unless otherwise noted. The saloon at Bit & Spur and the wine bar within Parallel 88 are fine places to drink as well as eat. Springdale is not big on nightlife.
Parallel 88 MODERN AMERICAN $$$
( 435-772-3588; Driftwood Lodge, 1515 Zion Park Blvd; breakfast $10-16, dinner $20-48; 7-10:30am & 5-10pm Mar-Oct, off-season hours vary) Chef Jeff Crosland has mastered 'casually elegant' with a top-notch seasonal menu and friendly, approachable service. Most nights he can be seen chatting with guests on the patio as they nosh on impossibly tender green-apple pork loin surrounded by impossibly gorgeous red-cliff views. Full bar.
Whiptail Grill SOUTHWESTERN $$
( 435-772-0283; 445 Zion Park Blvd; mains $10-16; 11am-7pm Apr-Oct; ) The old gas-station building isn't much to look at, but man, you can't beat the fresh tastes here: pan-seared tilapia tacos, chipotle chicken enchiladas, organic beef Mexican pizza... Outdoor patio tables fill up quick.
Oscar's Café MODERN SOUTHWESTERN $$
(948 Zion Park Blvd; breakfast & burgers $9-14, dinner $16-28; 8am-10pm) From green-chile laden omelets to pork _verde_ burritos (with a green salsa), Oscar's has the Southwestern spice going on. But it also does smoky ribs, shrimp and garlic burgers well. The living-room-like, Mexican-tiled patio with twinkly lights (and heaters) is a favorite hang-out in the evening.
Bit & Spur Restaurant & Saloon MODERN SOUTHWESTERN $$
(1212 Zion Park Blvd; mains $14-28; 5-10pm daily Mar-Oct, 5-10pm Thu-Sat Nov-Feb) Sweet-potato tamales and chile-rubbed rib-eyes are two of the classics at this local institution. Inside, the walls are wild with local art; outside on the deck it's all about the red-rock sunset. Full bar.
Café Soleil CAFE $
(205 Zion Park Blvd; breakfast & mains $5-10; 6:30am-7pm; ) The food is every bit as good as the free trade coffee. Try the Mediterranean hummus wrap or giant vegetable frittata; pizza and salads, too. Breakfast served till noon.
Park House Cafe CAFE $
(1880 Zion Park Blvd; breakfast & sandwiches $5-10; 7:30am-3:30pm Mar-Oct) Wake up as late as you like: Park House Cafe serves their Asiagobagel with egg and avocado – along with other breakfast items – until 2pm. Burgers, sandwiches and salads are all made from the freshest ingredients. Great little walled patio, too. Barbecue is served some summer evenings.
Flying Monkey PIZZERIA $$
(975 Zion Park Blvd; mains $10-16; 11am-9:30pm) Wood-fired goodness at great prices. Expect interesting ingredients like fennel and yellow squash on your roast veggie pizza or Italian sausage with the prosciutto on your oven-baked sandwich. Burgers, salads and pastas, too.
Mean Bean Coffee House CAFE $
(932 Zion Park Blvd; sandwiches $3-6; 7am-5pm Jun-Aug, 7am-2pm Sep-May; ) Probably the town's best brew. This great local hangout attracts outdoorsy types for their first cup of organic java, soy latte or chai of the day. Take your breakfast burrito or panini up to the roof deck.
Springdale Fruit Company Market MARKET $
(2491 Zion Park Blvd; sandwiches $8; 8am-8pm Apr-Oct, ) On-site orchards produce summertime fruit, for sale along with organic, vegan and gluten-free foodstuffs beginning in summer. Enjoy made-to-order focaccia sandwiches and fruit smoothies at picnic tables in the parklike surrounds.
Thai Sapa ASIAN $$
(145 Zion Park Blvd; mains $10-20; noon-9:30pm Apr-Oct, hours vary Nov-Mar) This mix of Thai, Chinese and Vietnamese cuisine is your only ethnic option in town; service can be spotty.
Orange Star DESSERTS $
( 435-772-0255; 868 Zion Park Blvd; sandwiches & smoothies $3-7; 11am-8pm Mar-Oct) Fresh fro-yo smoothies like the 'Angels Landing', with Ghirardelli chocolate and toffee chips.
Sol Foods Downtown Supermarket MARKET
( 435-772-3100; 995 Zion Park Blvd; 7am-11pm Apr-Oct, 9am-8pm Nov-Mar) The 'big' supermarket in Springdale.
Switchback Trading Co MARKET
(1149 Zion Park Blvd; noon-9pm Mon-Sat) The only liquor store is part of the Best Western complex.
#### Entertainment
OC Tanner Amphitheater THEATER
( 435-652-7994; www.dixie.edu/tanner; 300 Lion Blvd; mid-May–Aug) Outdoor amphitheater surrounded by red rock; stages classical, bluegrass, country and other concerts and performances.
Zion Canyon Giant Screen Theatre THEATER
(www.zioncanyontheatre.com; 145 Zion Park Blvd) Catch the 40-minute _Zion Canyon: Treasure of the Gods_ on a six-story screen – it's light on substance but long on beauty.
#### Shopping
Eclectic boutiques and outdoorsy T-shirt shops are scattered the length of Zion Park Blvd. Stunning photography is particularly well represented among area galleries – not surprising given Zion's beauty. Look, too, for the three-dimensional oil paintings of Anna Weiler Brown and the colorful multimedia works of Deb Durban, both locals. Hours vary off season.
David Petit Gallery ARTS & CRAFTS
(975 Zion Park Blvd; 10:30am-8pm Wed-Sat, 3-8pm Tue) Our favorite intrepid outdoorsman-photographer. His rock art and ruin photos are unlike any others.
David J West Gallery ARTS & CRAFTS
(801 Zion Park Blvd; 10am-9pm Tue-Sun Mar-Oct, to 8pm Nov-Feb) Iconic local-landscape photography; sells some photo gear.
Fatali Gallery ARTS & CRAFTS
(105 Zion Park Blvd; 11am-7pm Mar-Nov) Otherworldly colors, sensation-causing national-park photography.
De Zion Gallery ARTS & CRAFTS
(1051 Zion Park Blvd; noon-6pm Mar-Oct) Large studio, with many Utah artists represented.
Sundancer Books BOOKS
(975 Zion Park Blvd; 10am-7pm Mar-Oct, off-season hours vary) Great selection of area-related interest books.
Redrock Jewelry JEWELERY
(998 Zion Park Blvd; 10am-6pm Mar-Oct, off-season hours vary) Gorgeous, local artist-made jewelry.
#### Information
There's no town information office; go online to www.zionpark.com and www.zionnationalpark.com. The nearest full service hospital is in St George.
Doggy Dude Ranch ( 435-772-3105; www.doggyduderanch.com; 800 Hwy 9) Most local lodgings don't accept pets; board your pampered pooch 3.7 miles west of the park boundary.
Pioneer Lodge Internet Café (Zion Park Blvd; per 25min $3.50; 6:30am-9pm) Two internet terminals.
Zion Canyon Medical Clinic ( 435-772-3226; 120 Lion Blvd; 9am-5pm Tue-Sat Mar-Oct, 9am-5pm Tue Nov-Feb) Walk-in urgent-care clinic.
#### Getting Around
There's no public transportation to the town, but from April through October the free Springdale Shuttle operates between stops in town and Zion National Park. For more information, see Click here.
### Around Zion National Park
Just five miles west of Zion National Park, Rockville (no services) seems like a neighborhood extension of Springdale. There are a few old buildings, but otherwise it's mostly housing. B&Bs here can be a slightly cheaper alternative to those nearer the park.
The bicycle scene in _Butch Cassidy and the Sundance Kid_ was filmed in the nearby Grafton ghost town. You can wander freely around the restored 1886 brick meeting house and general store, and a nearby pioneer cemetery. A few pioneer log homes stand on private property. Getting to Grafton can be tricky. Turn south on Bridge Rd, cross the one-lane bridge and turn right. Bear right at the fork and follow signs for 2 miles to the ghost town.
A big backyard pool, gardens leading down to the river and a terrace for breakfast make Desert Thistle Bed & Breakfast ( 435-772-0251; www.thedesertthistle.com; 37 W Main St; r incl breakfast $110-145; ) the top choice, for summer especially. Rooms are posh. Bunk House at Zion ( 435-772-3393; www.bunkhouseatzion.com; 149 E Main St; r incl breakfast $55-80) is a bit more down-to-earth. The thoroughly green two-bedroom B&B serves organic breakfasts with ingredients from their orchard and uses 100% renewable energy, even employing an antique wood-fired stove and push-powered lawnmower.
Other alternatives include country farmhouse-like Rockville Rose ( 435-772-0800; www.rockvilleroseinn.com; 125 E Main St; r incl breakfast $95-115; ), floral-but-modern Dream Catcher Inn ( 435-772-3600, 800-953-7326; www.dreamcatcherinnzion.com; 225 E Main St; r incl breakfast $80-110; ) and the simple rooms at older Amber Inn ( 435-772-9597; www.amber-inn.com; 244 W Main St; r $100-115; ).
Fourteen miles west of Springdale, the next little community is Virgin; the turnoff to Kolob Terrace Rd and a couple of trading posts are here. Red Coyote Cafe (239 W Hwy 9; breakfast & sandwiches $4-9; 7:30am-4:30pm Mar-Oct, off-season hours vary; ) is a local hangout that often has live music on Saturday afternoons. Wine and beer available.
West of town, a 1.5-mile gravel-and-dirt road leads south to La Verkin Overlook. Stop for a fantastic 360-degree view of the surrounding 40 sq miles, from Zion to the Pine Valley Mountains.
Hurricane, 22 miles from Springdale, has the nearest full-size supermarkets and other services, including a couple of much-needed-after-dusty-backroads car washes.
### Cedar City
POP 27,800 / ELEV 5800FT
This sleepy college town comes to life every summer when the Shakespeare festival takes over. Associated events, plays and tours continue into fall. Year-round you can make one of the many B&Bs a quiet home-base for exploring the Kolob Canyons section of Zion National Park or Cedar Breaks National Monument. At roughly 6000ft,cooler temperatures prevail here as compared to Springdale (60 miles away) or St George (55 miles); there's even the occasional snow in May.
#### Sights & Activities
The play's the thing for most people visiting Cedar City. See relevant park sections for the best nearby hiking.
Frontier Homestead State Park Museum MUSEUM
(http://stateparks.utah.gov; 635 N Main St; admission $3; 9am-5pm Mon-Sat; ) Kids love the cabins and the brightly painted 19th-century buggies, as well as the garden full of old farm equipment to run through. Living history demos take place June through August.
Cedar Cycle CYCLING
( 435-586-5210; www.cedarcycle.com; 38 E 200 South; 9am-5pm Mon-Fri, 9am-2pm Sat) After you rent a bike (from $30 per day) the knowledgeable staff can point you to local trails.
### PAROWAN GAP
People have been passing this way for millennia, and the Parowan Gap (www.blm.gov; freely accessible) petroglyphs prove it. Look closely as you continue walking along the road to find panels additional to those signed. Archeo-astronomers believe that the gap in the rocks opposite the petroglyphs may have been used as part of an ancient, astronomically-based calendar. The Cedar City & Brian Head Tourism & Convention Bureau, in Cedar City, has colorful interpretive brochures explaining site details.
#### Festivals & Events
Cedar City is known for its year-round festivities. For a full schedule, see www.cedarcity.org.
Utah Shakespearean Festival CULTURAL
( 435-586-7878, 800-752-9849; www.bard.org;Southern Utah University, 351 W Center St) Southern Utah University has been hosting Cedar City's main event since 1962. From late June into September, three of the bard's plays and three contemporary dramas take the stage. From mid-September into late October three more plays are presented – one Shakespearean, one dramatic and one musical. Productions are well regarded, but you also shouldn't miss the extras: 'greenshows' with Elizabethan minstrels, literary seminars discussing the plays and costume classes are all free. Backstage and scene-changing tours cost extra. Note that children under six are not allowed at performances, but free childcare is available.
The venues are the open-air Adams Shakespearean Theatre, an 819-seat reproduction of London's Globe Theater; the modern 769-seat Randall L Jones Theatre, where backstage tours are held; and the less noteworthy Auditorium Theatre used for matinees and rainy days. Make reservations at least a few weeks in advance. At 10am on the day of the show, obscured-view gallery seats for the Adams performance go on sale at the walk-up ticket office (cnr 300 W & W Center Sts; 10am-7pm late Jun-Aug & mid-Sep–Oct).
Groove Fest MUSIC
(www.groovefestutah.com) A late September weekend grooves with folksy and funky sound.
Neil Simon Festival CULTURAL
(www.simonfest.org) American plays staged mid-July to mid-August.
Cedar City Skyfest SPORTS
(www.cedarcityskyfest.org) Hot-air balloons, kites and model rockets go off in September.
#### Sleeping
The following rates are for the high season (March through October), but weekends during the Shakespearean Festival may cost more.
Anniversary House B&B $$
( 435-865-1266, 800-778-5109; http://theanniversaryhouse.com; 133 S 100 W; r incl breakfast $99-119; ) Remarkably comfortable rooms, a great-to-talk-to-host and thoughtful extras make this one of our faves. Savor freshly baked cake and complimentary beverages in the mission-style dining room or lounge around in the landscaped backyard. Outdoor kennel available.
Garden Cottage B&B B&B $$
( 435-586-4919, 866-586-4919; www.thegardencottagebnb.com; 16 N 200 W; r incl breakfast $119-129; ) Romantic vines climb up the steep-roofed cottage walls, and in season a fantasia of blooms grow in encompassing gardens. If you like antiques and quilts, you're going to love Garden Cottage. The owner has done an amazing job displaying family treasures. No room TVs.
Big Yellow Inn B&B $$-$$$
( 435-586-0960; www.bigyellowinn.com; 234 S 300 W; r incl breakfast $99-199; ) A purpose-built Georgian Revival inn with room to roam: a dining room, a library, a den and many porches. Upstairs rooms are elegantly ornate. Downstairs, the ground-floor walk-out rooms are simpler and a bit more 'country'. The owners also oversee several adjunct B&B properties and vacation rentals around town.
Amid Summer's Inn B&B $$
( 435-586-2600, 888-586-2601; www.amidsummersinn.com; 140 S 100 W; r incl breakfast $109-179; ) Tasteful additions have brought the guestroom count to 10 at this 1930s home-based B&B. Common areas and some rooms have a Victorian feel; others are more over-the-top trompe l'oeil fantasies. Accommodating hosts; great breakfasts.
Iron Gate Inn B&B $$
( 435-867-0603, 800-808-4599; www.theirongateinn.com; 100 N 200 West; r incl breakfast $119-179; ) Rambling porches and a big yard surround the distinct 1897 Second Empire Victorian house with large, modern-luxury guest rooms. Enjoy your breakfast on the large shady patio.
Best Western Town & Country MOTEL $$
( 435-586-9900, 800-780-7234; 189 N Main St; r incl breakfast $86-109; ) Rooms are giant and rates are right at this well-cared- for Best Western.
#### Eating
How wonderful it would be if Cedar City had dining on a par with its B&Bs and top-notch theater. But alas, poor Yorick, it doth not. Hours are usually extended variably during Shakespeare weekends.
Sonny Boy's BBQ BARBECUE $
(126 N Main St; mains $6-14; 11am-9pm Mon-Thu, 11am-10pm Fri & Sat) Locals love the piles of slow-smoked meat and fun side dishes such as fried pickles. Eat in or take out.
Grind Coffeehouse CAFE $
(19 N Main St; sandwiches $7-10; 7am-7pm Mon-Sat, 8am-5pm Sun; ) Hang out with the locals and have a barista-made brew, a great hot sandwich or a big salad. Sometimes there's music on the menu.
Garden House AMERICAN $-$$
(164 S 100 West; lunch $8-12, dinner $14-22; 11am-9:30pm Mon-Sat) Homemade soups, sandwiches, pastas and seafood dishes top the menu at this house-turned-rambling restaurant. A senior-citizen fave.
Two popular and unpretentious Western steakhouses lie just outside town in rustic red-rock settings:
Rusty's Ranch House STEAKHOUSE $$
(Hwy 14; mains $15-28; 5-9pm Mon-Sat) Two miles east of Cedar City.
Milt's Stage Stop STEAKHOUSE $$
(Hwy 14; mains $16-30; 5-9pm) Five miles east of town.
#### Shopping
Groovacious Music Store MUSIC
(www.groovacious.com; 171 N 100 West; 10am-9pm Mon-Sat) The local music store (with awesome vinyl) hosts concerts and other events.
#### Information
Cedar City & Brian Head Tourism & Convention Bureau ( 435-586-5124, 800-354-4849; www.scenicsouthernutah.com; 581 N Main St; 8am-5pm Mon-Fri, 9am-1pm Sat) Area-wide info and free internet use.
Cedar City Ranger Station ( 435-865-3200; www.fs.fed.us/r4/dixie; 1789 N Wedgewood Ln; 8am-5pm Mon-Fri) Provides Dixie National Forest information.
Valley View Medical Center ( 435-868-5000; http://intermountainhealthcare.org; 1303 N Main St; 24hrs) Hospital.
Zions Bank (3 S Main St) Currency exchange & ATM.
#### Getting There & Around
You'll need private transportation to get to and around Cedar City.
### Hwy 14
As scenic drives go, Hwy 14 is awesome. It leads 42 miles over the Markagunt Plateau, cresting at 10,000ft for stunning vistas of Zion National Park and Arizona. The surrounding area is part of Dixie National Forest (www.fs.fed.us/r4/dixie). For information, check in with Cedar City Ranger Station. Though Hwy 14 remains open all winter, snow tires or chains are required between November and April.
Hiking and biking trails, past the Cedar Breaks National Monument turnoff on Hwy 14, have tremendous views; particularly at sunset. They include the short (less than a mile one-way) Cascade Falls and Bristlecone Pine Trail and the 32-mile Virgin River Rim Trail. A signed turnoff 24.5 miles from Cedar City leads to jumbled lava beds.
Boating and fishing are the activities of choice at Navajo Lake, 25 miles east of Cedar City. You can rent a motorboat ($75 to $120 per day) or stay over in a historic 1920s cabin at Navajo Lake Lodge ( 702-646-4197; www.navajolakelodge.com; cabins $70-120; May-Oct). The rustic lodgings include bedding, but no refrigerators.
Five miles further east, Duck Creek Visitor Center ( 435-682-2432; Hwy 14; 9am-4:30pm late May-early Sep) provides information for nearby trails and fishing in the adjacent pond and stream. Here at 8400ft, the 87 pine-shaded Duck Creek Campground ( 877-444-6777; www.recreation.gov; Hwy 14; tent & RV sites without hookups $10-30; late May-early Sep) sites are blissfully cool in summer. The ever-expanding log-cabin town Duck Creek Village (www.duckcreekvillage.com) has more services, including a couple of restaurants, realty offices, cabin rental outfits, a laundromat and an internet cafe. The village area is big with off-road enthusiasts – ATVs in summer and snowmobiles in winter.
About 7 miles east of Duck Creek, a signed, passable dirt road leads the 10 miles to Strawberry Point, an incredibly scenic overview of red-rock formations and forest lands.
### Cedar Breaks National Monument
Sculpted cliffs and towering hoodoos glow like neon tie-dye in a wildly eroded natural amphitheater encompassed by Cedar Breaks National Monument (www.nps.gov/cebr; per person $4). The majestic kaleidoscope of magenta, salmon, plum, rust and ocher rises to a height of 10,450ft atop the Markagunt Plateau. The compact park lies 22 miles east and north of Cedar City, off Hwy 14. There are no cedar trees here, by the way: early pioneers mistook the evergreen junipers for cedars.
This altitude gets more than a little snow, and the monument's one road, Hwy 148, is closed from sometime in November through to at least May. Summer temperatures range from only 40°F to 70°F (4°C to 21°C); brief storms drop rain, hail and even powdery white snow. In season, rangers hold geology talks and star parties at the small visitor center ( 435-586-9451; Hwy 148; 8am-6pm Jun–mid-Oct).
No established trails descend into the breaks, but the park has five viewpoints off Hwy 148 and there are rim trails. Ramparts Trail – one of southern Utah's most magnificent trails – leaves from the visitor center. The elevation change on the 3-mile round-trip is only 400ft, but it can be tiring because of the overall high elevation. Alpine Pond Trail is a lovely, though less dramatic, 4-mile loop.
The first-come, first-served Point Supreme Campground (tent & RV sites without hookups $14; late Jun-Sep) has water and restrooms, but no showers; its 28 sites rarely fill.
### Brian Head
The highest town in Utah, Brian Head towers over Cedar City, 35 miles southwest. 'Town' is a bit of an overstatement though; this is basically a big resort. From Thanksgiving through April, snow bunnies come to test the closest slopes to Las Vegas (200 miles). Snowmobiling in winter and mountain-biking in summer are also popular. The tiny Brian Head Visitor Center ( 435-677-2810; www.brianheadutah.com; Hwy 148; 9am-4:30pm Mon-Fri; ) leaves pamphlets out after hours. Cedar City & Brian Head Tourism & Convention Bureau in Cedar City has more info.
Advanced skiers might grow impatient with the short trails (except on a powder day), but there's lots to love for beginners, intermediates and free-riders at Brian Head Resort ( 435-677-2035; www.brianhead.com; Hwy 143; day lift ticket adult/child $45/32). Lines are usually short and it's the only resort in Utah within sight of the red-rock desert. Here's the lowdown: 1320ft vertical drop, base elevation 9600ft, 640 acres and seven high-speed triple lifts. A ski bridge connects all the lifts. A highlight is the kickin' six-lane snow-tubing area (with surface lift), and there's a mini-terrain park for snowboarders. Forty-two miles of cross-country trails surround Brian Head, including semi-groomed trails to Cedar Breaks National Monument.
During July and August the elevation keeps temperatures deliciously cool. Ride the summer chair-lift (day lift ticket $10; 9:30am-4:30pm Fri-Sun Jul-Sep) up to 11,000ft for an alpine hike or mountain biking. The visitor center puts out a list of area trails.
The resort's lodges and town's sports shops, such as Georg's Ski & Bike Shop ( 435-677-2013; www.georgsskishop.com; Hwy 143), rent skis and snowboards ($27 to $32 per day), mountain bikes ($35 to $45) and more. Rent an ATV or a guided snowmobile tour with Thunder Mountain Sports ( 435-677-2288; www.brianheadthunder.com; 539 N Hwy 143; 8:30am-5:30pm); half-days for each run are $99 to $150.
Check the ski resort website for lodging and skiing packages – two nights in Vegas, two nights in Brian Head can be quite reasonable. A long list of condo rentals is available on the visitor center website. But for our mountain-lodging buck, what could be better than warming by an outdoor fireplace or dining under giant timber-frame trusses like those at the Grand Lodge ( 888-282-3327, 435-677-4242; www.grandlodgebrianhead.com; 314 Hunter Ridge Rd; r $119-195; ). Villa apartments at Cedar Breaks Lodge & Spa ( 435-677-900, 877-505-6343; www.cedarbreakslodge.com; 222 Hunter Ridge Rd; apt $95-275; ) sleep four to eight and have kitchens – great for families. Both lodgings have indulgence-worthy spas.
Apple Annie's Country Store (The Mall, 259 S Hwy 143; ) is the local grocery store, post office and state liquor store. The Tex-Mex menu at Mi Pueblo (406 S Hwy 143; mains $9-20; 11am-9pm) has a long list of beef and seafood dishes. Bump & Grind Café ( 435-677-3111; 259 S Hwy 143; mains $4-11; 11am-9pm) serves a variety of pastas and sandwiches regularly, plus breakfast on some weekends.
From December through April there's a free ski shuttle that travels around town.
### FREMONT INDIAN STATE PARK
Sixty miles northwest of Cedar City, off I-70, Fremont Indian State Park & Museum ( 435-527-4631; http://stateparks.utah.gov; 3820 W Clear Creek Canyon Rd; admission $5; 9am-5pm) is a great introduction to one of the state's other ancient peoples. Fremont Indians inhabited more northerly areas than the well-known ancient group known as the Anasazi, or Ancestral Puebloans. Indications are that the Fremont were fairly sedentary agriculturalists who tended to settle in small groups. Though much is still up for debate, many sites were probably plowed-under on Mormon pioneer-settled ground (farmers do tend to like the same areas).
The park contains one of the largest collections of Fremont Indian rock art in the state: more than 500 panels on 14 interpretive trails. There's also a reconstructed kiva you can climb down into. Be sure to watch the visitor center film and pick up an interpretive brochure for the trails. If you want to learn more about the culture, _Traces of Fremont_ by Steven Simms is an excellent resource. Other Fremont sites include those in Dinosaur National Monument, Nine Mile Canyon and Sego Canyon.
### St George
Nicknamed 'Dixie' for its warm weather and southern location, St George has long been attracting winter residents and retirees. Brigham Young, second president of the Mormon church, was one of the first snowbirds in the one-time farming community. An interesting-if-small historic downtown core, area state parks and a dinosaur-tracks museum hold some attraction. But for travelers, the abundant and affordable lodging are what make this an oft-used stop between Las Vegas and Salt Lake City – or en route to Zion National Park after a late-night flight.
The town lies about 41 miles (up to an hour) from Zion National Park's south entrance, 30 miles (25 minutes) from the Kolob Canyons' entrance on I-15, and 57 miles (45 minutes) from Cedar City to the north.
#### Sights
Pick up a free, full-color, historic-building walking tour brochure at the visitor center. The intersection of Temple and Main Sts is at the heart of the old town center.
Dinosaur Discovery Site MUSEUM
(www.dinotrax.com; 2200 E Riverside Dr; adult/child $6/3; 10am-6pm Mon-Sat) St George's oldest residents aren't retirees from Idaho, but Jurassic-era dinosaurs. Entry gets you an interpretive tour of the huge collection of tracks, beginning with a video. The casts were first unearthed by a farm plow in 2000 and rare paleontology discoveries, such as dinosaur swim tracks, continue to be made.
Mormon Sites RELIGIOUS
The soaring 1877 Mormon Temple (440 S 300 East; visitor center 9am-9pm) was Utah's first. It has a visitor center, but is otherwise closed to the general public. Built concurrently, the red-brick MormonTabernacle (cnr Tabernacle & Main Sts; 9am-5pm) occasionally hosts free music programs and is open to touring.
Brigham Young Winter Home MUSEUM
(67 W 200 N; 9am-5pm) A tour of the Mormon leader's seasonal home and headquarters illuminates a lot about early town and experimental-farming history.
Jacob Hamblin Home MUSEUM
(Santa Clara Dr; 9am-5pm) For another evocative picture of the Mormon pioneer experience, head 5 miles north of town to Santa Clara and the 1863 Jacob Hamblin Home, where orchards still grow.
Daughters of Utah Pioneers Museum MUSEUM
(DUP; www.dupinternational.org; 145 N 100 East; 10am-5pm Mon-Sat) Two floors packed full with pioneer artifacts, furniture, photographs, quilts, guns and so on.
#### Activities
Trails crisscross St George. Eventually they'll be connected and the trail along the Virgin River will extend to Zion; get a map at the visitor center. Mountain-bike rental costs $30 to 45 per day. A handful of local golf courses are open to the public (many more are private). Reserve up to two weeks in advance at www.sgcity.org/golf. And don't forget that Snow Canyon State Park is quite close.
Green Valley Trail MOUNTAIN BIKING
(off Sunbrook Rd) Also called Bearclaw Poppy, this 6-mile trail offers first-rate, playground-like mountain biking on slickrock.
Paragon Climbing ROCK CLIMBING
( 435-673-1709; www.paragonclimbing.com) Paragon Climbing runs excellent introductory rock-climbing courses ($120 for 2½ hours) and guided mountain-biking excursions ($35 to $50 per hour).
Paragon Adventures ADVENTURE SPORTS
( 435-673-1709; www.paragonadventure.com) Book ahead for road or mountain-bike tours with Paragon Adventures. It also offers local rock-climbing lessons and tours, small-group canyoneering, interpretive hikes, zip-line courses – and babysitting. Trips from $55 per hour.
Red Rock Bicycle Company MOUNTAIN BIKING
( 435-674-3185; www.redrockbicycle.com; 446 W 100 S; 9am-7pm Mon-Fri, 9am-6pm Sat, 9am-3pm Sun) Rentals available.
Bicycles Unlimited MOUNTAIN BIKING
( 435-673-4492; www.bicyclesunlimited.com; 90 S 100 East; 9am-6pm Mon-Sat) Rentals available.
#### Tours & Outfitters
Meet Dixie's Famous
Pioneers Tour WALKING
( 436-627-4525; cnr 200 North & Main Sts; tour $3; 10am Tue-Sat Jun-Aug) Brigham Young and Jacob Hamblin are just two of the costumed characters you'll meet on this pleasant ramble through the old-town core.
#### Festivals & Events
A full festival list is available at www.stgeorgechamber.com.
Dixie Roundup SPORTS
( 435-628-8282) A mid-September weekend full of Western fun, including a parade and rodeo.
St George Marathon SPORTS
(www.stgeorgemarathon.com) This October event takes over the town, attracting runners from all 50 states.
#### Sleeping
Around about Eastertime, St George becomes Utah's spring-break capital. Head to St George Blvd and Bluff St near I-15 for chain motels. Pretty much every lodging offers a golf package. Tent campers will do best on nearby public lands; see Click here.
Seven Wives Inn B&B $$
( 435-628-3737, 800-600-3737; www.sevenwivesinn.com; 217 N 100 West; r & ste incl breakfast $95-185; ) Two 1800s homes lovely bedrooms and suites surround well-tended gardens and a small pool at this charming inn. Yes, as you can guess from the name, one of the owners harbored fugitive polygamists there in the 1880s.
Green Gate Village INN $$
( 435-628-6999, 800-350-6999; www.greengatevillageinn.com; 76 W Tabernacle St; r incl breakfast $119-159; ) Book a room or a whole house from among nine historic buildings brought together to make a historic village of sorts, complete with a general store. Antiques such as white-iron beds and ornate carved vanities figure prominently in all the lodgings.
Red Mountain Resort & Spa RESORT $$$
( 435-673-4905, 877-246-4453; http://redmountainspa.com; 1275 E Red Mountain Circle; r from $230; ) A Zen-chic sensibility pervades the low-profile adobe resort, right down to the silk pillows that echo the copper color of surrounding cliffs. Full meals, guided hikes, spa services and fitness classes are all included to varying degrees.
Temple View RV Resort CAMPGROUND $
( 435-673-6400, 800-776-6410; www.templeviewrv.com; 975 S Main St; tent/RV sites without hookups $31/42; ) The 260 sites at this mega resort mostly accommodate (up to 45ft) RVs, but there are a few tent spots. Amenities include a rec room, business center, swimming pool, gym, putting green and cable hookups.
Best Western Coral Hills MOTEL $-$$
( 435-673-4844; www.coralhills.com; 125 E St George Blvd; r incl breakfast $71-108; ) You can't beat being a block or two from downtown restaurants and historic sights. Waterfalls and spiffed-up decor set this locally owned franchise apart.
Dixie Palm Motel MOTEL $
( 435-673-3531, 866-651-3997; www.dixiepalmsmotel.com; 185 E St George Blvd; r $39-67; ) It may not look like much outside, but regular maintenance and TLC put the Dixie Palm at the head of the low-budget pack. The 15 rooms have minifridges and microwaves.
America's Best Inn & Suites MOTEL $
( 435-652-3030, 800-718-0297; www.stgeorgeinnsuites.com; 245 N Red Cliffs Dr; r incl breakfast $49-89; ) Well positioned off I-15, with good facilities.
Green Valley Spa RESORT $$$
( 435-628-8060, 800-237-1068; www.greenvalleyspa.com; 1871 W Canyon View Dr; r $169-399; ) Luxury sports resort: 4000-sq-ft golf center, 14 tennis courts and six swimming pools.
#### Eating & Drinking
All the big chain restaurants and megamarts you'd expect line up along I-15.
Twenty-Five on Main CAFE $$
(25 N Main St; mains $6-12; 8am-9pm Mon-Thu, to 10pm Fri & Sat) Homemade cupcakes are not all this bakery-cafe does well. We also like the breakfast panini, the warm salmon salad and the pasta primavera, overflowing with veggies.
Painted Pony MODERN AMERICAN $$-$$$
( 435-634-1700; 2 W St George Blvd, Ancestor Sq; sandwiches $9-12, dinner $24-35; 11am-10pm) Think gourmet comfort food. At dinner you might choose a juniper-brined pork chop, at lunch, meatloaf with a port wine reduction and rosemary mashed potatoes.
Xetava Gardens Cafe MODERN SOUTHWESTERN $$-$$$
( 435-656-0165; 815 Coyote Gulch Ct, Ivins; breakfast & sandwiches $6-12, dinner $15-32; 8am-4pm daily, plus 5:30-9pm Thu-Sat; ) We'd drive much further than 8 miles for the creative Southwestern cuisine served here in a stunning red-rock setting. Try dishes like organic blue-corn waffles and chile-rubbed lamb. Dinner reservations recommended.
Benja Thai & Sushi ASIAN $$
(W St George Blvd, Ancestor Sq; mains $12-15; 11:30am-10pm Mon-Sat, 5-9pm Sun) A pan-Asian menu is certainly more diverse than most offerings in St George. Eclectic specialty rolls share a menu with pad thai and teriyaki chicken.
Bear Paw Café CAFE $
(75 N Main St; mains $5-9; 7am-3pm Mon-Sat) Homey cafe with big breakfasts.
Thomas Judd's General Store ICE CREAM $
(76 Tabernacle St; ice cream $1.50-3; 11am-9pm Mon-Sat) Stop for a sweet scoop of ice cream or piece of nostalgic candy in Green Gate Village.
Anasazi Steakhouse STEAKHOUSE $$-$$$
( 435-674-0095; 1234 W Sunset Blvd; mains $15-33; 5-10pm) Grill your steak (or shrimp, or portabella mushroom...) yourself on a hot volcanic rock.
#### Entertainment
St George gets pretty quiet after dark. For any area music or events, check listings in free monthly newspaper the _Independent_ (www.suindependent.com).
Tuacahn Amphitheater THEATER
( 435-652-3300, 800-746-9882; www.tuacahn.org) Ten miles northwest in Ivins; hosts musicals in summer and other performances year-round.
St George Musical Theater THEATER
( 435-628-8755; www.sgmt.org; 37 S 100 West) Puts on musicals year-round.
#### Information
Additional information is available at www.utahsdixie.com and www.sgcity.org.
Chamber of Commerce ( 435-628-1658; www.stgeorgechamber.com; 97 E St George Blvd; 9am-5pm Mon-Fri) The visitor center caters to relocating retirees, and has loads of city info.
Dixie Regional Medical Center ( 435-251-1000; http://intermountainhealthcare.org; 1380 E Medical Center Dr; 24hr) Hospital.
St George Field Office ( 435-688-3200; 345 E Riverside Dr; 8am-4pm Mon-Fri) Get interagency information on surrounding public lands: USFS, BLM and state parks. Topographic maps and guides available.
Utah Welcome Center ( 435-673-4542; http://travel.utah.gov; Dixie Convention Center,I-15; 8:30am-5:30pm) Statewide information 2 miles south of St George. There's a wildlife museum (think taxidermy) onsite with the same hours.
#### Getting There & Around
St George is on I-15 just north of the Arizona border, 120 miles from Las Vegas and 305 miles from SLC.
###### Air
Taxis (to downtown $15) and all the standard chain car-rental companies are represented at the St George airport. Note that Las Vegas McCarran International Airport, 120 miles south, often has better flight and car-rental deals than Utah airports.
St George Municipal Airport (SGU; www.flysgu.com; 4550 S Airport Parkway) A new airport with expanded service.
Delta ( 800-221-1212; www.delta.com) Connects SLC and St George several times daily.
United Express ( 800-864-8331; www.united.com) Has four weekly flights to and from Los Angeles, CA.
###### Bus
Greyhound ( 435-673-2933, 800-231-2222; www.greyhound.com; 1235 S Bluff St) Buses depart from the local McDonald's en route to SLC ($65, 5½ hours) and Las Vegas, NV ($29, two hours).
St George Express ( 435-652-1100; www.stgeorgeexpress.com; 1040 S Main St) Shuttle service to Las Vegas, NV ($35, two hours) and Zion National Park ($25, 40 minutes).
### Around St George
Follow Hwy 18 northwest out of St George and you'll come to a series of parks and attractions before reaching higher elevations and Dixie National Forest. Go northeast of town on I-15 for more parks and a small ghost town.
##### SNOW CANYON STATE PARK
Red and white swirls of sandstone flow like lava, and actual lava lies broken like sheets of smashed marble in this small, accessible park. Snow Canyon ( 435-628-2255; http://stateparks.utah.gov; 1002 Snow Canyon Dr, Ivins; per vehicle $6; day use 6am-10pm; ) is a 7400-acre sampler of southwest Utah's famous land features, 11 miles northwest of St George. Easy trails, perfect for kids, lead to tiny slot canyons, cinder cones, lava tubes and fields of undulating slickrock. Summers are blazing hot: visit in early morning or come in spring or fall. The park was named after prominent Utah pioneers, not frozen precipitation, but for the record it does very occasionally snow here.
Hiking trails loop off the main road. Jenny's Canyon Trail is an easy 1-mile round-trip to a short slot canyon. Wind through a cottonwood-filled field, past ancient lava flows to a 200ft arch on Johnson Canyon Trail (2-mile round-trip). A 1000ft stretch of vegetation-free sand dunes serves as a playground for the kiddies, old and young, near a picnic area.
Cycling is popular on the main road through the park: a 17-mile loop from St George, where you can rent bikes. There's also great rock climbing in-park, particularly for beginners, with over 150 bolted and sport routes, plus top roping.
Apart from during the unrelenting summer, the 35-site campground ( 800-322-3770; http://utahstateparks.reserveamerica.com; tent/RV sites without hookups $20/16) is great, and so scenic. You can reserve any of the 30 sites (14 with electrical and water hookups) up to four months in advance. Showers and dump station available.
##### VEYO
The tiny village of Veyo lies 17 miles north of St George on Hwy 18. A warm spring-fed swimming pool (about 80°F, or 27°C) on the Santa Clara River is the main attraction at Veyo Pool & Crawdad Canyon Climbing Park ( 435-574-2300; www.veyopool.com; Veyo Pool Resort Rd; adult/child swim $6/4; 11am-8pm May-Aug). But there's also a cafe, picnicking area and sun deck. Eighty-foot high basalt walls in Crawdad Canyon are perfect for rock climbing and have been equipped with more than 100 bolted routes ($5 per day).
Back on the highway there are competing stores that sell homemade mini-pies.
##### MOUNTAIN MEADOWS MASSACRE MONUMENT
About 10 miles north of Veyo on Hwy 18 stands a remote monument to one of the darkest incidents in the Mormon settlement of Utah. In 1857, for reasons that remain unclear, Mormons and local Indians killed about 120 non-Mormon pioneers – including women and children – who were migrating through the area. The simple, freely-accessible monument, maintained by the LDS, is well-kept but provides little information. On September 11, 2011 it was declared a national historic landmark, so this may change. In the meantime, if you're interested in finding out more, the book _Massacre at Mountain Meadows_ by Ronald Walker and documentaries such as _Burying The Past: Legacy of the Mountain Meadows Massacre_ fully illuminate the subject. Honestly, the story is a lot more compelling than the sight.
##### PINE VALLEY MOUNTAIN WILDERNESS
Mountains rise sharply in the 70-sq-mile Pine Valley Wilderness Area (www.fs.fed.us/r4/dixie) in the Dixie National Forest, 32 miles northwest of St George off Hwy 18. The highest point, Signal Peak (10,365ft), remains snow-capped till July and rushing streams lace the mountainous area. The St George Field Office provides information and free backcountry permits.
When the desert heat blurs your vision, Pine Valley offers cool respite. Most hikes here begin as strenuous climbs. The 5-mile round-trip Mill Canyon Trail and the 6-mile Whipple Trail are most popular, each linking with the 35-mile Summit Trail.
Pine Valley Recreation Complex ( 877-444-6777; www.recreation.gov; tent & RV sites $12, day-use $2; May-Sep), 3 miles east of Pine Valley, has a couple of pine-shadedcampgrounds at 6800ft. They all have water but no showers or hookups; bring mosquito repellent.
##### SILVER REEF GHOST TOWN
A few of the old stone buildings are inhabited, others are crumbling at this 19th-century silver-mining ghost town. The restored Wells Fargo building (admission free; 10am-4pm Mon-Sat) houses a museum and art gallery. Diagrams of the rough-and-tumble town and mine give a feel of what it was like back in the day. You do need them because it's hard to imagine, giving the encroaching subdivision. Take exit 23 off I-15, 13 miles northeast of St George (past Leeds).
##### HILDALE-COLORADO CITY
Just 42 miles southeast of St George on Hwy 9, straddling the Utah-Arizona border,sit the twin towns of Hildale-ColoradoCity. Though the official Mormon church eschewed plural marriage in 1890, there are those that still believe it is a divinely decreed practice. The majority of the approximately 7000 residents here belong to the polygamy-practicing Fundamentalist Church of Jesus Christ of Latter-Day Saints (FLDS). The spotlight focused on this religious community when leader Warren Jeffs was convicted of being an accomplice to rape here in 2007. After that, many of the FLDS faithful, including Jeffs, moved to a fenced compound in Texas. There he was convicted of child sexual assault, for 'spiritual marriages' resulting in the pregnancies of underage girls, and sentenced to life in a Texas prison in 2011.
Other than residents' old-fashioned clothing and a proliferation of really large houses (for multiple wives and even more multiple children), these look like any other American towns. We recommend you respect their privacy. However, if you walk into a Wal-Mart in Washington or Hurricane and see several varying-age females shopping together wearing pastel-colored, prairie-style dresses and lengthy braids or elaborate up-dos, it's a pretty safe guess that they are sister wives. Other, less conspicuous sects are active in the state as well.
## SALT LAKE REGION
The vast Salt Lake Valley is what Brigham Young referred to when he announced 'this is the place!' to his pioneering followers in 1847. Today almost 80% of the state's population, nearly 2 million people, live along the eastern edge of the Wasatch Mountains from Ogden to Provo. Salt Lake City (SLC) sits smack in the middle of this concentration, but you'd never know it from the small size of the city. To the north and west is the Great Salt Lake and 100 miles of salt flats stretching into Nevada.
### Salt Lake City
Utah's capital city, and the only one with an international airport, has a surprisingly small-town feel. Downtown is easy to get around and, outside entertainment enclaves, come evening it's fairly quiet. You'd never know 1.2 million people live in the metro area. Yes, this is the Mormon equivalent of Vatican City, and the LDS owns a lot of land, but less than half the town's population are church members. The university and the great outdoors-at-your-doorstep have attracted a wide range of residents. A liberal spirit is evident everywhere from the coffeehouses to the yoga classes, where elaborate tattoos are the norm. Foodies will find much to love among the multitude of international and organic dining options (think Himalayan and East African). And when the trail beckons, you're a scant 45 minutes from the Wasatch Mountains' brilliant hiking and skiing. Friendly people, great food and outdoor adventure – what could be better?
#### Sights
Mormon Church-related sights mostly cluster near the down centerpoint for SLC addresses: the intersection of Main and South Temple St. (Streets are so wide – 132ft – because they were originally built so that four oxen pulling a wagon could turn around.) The downtown hub expects to experience a renaissance with the development of City Creek. To the west, the University Foothills District has most of the museums and kid-friendly attractions. For more tips, check out Click here.
##### TEMPLE SQUARE & AROUND
Temple Square PLAZA
(www.visittemplesquare.com; visitor centers 9am-9pm) The city's most famous sight occupies a 10-acre block surrounded by 15ft-high walls. LDS docents give free, 30-minute tours continually, leaving from the visitor centers at the two entrances on South and North Temple Sts. Sisters, brothers and elders are stationed every 20ft or so to answer questions. (Don't worry, no one is going to try to convert you – unless you express interest.) In addition to the noteworthy sights, there are administrative buildings and two theater venues.
Salt Lake Temple RELIGIOUS
(Temple Sq) Lording over the square is the impressive 210ft-tall Salt Lake Temple. Atop the tallest spire stands a statue of the angel Moroni who appeared to LDS founder Joseph Smith. Rumor has it that when the place was renovated, cleaners found old bullet marks in the gold-plated surface. The temple and ceremonies are private, open only to LDS in good standing.
Tabernacle RELIGIOUS
(Temple Sq; 9am-9pm) The domed, 1867 auditorium – with a massive 11,000-pipe organ – has incredible acoustics. A pin dropped in the front can be heard in the back, almost 200ft away. Free daily organ recitals are held at noon Monday through Saturday, and at 2pm Sunday. For more on Mormon Tabernacle Choir performances, which are not all held here, see Click here.
Family History Library LIBRARY
(www.familysearch.org; 35 N West Temple St; 8am-5pm Mon, 8am-9pm Tue-Sat) Thousands of people come to Salt Lake City every year to research their family history at the largest genealogical resource on Earth, the Family History Library. Because the LDS believes you must pray on your ancestors' behalf to help them along their celestial path, it has acquired a mind-boggling amount of genealogical information to help identify relatives. Volunteers scour the globe microfilming records in the tiniest of villages and then make them freely available here, and through libraries across the country.
Joseph Smith Memorial Building BUILDING
(15 E South Temple St; 9am-9pm Mon-Sat) East of the Brigham Young Monument is the Joseph Smith Memorial Building, which was, until 1987, the elegant Hotel Utah. Inside, there's a large-screen theater with eight daily screenings of the 65-minute _Joseph Smith: The Prophet of the Restoration_ , about Mormon beliefs.
Beehive House HOUSE
( 801-240-2671; 67 E South Temple St; 9am-8:30pm Mon-Sat) Brigham Young lived with one of his wives and families in the Beehive House during much of his tenure as governor and church president in Utah. The required tours, which begin on your arrival, vary in the amount of historic house detail provided versus religious education offered, depending on the particular LDS docent. The attached 1855 Lion House, which was home to a number of Young's other wives, has a self-service restaurant in the basement. Feel free to look around the dining rooms during mealtimes.
Brigham Young Monument MONUMENT
On Main St at South Temple St the Brigham Young Monument marks the zero point for the city.
Museum of Church History & Art MUSEUM
(www.churchhistorymuseum.org; 45 N West Temple St; 9am-9pm Mon-Fri, 10am-7pm Sat & Sun) Adjoining Temple Square, this museum has impressive exhibits of pioneer history and fine art.
City Creek PLAZA
(Social Hall Ave, btwn Regent & Richards Sts) An LDS-funded, 20-acre pedestrian plaza with fountains, restaurants and retail along City Creek was underconstruction at time of research.
##### GREATER DOWNTOWN
Salt Lake City Main Library LIBRARY
(www.slcpl.org; 210 E 400 South; 9am-9pm Mon-Thu, 9am-6pm Fri & Sat, 1-5pm Sun) You can do more than read a book at this library. Meander past dramatic glass-walled architecture, stroll through the roof garden or stop by the ground-floor shops (from gardening to comic-book publishing). Occasional concerts are held here too.
Utah State Capitol HISTORIC BUILDING
(www.utahstatecapitol.utah.gov; 8am-8pm Mon-Fri, 8am-6pm Sat & Sun) The 1916 Utah State Capitol, modeled after the US capitol, cost an amazing $2.7 million to build back in the day. After six years, and 500 cherry trees, a full renovation of the building and grounds was completed in 2007. Look for colorful Works Progress Administration (WPA) murals of pioneers, trappers and missionaries adorning part of the building's dome. Free hourly tours (from 9am to 4pm) start at the 1st-floor visitor center.
Other Historic Buildings HISTORIC SITE
(www.utahheritagefoundation.com) The Utah Heritage Foundation puts out a free self-guided downtown walking tour brochure available from the visitor center and online. It also has brochures for several other neighborhoods, and an MP3 downloadable audio tour of the Gateway and Warehouse district.
Pioneer Memorial Museum MUSEUM
(www.dupinternational.org; 300 N Main St; 9am-5pm Mon-Sat year-round, plus 1-5pm Sun Jun-Aug) You'll find relics from the early days at Daughters of Utah Pioneers (DUP) museums throughout Utah, but the Pioneer Memorial Museum is by far the biggest. The vast, four-story treasure trove is like Utah's attic, with a taxidermy two-headed lamb and human-hair artwork in addition to more predictable artifacts.
Clark Planetarium MUSEUM
( 801-456-7827; www.clarkplanetarium.org; 110 S 400 West; tickets adult/child $8/6; 10:30am-10pm Sun-Thu, 10:30am-11pm Fri & Sat) You'll be seeing stars at Clark Planetarium, home to the latest and greatest 3-D sky shows and Utah's only IMAX theater. There are free science exhibits, too. The planetarium is on the edge of the Gateway, a combination indoor-outdoor shopping complex anchored by the old railway depot.
Gilgal Garden GARDENS
(www.gilgalgarden.org; 749 E 500 South; 8am-8pm Apr-Sep, 9am-5pm Oct-Mar) Talk about obscure. Gilgal Garden is a quirky little green space hidden in a home-filled neighborhood. Most notably, this tiny sculpture garden contains a giant stone sphinx wearing Mormon founder Joseph Smith's face.
### KENNECOTT'S BINGHAM CANYON COPPER MINE
The view into the century-old mine (www.kennecott.com; Hwy 111; per vehicle $5; 8am-8pm Apr-Oct), 20 miles southwest of SLC, is slightly unreal. Massive dump trucks (some more than 12ft tall) look no larger than toys as they wind up and down the world's largest excavation. The 2.5-mile-wide and 0.75-mile-deep gash, which is still growing, is visible from space – and there's a picture from Apollo __ 11 inside the museum to prove it. Overall, it's a fascinating stop.
##### UNIVERSITY FOOTHILLS DISTRICT
Utah Museum of Natural History MUSEUM
(http://umnh.utah.edu; 200 Wakara Way; adult/child $7/5, 10am-5pm Mon-Sat) The massive Rio Tinto Center makes a suitable home for the museum's prize Huntington Mammoth, one of the most complete fossils of its kind in the world. After taking a hiatus, it and other Utah-found objects and fossils are once again on display – in a shiny new museum building.
This is the Place Heritage Park HISTORIC SITE
(www.thisistheplace.org; 2601 E Sunnyside Ave; park admission free, village adult/child $10/7 Jun-Aug; 9am-5pm Mon-Fri, 10am-5pm Sat; ) Dedicated to the 1847 arrival of the Mormons, the heritage park covers 450 acres. The centerpiece is a living-history village where, June through August, costumed docents depict mid-19th-century life. Admission includes a tourist-train ride and activities. The rest of the year, access is limited to varying degrees at varyingly reduced prices; you'll at least be able to wander around the exterior of the 41 buildings. Some are replicas, some are originals, such as Brigham Young's farmhouse.
Red Butte Garden GARDEN
(www.redbuttegarden.org; 300 WakaraWay; adult/child $8/6; 9am-9pm May-Aug, 9am-5pm Sep-Apr) Both landscaped and natural gardens cover a lovely 150 acres, all accessible by trail, here in the Wasatch foothills. Check online to see who's playing at their popular outdoor summer concert series.
Utah Museum of Fine Arts MUSEUM
( 801-581-7332; www.umfa.utah.edu; 410 Campus Center Dr; adult/child $7/5; 10am-5pm Tue, Thu & Fri, 10am-8pm Wed, 11am-5pm Sat & Sun) Soaring galleries showcase permanent collections of tribal, Western and modern art at the Utah Museum of Fine Arts.
Olympic Legacy Cauldron Park PARK
(www.utah.edu; Rice-Eccles Stadium, 451 S 1400 East; 10am-6pm Mon-Sat) The University of Utah, or 'U of U', was the site of the Olympic Village in 2002. This small on-site park has giant panels detailing the games and contains the torch. A 10-minutedramatic but heartfelt film booms with artificial fog and sound effects.
#### Activities
The best of SLC's outdoor activities are 30 to 50 miles away in the Wasatch Mountains (Click here), but gear is available in town. Bicycle rental ranges from $35 to $50 per day. In winter, public transportation links the town with resorts.
Church Fork Trail HIKING
(Millcreek Canyon, off Wasatch Blvd; day-use $3) Looking for the nearest workout with big views? Hike the 6-mile round-trip, pet-friendly trail up to Grandeur Peak (8299ft). Millcreek Canyon is 13.5 miles southwest of downtown.
Utah Olympic Oval SKATING
( 801-968-6825; www.olyparks.com; 5662 S 4800 West; adult/child $6/4) You can learn to curl as well as skate at Utah Olympic Oval, the site of speed-skating events in the 2002 Winter Olympics. Check ahead for public hours, which vary.
Miller Motorsports Park EXTREME SPORTS
( 435-277-7223; http://millermotorsportspark.com;2901 N Sheep Lane, Tooele) Feel the need for speed? Head 30 miles west of town, where you can take a lesson and get behind the wheel of a 325 horsepower Mustang GT race model (reservations required), kart race or do a zip-line. Book ahead. Utah Jazz' late Larry Miller built the raceway.
###### Outfitters
REI OUTDOORS
( 801-486-2100; www.rei.com; 3285 E 3300 South; 10am-9pm Mon-Fri, 9am-7pm Sat, 11am-7pm Sun) Rents and sells camping equipment, climbing shoes, kayaks and most winter-sports gear. It also stocks a great selection of maps and activity guides, and has an interagency public-lands help desk inside.
Wasatch Touring ADVENTURE SPORTS
( 801-359-9361; www.wasatchtouring.com; 702 E 100 South) Rents bikes, kayaks, climbing shoes and ski equipment.
Black Diamond Equipment ADVENTURE SPORTS
(www.bdel.com; 2092 E 3900 South; 10am-7pm, Mon–Sat 11am-5pm Sun) Retail store for leading manufacturer of climbing and ski gear that headquarters here in SLC.
#### Festivals & Events
Utah Pride Festival CULTURAL
(http://utahpridefestival.org) June gay pride festival with outdoor concerts, parade and 5km run.
Utah Arts Festival CULTURAL
(www.uaf.org) Concerts, exhibitions and craft workshops during three days; late June.
Days of '47 CULTURAL
(www.daysof47.com) A pioneer parade, rodeo and re-enacted encampment are all part of the July-long festival celebrating the city's first settlers.
South Salt Lake
Sights
1Hogle Zoo D1
2Olympic Legacy Cauldron Park C1
3Red Butte Garden D1
4This is the Place Heritage Park D1
5Tracy Aviary C2
6Utah Museum of Fine Arts C1
7Utah Museum of Natural History D1
Sleeping
8Parish Place Bed & Breakfast C2
9Skyline Inn D2
Eating
10Blue Plate Diner D2
11Forage B1
12Mazza C2
13Pago C1
Drinking
14Coffee Garden C1
Entertainment
15Franklin Covey Field B2
#### Sleeping
Downtown chain properties cluster around S 200 West near 500 South and 600 South; there are more in Mid-Valley (off I-215) and near the airport. At high-end hotels rates are lowest on weekends. Look for campingand alternative lodging in the Wasatch Mountains.
Parrish Place Bed & Breakfast B&B $$
( 801-832-0970, 855-832-0970; www.parrishplace.com; 720 E Ashton Ave; r incl breakfast $99-139; ) 'Comfortably antique' describes SLC's most reasonable, 19th-century mansion B&B. Rooms have both elegant and eclectic details – like a commode that is behind a decorative screen instead of a door. Continental breakfast arrives in a basket at your door daily. Hot tub and complimentary beverage center on site.
Peery Hotel HOTEL $-$$
( 801-521-4300, 800-331-0073; www.peeryhotel.com; 110 W 300 South; r $90-130; ) Egyptian-cotton robes and sheets, carved dark-wood furnishings, individually decorated rooms – prepare to be charmed by the 1910 Peery. Small but impeccable bathrooms have pedestal sinks and aromatherapy jams and jellies. This stately hotel stands smack in the center of the Broadway Ave entertainment district, walking distance to restaurants, bars and theaters. Parking $10 per day.
Hotel Monaco HOTEL $$-$$$
( 801-595-0000, 877-294-9710; www.monaco-saltlakecity.com; 15 W 200 South; r $139-249; ) Rich colors, sleek stripes and plush prints create a whimsical mix at this sassy boutique chain. Here, pampered guest pets receive special treatment, and the front desk will loan you a goldfish if you need company. Evening wine receptions are free; parking ($15) and internet access ($10) are extra.
Inn on the Hill B&B $$
( 801-328-1466; www.inn-on-the-hill.com; 225 N State St; r incl breakfast $120-180; ) Maxfield Parrish Tiffany glass adorns the entryway of this stunning 1906 Renaissance Revival mansion high above Temple Sq. Play billiards or read by the fire in one of three parlors.
Anniversary Inn B&B $$-$$$
( 801-363-4953, 800-324-4152; www.anniversaryinn.com; 678 E South Temple St; ste incl breakfast $129-249; ) Sleep among the tree trunks of an enchanted forest or inside an Egyptian pyramid: these 3-D themed suites are nothing if not over the top. The quiet location is near a few good restaurants, and not far from Temple Sq.
Grand America HOTEL $$$
( 801-258-6000, 800-621-4505; www.grandamerica.com; 555 S Main St; r $189-289; ) Rooms in SLC's only true luxury hotel are decked out with Italian marble bathrooms, English wool carpeting, tasseled damask draperies and other cushy details. If that's not enough to spoil you, there's always afternoon high tea or the lavish Sunday brunch. Paid parking ($15).
Crystal Inn & Suites MOTEL $-$$
( 801-328-4466, 800-366-4466; www.crystalinnsaltlake.com; 230 W 500 South; r incl breakfast $75-95; ) Restaurants and Temple Sq are within walking distance of the downtown, multistory branch of Crystal Inns, a Utah-owned chain. Smiling staff here are genuinely helpful and there are lots of amenities for this price point (including a huge, hot breakfast).
Skyline Inn MOTEL $
( 801-582-5350; www.skylineinn.com; 2475 E 1700 South; r $53-70; ) A good choice for bargain-hunting skiers and hikers. This indie motel is only 30 minutes from the slopes, and has a hot tub, too. Rooms could use some refurbishment, though.
Ellerbeck Mansion B&B B&B $$
( 801-355-2500, 800-966-8364; www.ellerbeckbedandbreakfast.com; 140 North B St; r incl breakfast $119-159) Rambling red-brick mansion with homey, eclectic decor. Walking distance to downtown.
Rodeway Inn MOTEL $
( 801-534-0808, 877-424-6423; www.rodewayinn.com; 616 S 200 West; r incl breakfast $59-109; ) Solid budget choice, within walking distance of downtown.
Avenues Hostel HOSTEL $
( 801-359-3855, 801-539-8888; www.saltlakehostel.com; 107 F St; dm $18, s/d with shared bath $30/40, with private bath $40/50; ) Well-worn hostel; a bit halfway house-like with long-term residents, but a convenient location.
#### Eating
Foodies may be surprised to learn how well you can eat in SLC. Many of Salt Lake City's bountiful assortment of ethnicand organically-minded restaurants are within the downtown core. There are also small enclaves in atmospheric neighborhoods 9th and 9th and 15th and 15th (near the intersection of 900 East and 900 South, 1500 East and 1500 South). Up in the foothills southeast of downtown are a few canyons options.
Copper Onion MODERN AMERICAN $$
(111 E Broadway; brunch $7-13, small plates $5-13, dinner $15-18; 11:30am-10pm Mon-Fri, 10:30am-10pm Sat & Sun) Locals can't stop raving about the farm-to-table fresh food at the Copper Onion. And for good reason: small plates like ricotta dumplings and pork belly salad have an earthy realness that calls out to be shared. Even the pastas are perfectly al dente. Design-driven rustic decor provides a convivial place to enjoy it all. Full bar available.
Downtown Salt Lake City
Top Sights
Salt Lake Temple C2
Tabernacle C2
Utah State Capitol C1
Sights
1Beehive House C2
2Brigham Young Monument C3
3City Creek C3
4Clark Planetarium A3
5Discovery Gateway A3
6Family History Library C2
7Gilgal Garden F4
8Joseph Smith Memorial Building C2
9Museum of Church History & Art C2
10Pioneer Memorial Museum C1
11Salt Lake City Main Library D4
Activities, Courses & Tours
12Wasatch Touring F3
Sleeping
13Anniversary Inn F3
14Avenues Hostel E2
15Crystal Inn & Suites B4
16Ellerbeck Mansion B&B D2
17Grand America C5
18Hotel Monaco C3
19Inn on the Hill C2
20Peery Hotel C4
21Rodeway Inn B5
Eating
22Copper Onion D4
23Curryer C4
24Downtown Farmers Market B4
25Lion House Pantry Restaurant C2
26Market Street Grill C4
27One World Everybody Eats D3
28Red Rock Brewing Company B4
29Sage's Cafe E4
30Sawadee F3
31Squatters Pub Brewery B4
32Takashi C4
33Wild Grape E2
Drinking
34Bayou C5
35Beerhive Pub C3
36Café Marmalade B1
37Gracie's C4
38Green Pig C4
39Salt Lake Roasting Co D4
Entertainment
40Assembly Hall C2
41Burt's Tiki Lounge C5
42Depot A2
43Energy Solutions Arena B3
44Gallivan Center C3
45Hotel/Elevate B3
46LDS Conference Center C2
47Rose Wagner Performing Arts Center B4
48Tabernacle C2
49Tavernacle Social Club D4
Shopping
50Gateway A2
51Ken Sanders Rare Books D4
52Sam Weller Books C4
53Utah Artist Hands C3
Red Iguana MEXICAN $$
(736 W North Temple; mains $10-16; 11am-10pm Mon-Thu, 11am-11pm Fri, 10am-11pm Sat, 10am-9pm Sun) Ask for a plate of sample mole if you can't decide which of the seven chile- and chocolate-based sauces sounds best. Really, you can't go wrong with any of the thoughtfully-flavored Mexican food at this always-packed, family-run restaurant.
Mazza MIDDLE EASTERN $$
(1515 S 1500 East; sandwiches $7-10, dinner $15-21; 11am-10pm Mon-Sat; ) Well-known items such as kebabs, schwarma and hummus are, of course, on the menu. But so are more regional specialties, many from Lebanon. Love what they do with lamb and eggplant. Great upscale-casual atmosphere, too.
Pago ORGANIC $$-$$$
( 801-532-0777; 878 S 900 East; mains $18-27; 11am-3pm & 5-10pm Tue-Sat) Seasonal eclectic mains include dishes like a Moroccan fried chicken with frisée or a truffle burger. Sit outside at the few sidewalk tables and you'll feel like part of the chummy neighborhood. Dinner reservations recommended.
Wild Grape MODERN AMERICAN $$-$$$
(481 E South Temple; breakfast & lunch $6-15, dinner $18-24; 8am-10pm Mon-Fri, 9am-10pm Sat & Sun) Billing itself as a 'new West' bistro, Wild Grape creates modern versions of country classics. We like the weekend brunch dishes best.
Squatters Pub Brewery AMERICAN $$
(147 W Broadway; mains $9-15; 11am-midnight Sun-Thu, until 1am Fri & Sat) Come for an Emigration Pale Ale, stay for the blackened tilapia salad. In addition to great microbrews, Squatters does a wide range of American casual dishes well. The lively pub atmosphere is always fun.
Lion House Pantry Restaurant AMERICAN $
(63 E South Temple St; meals $7-12; 11am-8pm Mon-Sat) Down-home, carb-rich cookin' just like your Mormon grandmother used to make – only it's served cafeteria-style in the basement of an historic house. Several of Brigham Young's wives used to live here (including this author's great-great-great grandmother).
Takashi JAPANESE $$-$$$
(18 W Market St; rolls $8-14, mains $15-25; 11:30am-2pm & 5:30-10pm Mon-Sat) The best of a number of surprisingly good sushi restaurants here in landlocked Salt Lake. Even LA restaurant snobs rave about the excellent rolls at ever-so-chic Takashi.
Forage MODERN AMERICAN $$$
( 801-708-7834; 370 E 900 South; mains $25-45; 5:30-10pm Tue-Sat) Food as art. The minimalist creative flourishes here attract both gourmets and awards; its five-course tasting menu is an event. Reserve ahead.
Ruth's Diner DINER $-$$
(4160 Emigration Canyon Rd; mains $6-16; 8am-10pm) Once a railcar diner, Ruth's has expanded into a sprawling institution. We love the canyon surrounds – and the eggs benedict. Summer concerts sometimes accompany dinner.
One World Everybody Eats ORGANIC $
(41 S 300 East; 11am-9pm Mon-Sat, 9am-5pm Sun; ) At this eco-conscious, community-oriented eatery, you decide what you pay and your portion size (they will provide suggestions). Daily-changing dishes include salads, stir-fries, pastas, Indian curries and the like.
Curryer INDIAN $
(300 South, btwn S State & S Main Sts; dishes $4-6; 11am-2pm) This former hot-dog cart, modified with a tandoori oven, serves up a tasty range of regional Indian food from butter chicken to vegan-friendly _aloo matar_ (spiced potatoes and peas).
Blue Plate Diner DINER $-$$
(2041 S 2100 East; breakfast & burgers $4-8, mains $8-10; 7am-9pm Sun-Thu, 7am-10pm Fri & Sat) A hip, retro diner with a soda fountain, colorful patio and postcards from around the country as decoration.
Sage's Cafe VEGETARIAN $$
(473 E Broadway; sandwiches $7-10, mains $13-16; 11am-2pm & 5-10pm Mon-Fri, 10am-10pm Sat & Sun; ) Creative, mostly vegan, mostly organic meals in a comfy former house.
Log Haven MODERN AMERICAN $$$
( 801-272-8255; Mill Creek Canyon Rd; mains $24-32; 5-10pm) Romantic log cabin restaurant in the hills.
Market Street Grill SEAFOOD $$-$$$
( 801-322-4668; 48 W Market St; breakfast $5-10, lunch specials $13, mains $19-28; breakfast, lunch & dinner) SLC's favorite seafood served at a cosmopolitan fish house.
Sawadee THAI $$
(754 E South Temple St; mains $9-11; 11am-2:30pm & 5-10pm Mon-Sat) Decent Thai food, fabulous dark-wood-and-bubbling-fountain decor.
Red Rock Brewing Company PUB $$
( 801-521-7446; 254 S 200 West; sandwiches $7-10, mains $14-18; 11am-11pm) So-so service, but this brewpub still attracts a crowd.
Downtown Farmers Market MARKET $
(Pioneer Park, cnr 300 South & 300 West; 8am-1pm Sat mid-Jun–late Oct, 4pm- dusk Tue Aug-Sep) Regionally-grown produce, ready-to-eat baked goodies and local crafts.
### SALT LAKE CITY FOR CHILDREN
Salt Lake is a kiddie-friendly city if there ever was one. In addition to some of the sights already listed, the wonderful hands-on exhibits at the Discovery Gateway (www.childmuseum.org; 444 W 100 South; admission $8.50; 10am-6pm Mon-Thu, 10am-8pm Fri & Sat, noon-6pm Sun; ) stimulate imaginations and senses.
Kids can help farmhands milk cows, churn butter and feed animals at Wheeler Historic Farm (www.wheelerfarm.com; South Cottonwood Regional Park, 6351 S 900 East; admission free, hay ride $2; 9:30am-5:30pm; ), which dates from 1886. There's also blacksmithing, quilting and hay rides in summer.
More than 800 animals inhabit zones such as the Asian Highlands on the landscaped 42-acre grounds at Hogle Zoo (www.hoglezoo.org; University Foothills District, 2600 East Sunnyside Ave; adult/child $9/7; 9am-5pm; ). Daily animal encounter programs help kids learn more about their favorite species.
Tracy Aviary (www.tracyaviary.org; 589 E 1300 South; adult/child $7/5; 9am-5pm; ) lets little ones toss fish to the pelicans as one of its interactive programs and performances. More than 400 winged creatures from around the world call this bird park home.
With 55 acres of gardens, full-scale working-petting farm, golf course, giant movie theater, museum, dining, shopping and ice cream parlor: what doesn't the Thanksgiving Point (3003 N Thanksgiving Way, Lehi; all-attraction pass adult/child $25/19; 10am-8pm Mon-Sat; ) have? The on-site Museum of Ancient Life (museum only adult/child $10/8) is one of the highest-tech and most hands-on dinosaur museums in the state. Kids can dig for their own bones, dress up a dinosaur, play in a watery Silurian reef... To get here take exit 287 off I-15; Lehi is 28 miles south of downtown SLC.
#### Drinking
Pubs and bars that also serve food are mainstays of SLC's nightlife, and no one minds if you mainly drink and nibble. In addition to those listed here, see Squatters and Red Rock breweries under Eating. A complete schedule of local bar music is available in the _City Weekly_ (www.cityweekly.net).
Gracie's BAR
(326 S West Temple; 11am-2am) Even with two levels and four bars, Gracie's trendy bar-restaurant still gets crowded. The two sprawling patios are the best place to kick back. Live music or DJs most nights.
Green Pig BAR
(31 E 400 South; 11am-2am) Your friendly neighborhood watering hole hosts poker tournaments, has live jam sessions and plays sporting events on big screens. The roof patio is tops.
Bayou PUB
(645 S State St; noon-1am) Known almost as much for its Cajun specialties and pub grub as for its vast selection of beer; by day office workers dine, by night they party. Live music weekends.
Beerhive Pub PUB
(128 S Main St; noon-1am) More than 200 beer choices, including many Utah-local microbrews, are wedged into this downtown storefront bar. Good for drinking and conversation.
Coffee Garden COFFEE SHOP
(895 E 900 South; 6am-11pm Sun-Thu, 6am-midnight Fri & Sat; ) Our favorite coffeehouse has a great laid-back vibe at the heart of the eclectic 9th and 9th neighborhood. A multitude of tasty homebaked goods come with and without the sin (gluten and fat-free available).
Salt Lake Roasting Co COFFEE SHOP
( 320 E 400 South; 7am-midnight; ) It's all about the beans here – from 100% Kona to Gayo Mountain shade-grown Sumatran. There's an SLRC branch cafe in the SLC Library.
#### Entertainment
We wouldn't say the nightlife is all that hot; major dance clubs change frequently and few are open more than a couple nights a week. See the _City Weekly_ (www.cityweekly.net) for listings. Classical entertainment options, especially around Temple Sq, are plentiful.
### WHAT THE...?
The beer you get in many a restaurant, and all grocery stores, doesn't exceed 3.2% alcohol content by weight. Whoa...how am I ever going to get buzzed, you ask? Well it may be easier than you think. The alcohol content for beers sold in the US is generally measured by volume, not weight. So a '3.2' beer is actually closer to a 4% beer by volume (a typical Budweiser is 5% by volume). So there's really not that big a difference.
###### Nightclubs
Tavernacle Social Club CLUB
(201 E Broadway; 5pm-1am Tue-Sat, 8pm-midnight Sun) Dueling pianos or karaoke nightly.
Hotel/Elevate CLUB
(155 W 200 South; 9pm-2am Thu-Sat) Top DJs spin house music and more; live music includes R&B and jazz.
Burt's Tiki Lounge CLUB
(726 S State St; 9pm-2am Thu-Sat) More divey club than tiki lounge; music may be punk, funk or ska – anything loud.
###### Live Music & Theater
In addition to venues listed below, there are also concerts on Temple Sq, at the Library and in Red Butte Gardens in the summertime. The Salt Lake City Arts Council provides a complete cultural events calendar on its website (www.slcgov.com/arts/calendar.pdf). Unless otherwise noted, reserve through ArtTix ( 801-355-2787, 888-451-2787; www.arttix.org).
Mormon Tabernacle Choir LIVE MUSIC
( 435-570-0080 for tickets; www.mormontabernaclechoir.org) Hearing the world-renowned Mormon Tabernacle Choir is a must-do on any SLC bucket list. A live choir broadcast goes out every Sunday at 9:30am. September through November, and January through May, attend in person at the Tabernacle (Temple Sq). Free public rehearsals are held here from 8pm to 9pm Thursday. From June to August and in December – to accommodate larger crowds –choir broadcasts and rehearsals are held at the 21,000-seat LDS Conference Center (cnr N Temple & Main St). Performance times stay the same, except that an extra Monday-to-Saturday organ recital takes place at 2pm.
Gallivan Center CONCERT VENUE
(www.thegallivancenter.com; 200 South, btwn State & Main Sts) Bring a picnic to the outdoor concert and movie series at the Gallivan Center, an amphitheater in a garden; runs in summer.
Assembly Hall CONCERT VENUE
(www.visittemplesquare.com; TempleSq) A lovely 1877 Gothic building in Temple Sq; hosts concerts big and small.
Rose Wagner Performing Arts Center THEATER
(138 W 300 South) Many of SLC Arts Council's dramatic and musical theater performances are staged here.
Depot CONCERT VENUE
( 801-355-5522; 400 W South Temple; www.smithstix.com) Primary concert venue for rock acts.
###### Sports
Utah Jazz BASKETBALL
( 801-325-2500; www.nba.com/jazz) Utah Jazz, the men's professional basketball team, plays at the Energy Solutions Arena (www.energysolutionsarena.com; 301 W South Temple St), where concerts are also held.
Utah Grizzlies ICE HOCKEY
( 801-988-7825; www.utahgrizzlies.com) The International Hockey League's Utah Grizzlies plays at the Maverik Center (www.maverikcenter.com; 3200 S Decker Lake Dr, West Valley City), which hosted most of the men's ice-hockey competitions during the Olympics.
Salt Lake Bees BASEBALL
( 801-325-2273 for tickets; www.slbees.com) The AAA minor-league affiliate of the Anaheim Angels plays at Franklin Covey Field (77 W 1300 South).
#### Shopping
An interesting array of boutiques, antiques and cafes line up along Broadway Ave (300 South), between 100 and 300 East. Drawing on Utah pioneer heritage, SLC has quite a few crafty shops and galleries scattered around. A few can be found on the 300 block of W Pierpont Ave. Many participate in the one-day Craft Salt Lake (www.craftlakecity.com) expo in August.
Sam Weller Books BOOKS
( 801-328-2586; 254 S Main; 10am-7pm Mon-Sat) The city's biggest and best independent bookstore also has a praise-worthy local rare book selection. Note that at press time, Weller's was looking for a new downtown location.
Utah Artist Hands ARTS & CRAFTS
(61 W 100 South) Local artists' work, all made in-state.
Sewing Parlor ARTS & CRAFTS
(339 W Pierpont; 11:30am-6pm Wed-Fri, 1-6pm Tue & Sat) Pick up the supplies to create your own clothing, or have something custom made here.
Ken Sanders Rare Books BOOKS
(www.kensandersbooks.com; 268 S 200 East) Specializes in Western authors.
Gateway MALL
(200 South to 50 N, 400 West to 500 West) Major-label shopping mall right downtown.
#### Information
###### Emergency
Local police ( 801-799-3000; 315 E 200 South)
###### Media
City Weekly (www.cityweekly.net) Free alternative weekly with good restaurant and entertainment listings; twice annually it publishes the free _City Guide_.
Deseret News (www.desnews.com) Ultraconservative, church-owned paper.
Salt Lake Magazine (www.saltlakemagazine.com) Lifestyle and food.
Salt Lake Tribune (www.sltrib.com) Utah's largest-circulation daily paper.
###### Medical Services
University Hospital ( 801-581-2121; 50 N Medical Dr) For emergencies, 24/7.
###### Money
Note that it can be difficult to change currency in Utah outside SLC.
Wells Fargo (79 S Main St) Convenient currency exchange and ATM.
###### Post
Post office (www.usps.com; 230 W 200 South)
###### Tourist Information
Public Lands Information Center ( 801-466-6411; www.publiclands.org; REI Store, 3285 E 3300 South; 10:30am-5:30pm Mon-Fri, 9am-1pm Sat) Recreation information for nearby public lands (state parks, BLM, USFS), including the Wasatch-Cache National Forest.
Visitor Information Center ( 801-534-4900; Salt Palace Convention Center, 90 S West Temple; 9am-6pm Mon-Fri, 9am-5pm Sat & Sun) Publishes free visitor-guide booklet; large gift shop on site.
###### Websites
Downtown SLC (www.downtownslc.org) Arts, entertainment and business information about the downtown core.
Lonely Planet (www.lonelyplanet.com/usa/southwest/salt-lake-city) Planning advice, author recommendations, traveler reviews and insider tips.
Salt Lake Convention & Visitors Bureau (www.visitsaltlake.com) SLC's official information website.
### GAY & LESBIAN SLC
Salt Lake City has Utah's only gay scene, however limited. Pick up the free _Q Salt Lake_ (www.qsaltlake.com) __ for listings. Utah Pride Festival, one weekend in June, is a big party and parade. The town's closest thing to a gay-ish neighborhood is 9th and 9th (900 South and 900 East), where Coffee Garden is the neighborhood cafe. An upbeat coffee shop inside the Utah Pride Center, Café Marmalade (www.utahpridecenter.com; 361 N 300 West; 7am-9pm Mon-Fri, 8am-9pm Sat, 10am-9pm Sun) has open-mike nights, weekend BBQs and concerts, and the largest GLBT library in the state.
GLBT-friendly entertainment venues include:
Club Edge (615 N 400 West) Large dancefloor and DJs; Sunday is Latin gay night.
Paper Moon (3737 S State St) Nightclub boasting a big tube of lipstick and stripper poles; had a lesbian orientation, now attracts a mixed community.
#### Getting There & Away
Springdale and Zion National Park are 308 miles to the south; Moab and Arches are 234 miles south and east.
###### Air
Five miles northwest of downtown, Salt Lake City International Airport (SLC; www.slcairport.com; 776 N Terminal Dr) has mostly domestic flights, though you can fly direct to Canada and Mexico. Delta (www.delta.com) is the main SLC carrier.
###### Bus
Greyhound ( 800-231-2222; www.greyhound.com; 300 S 600 West) connects SLC with southwestern towns, including St George, UT ($55, six hours); Las Vegas, NV ($62, eight hours); and Denver, CO ($86, 10 hours).
###### Train
Traveling between Chicago and Oakland/Emeryville, the California Zephyr from Amtrak ( 801-322-3510, 800-872-7245; www.amtrak.com) stops daily at Union Pacific Rail Depot (340 S 600 West). Southwest destinations include Denver, CO, ($115, 15 hours) and Reno, NV ($64, 10 hours). Schedule delays can be substantial.
### THE BOOK OF MORMON, THE MUSICAL
Singing and dancing Mormon missionaries? You betcha...at least on Broadway. In the spring of 2011 _The Book of Mormon_ , the musical, opened to critical acclaim at the Eugene O'Neill Theatre in New York. The light-hearted satire about missionaries in Uganda came out of the comic minds that also created the _Avenue Q_ musical and the animated TV series _South Park_. No wonder people laughed them all the way to nine Tony Awards. The LDS church's official response? Actually quite measured, avoiding any direct criticism. Though it was made clear that their belief is that while the Book the musical can entertain you, the Book the scripture can change your life.
#### Getting Around
Two major interstates cross at SLC: I-15 runs north-south, I-80 east-west. I-215 loops the city. The area around Temple Square is easily walkable, and free public transportation covers much of the downtown core, but to go beyond you will need your own vehicle.
###### To/From the Airport
Express Shuttle ( 800-397-0773; www.xpressshuttleutah.com) Shared van service, $16 to downtown.
Yellow Cab ( 801-521-2100) Private taxi; from $25 to downtown.
Utah Transit Authority (UTA; www.rideuta.com; one-way $2) Bus 550 travels downtown from the parking structure between terminals 1 and 2.
###### Car & Motorcycle
National rental agencies have SLC airport offices.
Rugged Rental ( 801-977-9111, 800-977-9111; www.ruggedrental.com; 2740 W California Ave; 8am-6pm Mon-Sat) Rents 4WDs, SUVs and passenger cars. Rates are often better here than at the majors.
###### Public Transportation
UTA (www.rideuta.com) Trax, UTA's light-rail system, runs from Central Station (600 W 250 South) west to the University of Utah and south past Sandy. The center of downtown SLC is a free-fare zone. During ski season UTA buses serve the local ski resorts ($7 round-trip).
### CONNECT PASS
Salt Lake City Visitors Bureau (www.visitsaltlake.com) sells one- to three-day discounted attraction passes (one day, adult/child $24/20) online and at the visitor center. But unless you plan to visit every child-friendly attraction in the town – and some outside of town – it probably isn't worth your while.
### Antelope Island State Park
The Great Salt Lake is the largest body of water west of the Great Lakes, but it's hard to say just exactly how big it is. Since 1873 the lake has varied from 900 to 2500 sq miles. Maximum depths have ranged from 24ft to 45ft – it's wide and shallow, like a plate. Spring runoff raises levels; summer's sweltering heat lowers them. Evaporation is why the lake is so salty, but its salinity varies drastically, from 6% to 27% (compared with only 3.5% for seawater), depending on location and weather.
The lake is recognized as a Unesco World Heritage Site for its importance for migratory routes. During fall (September to November) and spring (March to May) migrations, the hundreds of thousands of birds descend on the park to feast on tiny brine shrimp along the lakeshore en route to distant lands. The best place to experience the lake (and see the birds) is at Antelope Island State Park ( 801-773-2941; http://stateparks.utah.gov; Antelope Dr; day use per vehicle $9; 7am-10pm May-Sep, off-season hours vary), 25 miles north of SLC. White-sand beaches, birds – and buffalo – are what attract people to the pretty, 15-mile-long park. That's right: the largest island in the Great Salt Lake is home to a 500-strong herd of American bison, or buffalo. The fall roundup, for veterinary examination, is a thrilling spectacle. Also making their year-round home here are burrowing owls and raptors as well as namesake antelope, bighorn sheep and deer.
Inquire about the many ranger-led activities, watch an introductory video and pick up a map at the visitor center ( 9am-5pm). Nineteen miles of hiking trails provide many opportunities to view wildlife; however, some trails are closed during mating and birthing seasons. There is an 8-mile driving loop and a dirt-road spur that leads 11 miles to Fielding Garr Ranch ( 9am-5pm). Take a look around what was a working farm from 1848 until 1981, back when the state park was created.
North of the visitor center there's a small marina and simple Buffalo Island Grill (mains $6-14; 11am-8pm May-Sep). The white, sandy beach to the south on Bridger Bay has showers and flushing toilets that both swimmers (more like floaters with all that salt) and campers use. The 18-site Bridger Bay Campground ( 800-322-3770 for reservations; http://utahstateparks.reserveamerica.com; tent & RV sites $13) has shelters for shade, water and pit toilets, but no hookups.
To get to the park, head west from I-15 exit 335 and follow the signs; a 7-mile causeway leads to the island.
### Brigham City & Around
POP 17,100 / ELEV 4315 FT
Drive north on I-15 from Salt Lake City, past Ogden (Click here), the gateway to the Wasatch Mountains ski resorts, and after 50 miles you'll get to the turnoff for Brigham City. The town is pretty small, with a few natural attractions, and one famous restaurant. The stretch of Hwy 89 south of town is known as the 'Golden Spike Fruitway' – from July through September it is crowded with fruit stands vending the abundant local harvest. One week in September Brigham City celebrates 'Peach Days'. Contact Box Elder County Tourism ( 435-734-2634; www.boxelder.org) for area information.
West of town, the Bear River Migratory Bird Refuge (www.fws.gov/bearriver; W Forest St; admission free; dawn-dusk) engulfs almost 74,000 acres of marshes on the northeastern shores of the Great Salt Lake. The best time for bird-watchers is during fall (September to November) and spring (March to May) migrations. Birds banded here have been recovered as far away as Siberia and Colombia. Cruising along the 12-mile, barely elevated touring road feels like you're driving on water. You can hear the replicated migratory calls and find out more year round at the Wildlife Education Center ( 435-734-6426; 2155 W Forest St; admission free; 10am-5pm Mon-Fri, 10am-4pm Sat). The center is just after the I-15 intersection; the driving tour is 16 miles west. Free bird-watching tours leave from here twice daily; reserve ahead.
### SCENIC DRIVE: PONY EXPRESS TRAIL
Follow more than 130 miles of the original route that horse-and-rider mail delivery took on the Pony Express Trail Backcountry Byway (www.byways.org) from Fairfield to Callao. The trail begins at one of the former stops, in Camp Floyd/Stagecoach Inn State Park (http://stateparks.utah.gov; adult/child $2/free; 9am-5pm Mon-Sat), 25 miles southwest of I-15 along Hwy 73. Most of the road is maintained gravel or dirt and is passable to ordinary cars in good weather. In winter, snow may close the route; watch for flash floods in summer.
Get into hot water year-round at Crystal Hot Springs ( 435-279-8104; www.crystalhotsprings.net; 8215 N Hwy 38; pool adult/child $6.50/4.50, slides $10; noon-10pm Mon-Fri, 10am-10pm Sat, 11am-7pm Sun), 10 miles north in Honeyville. Adults float in different tem perature soaking pools while kids zip down the water slides, which are open shorter hours than the pools from September through May. The log lodge and pools are well taken care of. There's also a small campground (tent/RV sites with hookup $15/25).
Brigham City is an easy day trip from Salt Lake, and there are a few motels, including a decent Days Inn ( 435-723-3500, 888-440-2021; www.daysinn.com; 1033 S 1600 West; r incl breakfast $75-90; ).
Utahans have been known to travel for hours to eat at Maddox Ranch House ( 435-723-8545; 1900 S Hwy 89; mains $17-25; 11:30am-9:30pm Tue-Sat), where they've been cutting thick beef steaks, cut from locally raised livestock, since 1949. You can still see the ranch out back where they originally started in the cattle business. Fried chicken and bison steaks are popular here, too. Don't expect anything fancy. This is a family-owned place used to serving families. No reservations accepted; expect to wait even if you go early. Out back at Maddox Drive-In (1900 S Hwy 89; mains $4-10; 11am-8:30pm Tue-Sat), carhop waiters deliver the famous fried chicken and bison burgers to your car window. Don't miss the homemade sarsaparilla soda.
### SETTING SPEED RECORDS: BONNEVILLE SALT FLATS
Millennia ago, ancient Lake Bonneville covered northern Utah and beyond. Today, all that remains is the Great Salt Lake and 46 sq miles of shimmering white salt. The surface you see is mostly made up of sodium chloride (common table salt) and is 12ft deep in spots, though officials are worried about shrinkage and have started salt reclamation efforts. The Bonneville Salt Flats are now public lands managed by the BLM ( 801-977-4300; www.blm.gov/ut/st/en/fo/salt_lake/recreation/bonneville_salt_flats.html), and are best known for racing. The flat, hard salt makes speeds possible here that aren't possible anywhere else.
On October 15, 1997, Englishman Andy Green caused a sonic boom on the salt flats by driving the jet-car _ThrustSSC_ to 763.035mph, setting the first ever supersonic world land-speed record. Several clubs hold racing events throughout the year; for a complete list, check the BLM website. Driving up to the flats is a singular optical experience. The vast whiteness tricks the eye into believing it's snowed in August, and the inexpressible flatness allows many to see the Earth's curvature. You may recognize the scene from movies, such as _Con Air_ and _Independence Day_ , that filmed scenes here.
The flats are about 100 miles west of SLC on I-80. Take exit 4, Bonneville Speedway, and follow the paved road to the viewing area parking lot (no services). From here you can drive on the hard-packed salt during late summer and fall (it's too wet otherwise). Obey posted signs: parts of the flats are thin and can trap vehicles. Remember, salt is insanely corrosive. If you drive on the flats, wash your car – especially the undercarriage –afterward. If you're traveling west, there's a rest stop where you can walk on the sand (and wash off your shoes in the bathroom). The nearest town is Wendover on the Utah–Nevada state line.
### Logan & Around
POP 42,700 / ELEV 4775FT
Logan is a quintessential old-fashioned American community with strong Mormonroots and a long downtown core. It's situated 80 miles north of Salt Lake City in bucolic Cache Valley, which offers year-round outdoor activities. Ask about the possibilities at Cache Valley Visitor Bureau ( 435-752-2161, 800-882-4433; www.tourcachevalley.com; 199 N Main St; 9am-5pm Mon-Fri).
The 19th-century frontier comes to life with hands-on living history activities at a Shoshone Indian camp and a pioneer settlement at the American West Heritage Center (www.awhc.org; 4025 S Hwy 89; adult/child $7/5; 11am-4pm Tue-Sat Jun-Aug, off-season hours vary; ), south of town. The center hosts many popular festivals, including weeklong Festival of the American West in July.
There are a couple of B&Bs around town, and midrange chain motels are well represented on Hwy 89. The comfy Best Western Weston Inn ( 435-752-5700, 800-532-5055; http://westoninn.com; 250 N Main; r incl breakfast $75-99; ) is right downtown. Twenty-five miles east in Logan Canyon, Beaver Creek Lodge ( 435-946-3400, 800-946-4485; www.beavercreeklodge.com; Mile 487, Hwy 89; r $109-149) is a great getaway, with horseback riding, snowmobiling, skiing and other activities. No room phones.
For all-round American food, Angie's Restaurant (690 N Main St; mains $5-12; 6am-10pm) is very popular. The old bungalows along 100 East are home to a couple of interesting eateries, including the Crepery (130 N 100 East; mains $3-10; 9am-9pm Mon-Sat), where inventive crepe-stuffings include savory egg dishes and sweet s'mores (with marshmallow, chocolate and graham crackers).
## WASATCH MOUNTAINS
Giant saw-toothed peaks stand guard along the eastern edge of Utah's urban centers. When the crush of civilization gets too much, locals escape to the forested slopes. The Wasatch Mountain Range is nature's playground all year long, but in winter a fabulous low-density, low-moisture snow –300in to 500in of it a year – blankets the terrain. Perfect snow and thousands of acres of high-altitude slopes helped earn Utah the honor of hosting the 2002 Winter Olympics. The skiing in the Wasatch range is some of the best in North America.
Resort towns cluster near the peaks; Park City, on the eastern slopes, is the most well known and quasi-cosmopolitan of the bunch. Salt Lake City resorts, on the western side, are easiest for townies to reach. Ogden is the sleeper of the bunch and Sundance is known as much for its film festival as its ski trails. Most areas lie within 45 to 60 minutes of the SLC airport, so you can leave New York or Los Angeles in the morning and be skiing by noon.
#### Information
###### Season
Ski season runs mid-November to mid-April – only Snowbird stays open much past Easter. However, snow varies: the 2010-11 winter set an all-time record, and deep powder hung around until June. Saturday is busiest; Sunday ticket sales drop by a third because LDS members are in church. Summer season is from late June until early September.
###### Hours
Day lifts usually run from 9am to 4pm.
###### Prices
Children's prices are good for ages six to 12; under sixes usually ski free. All resorts rent equipment (about $30 per day for ski or snowboard packages, $35 per day for a mountain bike). You may save a few bucks by renting off-mountain, but if there's a problem with the equipment, you're stuck. Ski schools are available at all resorts.
###### Conditions
Most resorts have jumped into the digital age and have powder reports, blogs and weather condition updates you can sign up to receive on their websites.
###### Rules
No pets are allowed at resorts and four-night minimum stays may be required December through March.
Ski Utah ( 800-754-8724; www.skiutah.com) Puts out excellent annual winter vacation guides – in paper and online.
### THE REMOTE NORTHWEST
On May 10, 1869, the westward Union Pacific Railroad and eastward Central Pacific Railroad met at Promontory Summit. With the completion of the transcontinental railroad, the face of the American West changed forever. Golden Spike National Historic Site (www.nps.gov/gosp; per vehicle $7; 9am-5pm), 32 miles northwest of Brigham City on Hwy 83, has an interesting museum and films, auto tours and several interpretive trails. Steam-engine demonstrations take place June through August. Aside from Golden Spike National Historic Site, few people visit Utah's desolate northwest corner. But while you're here...
At the end of a dirt road (4WD recommended but not required), 15 miles west of the Golden Spike visitor center, there's a wonderfully unique outdoor art installation, the Spiral Jetty (www.spiraljetty.org). Created by Robert Smithson in 1970, it's a 1500ft coil of rock and earth spinning out into the water. It's a little hard to find; get directions from the visitor center.
###### Dangers & Annoyances
Backcountry enthusiasts: heed avalanche warnings! Take a course at a resort, carry proper equipment and check conditions. Drink plenty of fluids: dehydrated muscles injure easily.
Utah Avalanche Center ( 888-999-4019; http://utahavalanchecenter.org)
Road conditions ( 511)
#### Getting Around
Buses and shuttles are widely available, so you don't need to rent a car to reach most resorts. Advanced skiers looking for knock-your-socks-off adventure should definitely consider a backcountry tour.
Ski Utah Interconnect Adventure Tour ( 801-534-1907; www.skiutah.com/interconnect; mid-Dec–mid-Apr) Six resorts in one day; $295 price tag includes lunch, lift tickets and all transportation.
### LOGAN CANYON SCENIC BYWAY
Pick up a free interpretive trail guide at the Cache Valley Visitor Bureau in Logan before you head off on the 40-mile riverside drive through Logan Canyon Scenic Byway (http://logancanyon.com; Hwy 89 btwn Logan & Garden City). Wind your way up through the Bear River Mountains, past Beaver Mountain, before descending to the 20-mile-long Bear Lake, a summer water-sports playground. Along the way there are numerous signposted hiking and biking trails and campgrounds, which are all part of the Uinta-Wasatch-Cache National Forest (www.fs.usda.gov). It's beautiful year-round, but July wildflowers and October foliage are particularly brilliant. Note that parts of the route may be closed to snow December through May and campgrounds may not open until late June. Check conditions with the Logan Ranger District Office ( 435-755-3620; 1500 East Hwy 89; 8:30am-4:30pm).
### Salt Lake City Resorts
Because of Great Salt Lake-affected snow, SLC resorts receive almost twice as much snow as Park City. The four resorts east of Salt Lake City sit 30 to 45 miles from the downtown core at the end of two canyons. Follow Hwy 190 up to family-oriented Solitude and skier fave Brighton in Big Cottonwood Canyon. In summer you can continue over the mountain from to Heber and Park Cities. To the south, Little Cottonwood Canyon is home to the seriously challenging terrain at Snowbird and the all-round ski-purist special, Alta. Numerous summer hiking and biking trails lead off from both canyons.
#### Information
For lodging-skiing package deals, see www.visitsaltlake.com or contact resorts directly.
Cottonwood Canyons Foundation ( 801-947-8263; www.cottonwoodcanyons.org) USFS ranger-led programs available at Alta, Brighton and Snowbird.
Ski Salt Lake Super Pass (www.visitsaltlake.com/ski_salt_lake; 4-day pass adult/child $208/120) Pass includes one day's lift ticket for each of the four resorts and all your transportation on UTA ski buses and light rail in town.
#### Getting Around
December through April, reach the resorts for $7 round-trip via SLC's public transit system, UTA. Bus route 951 goes from the downtown core to Snowbird and Alta. Six ski-service park-and-ride lots are available around town. The most convenient is Wasatch, from where you can take bus 960 to Solitude and Brighton or bus 951 or 990 to Snowbird and Alta. Buses also run between resorts in the same valley.
Alta Shuttle ( 435-274-0225, 866-274-0225; www.altashuttle.com) Shared van service between SLC and Snowbird or Alta.
Canyon Transportation ( 801-255-1841, 800-255-1841; www.canyontransport.com) Shared van service between SLC and Solitude, Brighton, Snowbird or Alta; from $38 one-way. Private service available to other destinations.
UTA ( 801-743-3882; www.rideuta.com)
Wasatch Park & Ride Lot (6200 S Wasatch Blvd)
##### SNOWBIRD SKI & SUMMER RESORT
If you can see it, you can ski it at Snowbird ( 801-933-2222, 800-232-9542; www.snowbird.com; Little Cottonwood Canyon; day lift ticket adult/child $74/40), the industrial-strength resort with extreme steeps, long groomers, wide-open bowls (one of them an incredible 500 acres across) and a kick-ass terrain park. The challenging slopes are particularly popular with speed demons and testosterone-driven snowboarders. The 125-passenger aerial tram (tram only round-trip $14; 9am-4pm Dec-May, 11am-8pm Jun-Aug, 11am-5pm Sep-Nov) ascends 2900ft in only 10 minutes; die-hards do 'tram laps', racing back down the mountain to re-ascend in the same car they just rode up on. If you like to ski like a teenager, you'll flip out when you see this mountain.
### SKI FOR FREE
After 3pm you ski for free on the Sunnyside lift at Alta. The program is set up to get beginners, or those for whom it's been a while, back on the slopes.
The lowdown: 3240ft vertical drop, base elevation 7760ft; four high-speed quads, six double lifts, one tramway; 2500 acres, 27% beginner, 38% intermediate, 35% advanced. The only conveyor-pull tunnel in the US links the need-for-speed Peruvian Gulf area and intermediate terrain in Mineral Basin. Wednesday, Friday and Saturday, one lift remains open until 8:30pm for night skiing. Skiers (not boarders) can get an $88 Alta-Snowbird pass, which permits access to both areas, for a total of 4700 skiable acres. Snowbird has the longest season of the four SLC resorts, with skiing usually possible mid-November to mid-May. But that's not all, inquire about snowmobiling, backcountry tours and snowshoeing in winter.
In summer, the Peruvian lift and tunnel offer access to Mineral Basin hiking and wildflowers. Good, though strenuous, trails include the White Pine Lake Trail (10,000ft), which is just over 3 miles one-way. Watch rocky slopes around the lake for the unique pika – a small, short-eared, tailless lagomorph (the order of mammals that includes rabbits). At the end of the canyon road is Cecret Lake Trail, an easy 1-mile loop with spectacular wildflowers (July and August). Pick up basic trail maps at the resort.
An all-activities pass (Activity Center; adult/child $39/24; 11am-8pm mid-Jun–Aug) includes numerous diversions: take a tramway up to Hidden Peak, ride the luge-like Alpine Slide, zipline down 1000ft, climb a rock wall or trampoline bungee jump. Full suspension mountain bikes can be rented for three hours ($35). Horseback riding, backcountry 4WD and ATV tours are available, too (from $40 per hour).
Snowbird has five kinds of accommodation, including hotels and condos, all booked through the resort's central phone number and website; packages including lift tickets are available. In summer, prices drop precipitously. The splashy black-glass-and-concrete 500-room Cliff Lodge (r $450-611; ) is like a cruise ship in the mountains, with every possible destination-resort amenity – from flat-screen TVs to a recently-remodeled, luxurious full-service spa. Request a 'spa level' room to have unlimited access to the rooftop pool. Otherwise check out the dramatic 10th-story glass-walled bar and settle for the level-three swimming pool with ski run views. Right at the heart of the resort's Snowbird Center pedestrian village, this lodge always bustles.
At the other end of the quietness spectrum, we also recommend the Inn at Snowbird (r $315-500; ), with a simpler, almost residential feel to it. Studio rooms have kitchens and wood-burning fireplaces. (Bring groceries and you'll save a bundle.)
Snowbird resort has 15 eating outlets, including standards like a coffee shop, pizzaplace, steakhouse and aprés-ski bars. General Gritts (Snowbird Center; 11am-6pm) grocery store has a deli and liquor sales. Everyone loves looking out through 15ft windows to spectacular mountain views at the 10th-floor Aerie Restaurant ( 801-933-2160; Cliff Lodge; mains $24-38; 7am-11am & 5-10pm Dec-Feb, 6-9pm Apr-Oct). The menu lives up to the fine prices; reservations are a must. The adjacent lounge has a full bar and sushi menu. The 3000-sq-ft deck at Creekside Café & Grill (Gadzoom lift base; breakfast & sandwiches $6-10; 9am-2:30pm Dec-Apr) is a great place to grab a sandwich slopeside. The Plaza Deck, a huge patio at Snowbird Center, is a favorite place to gather; there's often live music weekend afternoons.
##### ALTA
Dyed-in-the-wool skiers make a pilgrimage to Alta ( 801-359-1078, 888-782-9258; www.alta.com; Little Cottonwood Canyon; day lift pass adult/child $69/36), at the top of the valley. No snowboarders are allowed here, which keeps the snow cover from deteriorating, especially on groomers. Locals have grown up with Alta, a resort filled not with see-and-be-seen types, but rather the see-and-say-hello crowd. Wide-open powder fields, gullies, chutes and glades, such as East Greeley, Devil's Castle and High Rustler, have helped make Alta famous. Warning: you may never want to ski anywhere else.
The lowdown: 2020ft vertical drop, base elevation 8530ft; 2200 skiable acres, 25% beginner, 40% intermediate, 35% advanced; three high-speed chairs, four fixed-grip chairs. You can ski from the Sunnyside lift for free after 3pm, which is great for families with little ones who tire easily (lifts close at 4:30pm). Get the $88 Alta-Snowbird pass, which permits access to both areas for a stunning 4700 acres of skiing. Expert powder hounds, ask about off-piste snow-cat skiing in Grizzly Gulch ($325 for five runs).
No lifts run in summer, but there are 10 miles of local trails. From July to August,Albion Basin (www.fs.fed.us/wildflowers/regions/intermountain/AlbionBasin) is abloom with wildflowers. July, when an annual wildflower festival is held, is usually peak season.
The lodging options at Alta are like the ski area: simple and just as it's been for decades. Every place here has ski-in, ski-out access and a hot tub. Winter rates, as listed, include breakfast and dinner and require a four-night minimum stay. Lodge restaurants and snack bars are seasonal (December through March) and open to the public.
Alta Lodge ( 801-742-3500, 800-707-2852; www.altalodge.com; dm $146, d $320-590, d without bath $275-378; ) is a mid-century modernist interpretation of a cozy mountain lodge. The attic bar (open to nonguests) is frequented by intellectuals playing backgammon. Expect to make friends there and at family-style dinners in this classical comfortable Alta lodge.
Granite-block-built Snowpine Lodge ( 801-742-2000; www.thesnowpine.com; male dm $109, r per person with private bath $169-239, with shared bath $125), Alta's most basic, is the die-hard skier's first choice. An eight-room expansion overlooks Eagle's Nest and Albion Basin.
You'll likely see families with teenagers embarrassed by their parents at the always-fun Alta Peruvian ( 801-742-3000, 800-453-8488; www.altaperuvian.com; dm $132, r per person with/without bath $204/158; ). Spacious knotty-pine common areas (movies shown nightly) make up for the tiny rooms. The bar here is Alta's après-ski scene. None of the previous two lodges have room TVs.
Enjoy all the creature comforts of a city hotel at Rustler Lodge ( 801-742-2200, 888-532-2582; www.rustlerlodge.com; dm $200, d $625-950, d without bath $380; ). Take an early morning stretch class before you hit the slopes and refresh in the eucalyptus sauna afterwards.
Sleep surrounded by July and August wildflowers at Albion Basin Campground ( 800-322-3770; www.reserveamerica.com; LittleCottonwood Canyon Rd; campsites $17; Jul-Sep). The 19 sites sit at 9500ft, among meadows and pine trees, 11 miles up the canyon. Drinking water; no showers, no hookups.
Chef Curtis Kraus uses locally produced ingredients whenever possible on his seasonally-changing, ingredient-driven menu at Shallow Shaft Restaurant (10199 E Hwy 210, Alta Town; mains $12-28; 5-10pm Dec-April, 6-9pm Thu-Sat Jul-early Sep). Mid-mountain, try Collin's Grill (Watson's Shelter, Wildcat Base; mains $11-22; 11am-2:30pm Dec-Apr) for homemade artisanal soups and French Country mains (make reservations) and Alf's (Cecret lift base; sandwiches $6-10; 9:30am-4pm) for a self-service burger and a look at the antique skis on the walls.
For more general information, see www.discoveralta.com.
##### SOLITUDE
Though less undiscovered than it once was, you can feel sometimes as if you've got the mountain to yourself at Solitude ( 801-534-1400, 800-748-4754; www.skisolitude.com; Big Cottonwood Canyon Rd; day lift ticket adult/child $68/42). It's still something of a local secret, so there's room to learn plus lots of speedy, roller-coaster-like corduroy to look forward to once you've gotten your ski legs. They added three new quads in recent years. If you're an expert, you'll dig the 400 acres of lift-assist cliff bands, gullies, over-the-head powder drifts and super-steeps at off-piste Honeycomb Canyon. Everything here, including the expert grooming, is first class. Some facilities, such as the ice skating rink (Village; admission free 3-8pm Jan-Mar), are only open to overnight guests.
The lowdown: 2047ft vertical drop, base elevation 7988ft; 1200 acres, 20% beginner, 50% intermediate, 30% advanced; eight lifts. Ask about helicopter skiing with Wasatch Powderbird Guides ( 801-742-2800; www.powderbird.com; per day from $1120); scenic flights, too.
North of the resort's lodges, Solitude's Nordic Center (day pass adult/child $17/free; 8:30am-4:40pm Dec-Mar & Jun-Aug) has 12 miles of groomed classic and skating lanes and 6 miles of snowshoeing tracks through enchanting forests of aspen and pine. In summer the Nordic Center becomes a visitor center and the boardwalk encircling Silver Lake becomes the easiest nature trail around, great for children and the mobility-impaired. Ask about guided owl-watching walks and other activities. No swimming, no dogs allowed; this is SLC's watershed.
June through August, the Sunrise lift (daypass $15) opens for chair-assist mountain- biking and hiking from Wednesday through Sunday. You can also rent mountain bikes and motorized mountain scooters, and play disc (Frisbee) golf at the resort.
Many hiking trails leave from various trailheads outside the resorts along Hwy 190. Look for trailhead signs. One of the most attractive hikes is the 2-mile round-trip Lake Blanche Trail, beginning at the Mill B South Fork trailhead, about 5 miles into the canyon.
Most of the 'Village' lodgings at Solitude are atmospheric, Alpine-esque condos. Central reservations ( 800-748-4754; www.skisolitude.com) often has packages that cut room rates by as much as 50%. Of the four full-kitchen properties, we prefer the wood-and-stone rooms at Creekside Lodge (apt $270-425; ), with working fireplaces and balconies. The Inn at Solitude (r $269-299; ) is the only hotel-style lodging, with an on-site spa and hot tub; no balconies. All accommodations share Club Solitude's heated outdoor pool, sauna, fitness room, games room and movie theater.
Cozy up fireside at St Bernard's ( 801-535-4120; Inn at Solitude; breakfast buffet $14, mains $28-32; 7:30-11am & 5-10pm Dec-Mar) for an unexpectedly good French dinner with wine pairing. The foodie's fave is Kimi's Mountainside Bistro (Village; mains $18-25; 11am-10pm Dec-Mar; Wed-Fri 5-9pm, 10am-2pm & 5-9pm Sat & Sun late-May–mid-Oct), which serves down-to-earth artisanal American meals much of the year. You can tip a pint at the Thirsty Squirrel (Village; 2-9pm Dec-Mar) – though Big Cottonwood Canyon's best après-ski and bar scene is at Brighton.
For an adventurous treat, hike or snowshoe a mile into the woods for a sumptuous, but unpretentious, five-course meal in a bona-fide canvas Yurt ( 801-536-5709; www.skisolitude.com/yurt.cfm; dinner winter/summer $100/65; 5:30pm Tue-Sun Dec-Mar, 6:30pm Wed-Sun Jul-Sep). Be sure to reserve way ahead, and bring your own wine; corkage is included in price. (There's another yurt dinner at the Canyons in Park City, but this is the original and the best.)
A great alternative to resort or city sleeping, eating and drinking is the classic mountain roadhouse, Silver Fork Lodge ( 801-533-9977, 888-649-9551; www.silverforklodge.com; 11332 E Big Cottonwood Canyon; breakfast & sandwiches $6-10, dinner $15-26, r incl breakfast $145; 8am-9pm Sun-Thu, 8am-9:30pm Fri & Sat), a mile west of Solitude. Creative comfort food is served in the rustic dining room, which feels like a cozy log cabin with its crackling fireplace. Western furnishings outfit the twin, queen and bunk-bed rooms simply; the creaking floors only add character. In summer, sit outside and watch hummingbirds buzz across gorgeous alpine scenery. All year, warm up in the hot tub.
##### BRIGHTON
Slackers, truants and bad-ass boarders rule at Brighton ( 801-532-4731, 800-873-5512; www.brightonresort.com; Big Cottonwood Canyon Rd; day lift ticket adult/child $62/29). But don't be intimidated: the low-key resort where many Salt Lake residents first learned to skiremains a good first-timers' spot, especially if you want to snowboard. Thick stands of pines line sweeping groomed trails and wide boulevards, and from the top, the views are gorgeous. The whole place is a throwback: come for the ski-shack appeal coupled with high-tech slope improvements and modernized lodge.
The lowdown: 1745ft vertical drop, base elevation 8755ft; 1050 acres, 21% beginner, 40% intermediate, 39% advanced; six chair lifts. One hundred percent of Brighton's terrain is accessible by high-speed quads. There's a half-pipe and terrain park and a liberal open-boundary policy on non-avalanche-prone days. The park has some of the best area night skiing (200 acres, 22 runs) until 9pm, Monday to Saturday. A magic carpet slope lift means beginners can just step on and go, or you can leave the kiddies behind at the day-care center.
No lifts operate during summer months, but locals still come up to go hiking in the alpine meadows and to picnic by area lakes.
The 20 basic rooms at Brighton Lodge ( 801-532-4731, 800-873-5512; www.brightonresort.com; dm $102, r $225-275) go quick; they're retro,but a good deal within spitting distance of the lifts. No room TVs, but there are more than 200 movies you can watch in the common room, or just sit by the fireplace after you've hot-tubbed it. Room prices are crazy low in summer (from $38 including breakfast).
The Milley Chalet ( 8:30am-4:30pm) is themodern ski-lodge base, with various self-service food options. For après-ski drinks and pub grub, you gotta go to the A-frame right on the hill. Molly Green's (Brighton Manor; pizza $8-18, mains $7-13; 11am-10pm Mon-Sat, 10am-10pm Sun Dec-Mar) has a roaring fire, a gregarious old-school vibe and great slopeside views. Sunday brunch is always a big hit, too. Brighton Store & Cafe (11491 Big Cottonwood Canyon Rd; breakfast & sandwiches $6-8; 8am-3pm) serves year-round.
Lands near the top of Big Cottonwood Canyon are part of the Uinta-Wasatch-Cache National Forest (www.fs.usda.gov). Camp at 44-site, first-come, first-served Redman Campground (Solitude Service Rd; campsites $17; late Jun-Sep) and you'll be sleeping under tall pines at a high-elevation creekside ground (8300ft) near the top of the canyon. Several trails lead off from here and Silver Lake is nearby. Water available; no showers, no hookups.
### Park City
POP 8100 / ELEV 6900FT
Century-old buildings line the one main street, looking particularly charming after a new dusting of snow, or at nightfall when the twinkling lights outlining the eaves have been turned on. It's hard to imagine that this one-time silver boomtown ever went bust. Condos and multimillion-dollar houses abut the valleys and center at Utah's premier ski village. Fabulous restaurants abound, and the skiing is truly world class.
Park City skyrocketed to international fame when it hosted the downhill, jumping and sledding events at the 2002 Winter Olympics. Today it's the permanent home base for the US Ski Team; at one time or another most US winter Olympians train at the three ski resorts and Olympic Park here. Though the eastern front gets fewer inches per year than the western front of the Wasatch Mountains, there's usually snow from late November through mid-April. Winter is the busy high season.
Come summer, more residents than visitors gear up for hiking and mountain biking among the nearby peaks. June to August, temperatures average in the 70s (low 20s in Celsius); nights are chilly. Spring and fall can be wet and boring; resort services, limited in summer compared with winter, shut down entirely between seasons. Even some restaurants take extended breaks, in May especially.
#### Sights & Activities
Skiing is the big area attraction, but there are activities enough to keep you more than busy in both summer and winter. Most are based out of the three resorts: Canyons, Park City Mountain and Deer Valley.
Utah Olympic Park ADVENTURE SPORTS
( 435-658-4200; www.olyparks.com/uop; 3419 Olympic Pkwy; admission free; 10am-6pm) Visit the site of the 2002 Olympic ski jumping, bobsledding, skeleton, Nordic combined and luge events, which continues to host national competitions. There are 10m, 20m, 40m, 64m, 90m and 120m Nordic ski-jumping hills as well as a bobsled-luge run. The US Ski Team practices here year round –in summer, the freestyle jumpers land in a bubble-filled jetted pool, and the Nordic jumpers on a hillside covered in plastic. Call for a schedule; it's free to observe. The engaging and interactive Alf Engen Ski Museum, also on-site, traces local skiing history and details the 2002 Olympic events. Experts offer 45-minute guided tours (adult/child $7/5; 11am-4pm) on the hour.
Not content to just watch the action? No problem. Reserve ahead and you adults can take a 70mph to 80mph bobsled ride (summer/winter $60/200) with up to an incredible 4 to 5Gs of centrifugal force. The summer Quicksilver Alpine Slide (driver/rider $60/200) is suitable for drivers over eight years old and riders who are three to seven. Clip on a harness and ride the 50mph Extreme Zipline (100-250lbs, per ride $20) or the shorter Ultra Zipline (50-275lbs, per ride $15). Saturday in summer there is a Freestyle Show (admission $10) that takes off at 1pm. Inquire about bobsled, skeleton, free-jump and free-style lessons year round.
###### Skiing, Snowboarding & Sledding
All three resorts and in-town sports shops have equipment rental (day ski rental adult/child from $36/25) and ski lessons. Plan ahead online and you can use the Quick Start Program (www.parkcityinfo.com/quickstart) to trade your airline boarding pass for a free same-day afternoon lift ticket at Park City's three resorts.
Canyons SNOW SPORTS
( 435-649-5400, 888-604-4169; www.thecanyons.com; 4000 Canyons Resort Dr; two-day lift ticket adult/child $170/102) Nearly $60 million is scheduled to be invested in Canyons in the coming years. With it, the resort's identity is evolving, and it is poised to compete with the country's best. Phase one has introduced the first North American 'bubble' lift, with an enclosed, climate-controlled top, along with 300 new acres of advanced skiable acreage and an increased snow-making capability. So far six lodging properties are on site and new restaurants are being added. The resort currently sprawls across nine aspen-covered peaks 4 miles outside of town, near the freeway.
The lowdown: 3190ft vertical drop, base elevation 6800ft; 4000 acres, 10% beginner, 44% intermediate, 46% advanced; 19 lifts, including a gondola. Varied terrain on 176 trails means there's something for all levels,with wide groomers for beginners and intermediates and lots of freshies on a powder day. Experts: head to Ninety-Nine 90. There's a liberal open-boundary policy (heed avalanche warnings) as well as six natural half-pipes, one of them a whopping mile long, perfect for boarding. Cross-country skiing and sleigh rides, for pleasure or to dinner, are also available. You can even ride along on (two hours, $95) or drive (eight hours, $395) a state-of-the-art Snow Cat groomer. Sightseers could take the recently relocated gondola (round-trip $20) up for not only views, but for Belgian waffles or lunch in the Red Pine area.
Park City
Activities, Courses & Tours
1Aura Spa C5
Sleeping
2Sky Lodge B3
3Treasure Mountain Inn C6
4Washington School House B4
Eating
5Bistro 412 C5
6Easy Street Steak & Seafood B3
7Eating Establishment C6
8Jean Louis Restairant B3
Shabu (see 18)
9Talisker B4
10Taste of Saigon B4
Uptown Fare (see 3)
11Wahso B4
12Wasatch Brew Pub C6
13Zoom B3
Drinking
14High West Distillery & Saloon A2
15No Name Saloon & Grill B5
16O'Shucks C5
17Park City Roasters B3
18Sidecar Bar C5
19Spur C6
Entertainment
20Egyptian Theatre Company C5
21Park City Box Office B3
Park City Mountain Resort SNOW SPORTS
( 435-649-8111, 800-222-7275; www.parkcitymountainresort.com; 1310 Lowell Ave; two-day lift ticket adult/child $178/112; ) From boarder dudes to parents with tots, everyone skis Park City Mountain Resort, host of the Olympic snowboarding and giant slalom events. The awesome terrain couldn't be more family-friendly – or more accessible, rising right over downtown.
The lowdown: 3100ft vertical drop, base elevation 6900ft; 3300 acres, 17% beginner, 52% intermediate, 31% advanced; seven high-speed lifts, eight fixed-grip chairs, one magic carpet. Park City's skiable area coversnine peaks, ranging from groomers to wide-open bowls (750 acres of them!) to cotton-mouth-inducing super steeps and the nation's only superpipe. Experts: make a beeline to Mount Jupiter; the best open trees are in the Black Forest. For untracked powder, take the Eagle lift up to Vista. Test your aerial technique on an Olympic-worthy boarding and freestyle course at three amazing terrain parks. Kids' trails are marked with snowbug statues near the magic carpetlift and the resort will hook teens up with area locals who provide the lay of the land. Check out the online activity planner at www.mymountainplanner.com. To avoid crowds, stay out late: night skiing lasts until 9pm. In winter there's open-air ice skating (admission $9; 1am-5pm) at the Resort Center.
Though the resort has no affiliated hotels, it does offer package lodging-skiing deals with nearby properties, and restaurants and après-ski are on site. The fact that Town Lift takes you right from Main St up to the village area makes all downtown accommodations accessible.
Gorgoza ParkSNOW SPORTS
(3863 West Kilby Rd, at I-80; 4hr adult/child 6 & under $30/15; 1-8pm Mon-Fri, noon-8pm Sat & Sun mid-Dec–Mar; ) Lift-served snow tubing takes place at Park City Mountain's Gorgoza Park, 8 miles north of town, off I-80. Plunge down three beginner or four advanced lanes; for kids under 12 there's a miniature snowmobile track (per ride $9), and for littler ones the Fort Frost play area (admission $6) with carousel. The Park City Mountain Resort-wide shuttle ( 435-645-9388) will take you out there directly if you reserve.
Deer Valley SNOW SPORTS
( 435-649-1000, 800-424-3337; www.deervalley.com; Deer Valley Dr; day lift ticket adult/child $90/56, round-trip gondola ride $15) Want to be pampered? Deer Valley, a resort of superlatives, has thought of everything from tissue boxes at the base of slopes to ski valets. Slalom, mogul and freestyle-aerial competitions in the 2002 Olympics were held here, but the resort is as famous for superb dining, white-glove service and uncrowded slopes as meticulously groomed as the gardens of Versailles. Note that there's no snowboarding allowed.
The lowdown: 3000ft vertical drop, base elevation 6570ft; 2026 acres, 27% beginner,41% intermediate, 32% advanced; one high-speed gondola, 11 high-speed quads, nine fixed-grip chairs. Every trail follows the fall line perfectly, which means you'll never skate a single cat-track. Lady Morgan has 200 acres of new terrain (65 acres of which is gladed), well separated from the Jordanelle Gondola area. Only a prescribed number of daily lift tickets are sold, so powder hounds can find hundreds of acres of untracked glades and steeps, days after a storm.
Resort-owned snowmobiling ( 435-645-7669; 1-hr $99; 9am-5pm) takes place 5 miles down the road on Garff Ranch; reserve ahead.
White Pine Touring SKIING
( 435-649-8710; www.whitepinetouring.com; 1790 Bonanza Dr; 3-hr tour $175) Guided cross-country ski trips take you 20 minutes away from Park City and can include yurt camping accommodations. In town, the associated Nordic Center (cnr Park Ave & Thames Canyon Dr; day pass adult/child $18/10; 9am-6pm) grooms a 12-mile cross-country course (rental available) with 2-, 3- and 6-mile loops of classic and skating lanes. Skate skiing lessons available.
Wasatch Powderbird SKIING
( 801-742-2800, 800-974-4354; www.powderbird.com; full-day $1050) Advanced skiers can arrange area heli-skiing packages that include six to seven runs.
###### Other Snow Sports
Activity pick-up service is available from most resorts. Reservations are always a must.
All Seasons Adventures SNOW SPORTS
( 435-649-9619; www.allseasonsadventures.com; per hr $35-250) Dog sledding, sleigh riding, cross-country skiing, snowshoe tours and geocaching treasure hunts offered.
Rocky Mountain Recreation of Utah SNOW SPORTS
( 435-645-7256, 800-303-7256; www.rockymtnrec.com; per hr $70-300) Snowmobile tours, horse-drawn sleigh rides (to dinner or around) and dog sledding.
###### Hiking
You'll feel on top of the world in the peaks over Park City, where over 300 miles of trails crisscross the mountains. Pick up a summer trail map at the visitor center.
Mountain Vista Touring HIKING
( 435-640-2979; www.parkcityhiking.com; half-day $85; mid-Apr–mid-Nov) Guided trips include hot springs and moonlight hikes.
###### Mountain Biking
Park City's big secret is its amazing mountain biking. The visitor center has trail maps and you can rent bikes (from $40 per day) from sports shops in town and at all the resorts; some even have lift-assist riding.
Mid-Mountain Trail MOUNTAIN BIKING
One of the best for mountain biking is this 15-mile one-way trail, which follows the topography at 8000ft, connecting Deer Valley to Olympic Park. You could also start at Park City Mountain, bike the steep Spiro Trail up to Mid-Mountain, then return on roads for a 22-mile loop.
Historic Union Pacific Rail Trail TRAIL
(http://stateparks.utah.gov; admission free; 24hr) A 28-mile multiuse trail that's also a state park. Pick it up at Bonanza Dr just south of Kearns Blvd.
### SCENIC DRIVE: MIRROR LAKE HWY
This alpine route, also known as Hwy 150, begins about 12 miles east of Park City in Kamas and climbs to elevations of more than 10,000ft as it covers the 65 miles into Wyoming. The highway provides breathtaking mountain vistas, passing by scores of lakes, campgrounds and trailheads in the Uinta-Wasatch-Cache National Forest (www.fs.fed.us). Note that sections may be closed to traffic well into spring due to heavy snowfall; check online.
White Pine Touring CYCLING
( 435-649-8710; www.whitepinetouring.com; 1790Bonanza Dr; 3-hr tour for 2 people $170) Bike rentals and guided biking tours
###### Other Summer Activities
Park City Mountain Resort ADVENTURE SPORTS
(www.parkcitymountainresort.com; 1310 Lowell Ave; 10:30am-5pm Jun-Aug) We love the Town Lift-served hiking and mountain biking (day pass $20). Park City Mountain also operates a 3000ft-long alpine slide (per ride $10), where a wheeled sled flies down 550ft along a cement track, as well as a super-long zipline ride (2300ft long, 550ft vertical; $20). Kids not tired yet? Check out the adventure zone (admission $20) with its climbing wall, spiderweb climb, boulderclimb and slide. Note that hours vary depending on the activity and the month.
Canyons ADVENTURE SPORTS
(www.thecanyons.com; 4000 Canyons Resort Dr; 10am-5pm Jun-Aug) A scenic ride on the gondola (round-trip $15) is great for sightseers, but hiking trails also lead off from here. Mountain bikers should head over to the Gravity Bike Park (day pass $25), which has varied trails accessed by the High Meadow Lift. Other activities include disc golf, miniature golf, lake pedal boats and hot-air balloon rides. On weekends in summer and winter live-music concerts rock the base area.
Deer Valley ADVENTURE SPORTS
(www.deervalley.com; Deer Valley Dr; day lift pass $20; 10am-5pm mid-Jun–early Sep) In summer, Deer Valley has more than 50 milesof hiking and mountain-biking trails served by its three operating lifts. Horseback riding and free guided hikes are available by request.
Rocky Mountain Recreation of Utah HORSEBACK RIDING
( 435-645-7256, 800-303-7256; www.rockymtnrec.com; Stillman Ranch, Weber Canyon Rd) Horseback rides ($70 per hour), wagon rides with dinner ($75) and guided pack and fly-fishing trips ($295 per day).
All Seasons Adventures HORSEBACK RIDING
( 435-649-9619; www.allseasonsadventures.com;half-day $60-150) Area guided kayaking, hiking, mountain biking, horseback riding, ATV riding and geocaching scavenger races.
National Ability Center ADVENTURE SPORTS
(NAC; 435-649-3991; www.nac1985.org; 1000 Ability Way) Year-round adapted sports program for people with disabilities and their families: horseback riding, rafting, climbing and biking.
###### Wellness & Massage
When you've overdone it on the slopes, a spa treatment may be just what the doctor ordered. Deer Valley and the Canyons both have swanky spas.
Aura Spa SPA
( 435-658-2872; 405 Main St; 1hr from $85) Schedule energy-balancing chakra work after your rubdown at in-town Aura Spa.
The Shop YOGA
(www.parkcityyoga.com; 1167 Woodside Ave; by donation) Stretch out the kinks with an Anusara yoga class at this amazing warehouse space. Walk-ins welcome.
#### Festivals & Events
Sundance Film Festival FILM
(www.sundance.org) Independent films and their makers, movie stars and their fans fill the town to bursting for 10 days in late January. Passes, ticket packages and the few individual tickets sell out well in advance; plan ahead.
#### Sleeping
Prices in this section are for high winter season (mid-December through mid-April, minimum stays required); during Christmas, New Year's and Sundance it costs more. There's a dearth of budget lodging in Park City in winter. Consider staying down in Salt Lake or Heber Valley. Also check the ski resorts' websites for packages that combine condo or hotel accommodations and lift tickets, which can be a good deal. All three ski resorts have condo rentals that can be booked directly. Resort lodging has ski-in advantages, but staying near nightlife in the old town can be more fun. Note that off-season, rates drop 50% – or more. For a complete list of the more than 100 condos, hotels and resorts in Park City, log onto www.visitparkcity.com.
Sky Lodge LUXURY HOTEL $$$
( 435-658-2500, 888-876-2525; www.theskylodge.com; 201 Heber Ave; ste $285-495; ) The urban loft-like architecturecontaining the chic Sky Lodge suites both complements and contrasts the three historic buildings which house the property's restaurants. You can't be more stylish, or more central, if you stay here.
### GETTING INTO SUNDANCE FILM FESTIVAL
In late January, this two-week festival takes over both Park City and Sundance Resort completely. Films screen not just there but at venues in Salt Lake City and Ogden as well. Room rates soar across the Wasatch front, yet rooms are snapped up months in advance. Passes ($300 to $3000), ticket packages ($300 to $1000) and individual tickets ($15) are similarly difficult to get. You reserve a timeslot to purchase online at www.sundance.org/festival, starting in December (sign up for text-message announcements). You then call during your appointed hour to reserve, but there are no guarantees. Note that seats may be a little easier to secure during week two (week one is generally for the industry). Any remaining tickets are sold a few days ahead online and at the main Park City Box Office (Gateway Center, 136 Heber Ave; 8am-7pm mid-Jan–late Jan). If you don't succeed, do like the locals and go skiing. The slopes are remarkably empty during this two-week period.
Washington School House BOUTIQUE HOTEL $$$
( 435-649-3800, 800-824-1672; http://washingtonschoolhouse.com; 543 Park Ave; ste incl breakfast $700; ) Architect Trip Bennett oversaw the restoration that turned an 1898 limestone schoolhouse on a hill into a luxurious boutique hotel with 12 suites. How did the children ever concentrate when they could gaze out at the mountains through 9ft-tall windows instead?
Old Town Guest House B&B $$
( 435-649-2642, 800-290-6423; www.oldtownguesthouse.com; 1011 Empire Ave; r incl breakfast $99-199; ) Grab the flannel robe, pick a paperback off the shelf and snuggle under a quilt on your lodgepole bed or kick back on the large deck at this comfy in-town B&B. The host will gladly give you the lowdown on the great outdoors, guided ski tours, mountain biking, and the rest.
Woodside Inn B&B $$
( 435-649-3494, 888-241-5890; 1469 Woodside Ave; r $159-299, ste $299-399, both incl breakfast; ) A contemporary take on the B&B; this purpose-built, condo-looking inn has eight guest quarters (most with whirlpool tubs) and a dining room and den to share. Having hosts that will help with everything, including airport transfers, is a great advantage.
St Regis Deer Valley LUXURY HOTEL $$$
( 435-940-5700, 877-787-3447; 2300 Deer ValleyDr East; r $500-1000; ) You have to ride a private funicular just to get up to the St Regis. So whether you're lounging by the outdoor fire pits, dining on an expansive terrace or peering out over your room's balcony rail, the views are sublime. The studied elegant-rusticity here is the height of Deer Valley's luxury lodging.
Treasure Mountain Inn HOTEL $$$
( 435-655-4501, 800-344-2460; www.treasuremountaininn.com; 255 Main St; ste $235-295; ) Park City's first member of the Green Hotel Association utilizes wind energy and serves organic food in its breakfast restaurant. Some of the upscale condos have fireplaces, all have kitchens, and they're decorated in earthy tones.
Hyatt Escala Lodge HOTEL $$$
( 435-940-1234, 888-591-1234; 3551 North Escala Court; r $269-299, ste $309-419; ) Finished in 2011, the upscale lodge rooms are all meant to have a residential feel. Indeed, suites have full kitchens and a personal grocery shopping service is available throughout. From here you're not more than a few ski strides away from the Canyons resort lifts.
Park City Crash Pads CONDO $-$$
( 435-901-9119, 877-711-0921; www.parkcitycrashpads.com; r $119-170) Take advantage of the condo market through this reasonable consolidator. Buildings and facilities may not be the newest, but all rooms have 300-thread-count duvets, iPod clock radios, and many have kitchens.
Chateau Après Lodge MOTEL $-$$
( 435-649-9372, 800-357-3556; www.chateauapres.com; 1299 Norfolk Ave; dm $40, d/q $105/155; ) The only budget-oriented accommodation in town is this basic, 1963 lodge – with a 1st-floor dorm – near the town ski lift. Reserve ahead.
Park City Peaks HOTEL $$
( 435-649-5000, 800-333-3333; www.parkcitypeaks.com; 2121 Park Ave; r $149-249; ) Comfortable, contemporary rooms include access to heated outdoor pool, hot tub, restaurant and bar. Great deals off season. December through April, breakfast is included.
Goldener Hirsch LUXURY HOTEL $$$
( 435-649-7770, 800-252-3373; www.goldenerhirschinn.com; Deer Valley, 7570 Royal St; r incl breakfast $299-639; ) You can tell the Goldener was fashioned after a lodge in Salzburg by the hand-painted Austrian furniture, feather-light duvets and European stone fireplaces. 'Stay & Ski Deer Valley' packages available.
Park City RV Resort CAMPGROUND $
( 435-649-8935; www.parkcityrvresort.com; 2200Rasmussen Rd; tent sites $21, RV sites with hookups $30-45; ) Amenities galore (games room, playground, laundry, hot tub, fishing pond, kids' climbing wall...), 6 miles north of town at I-80.
Holiday Inn Express HOTEL $-$$
( 435-658-1600, 888-465-4329; www.holidayinnexpress.com; 1501 W Ute Blvd; r incl breakfast $170-207; ) Save money by staying outside downtown, near Kimball Junction stores and restaurants.
Shadow Ridge Resort Center HOTEL $$-$$$
( 435-649-4300, 800-451-3031; www.shadowridgeresort.com; 50 Shadow Ridge Rd; r $189-299; ) A hundred yards from Park City Mountain lifts.
Waldorf Astoria LUXURY HOTEL $$$
( 435-647-5500; www.parkcitywaldorfastoria.com;2100 Frostwood Dr; r $729-1500; ) Top luxury property at the Canyons.
#### Eating
Park City is well known for exceptional upscale eating – a reasonable meal is harder to find. In the spring and summer, look for half-off main-dish coupons in the _Park Record_ newspaper. _Park City Magazine_ puts out a full menu guide. In addition to the places listed here, the three ski resorts have numerous other eating options in season. Assume dinner reservations are required at all top-tier places in winter. Note that from April through November restaurants reduce open hours variably, and may take extended breaks.
Talisker MODERN AMERICAN $$$
( 435-658-5479; 515 Main St; mains $21-42; 5:30-10pm) Talisker elevates superb food to the sublime: lobster hush puppies, anyone? Settle into one of the four individually-designed dining rooms and see what long-time resident and chef Jeff Murcko has to offer on his daily changing menu. The chef also oversees the menus at Canyons resort restaurants.
J&G Grill INTERNATIONAL $$$
( 425-940-5760; St Regis Deer Valley, 2300 Deer Valley Dr E; mains $20-32; 7am-2pm & 6-9pm) Excellent meat and fish here might have a sublimely simple grill treatment or a Malaysian-Thai influence. Either way, we prefer to enjoy it at the convivial communal table, where you can mingle with 20 other discriminating diners.
Jean Louis Restaurant INTERNATIONAL $$$
( 435-200-0602; 136 Heber Ave; mains $27-40; dinner) Renowned restaurateur, chef and quite the character, Jean Louis has created an upscale, world-cuisinerestaurant that still manages to feel warm and welcoming. Here, it's all about good food.
Easy Street Steak & Seafood STEAKHOUSE $$-$$$
( 435-658-9425; 201 Heber Ave; breakfast & brunch $10-16, burgers $15, mains $25-40; 9am-10pm Dec-Mar; 5-10pm Mon-Fri, 9am-2pm & 5-10pm Sat & Sun Apr-Nov) The high ceilings and tall windows of the old Utah Coal & Lumber building are perfect for a fine steakhouse. Or you could have the wild-mushroom bruschetta and succulent rib-eye served in the more casual bar downstairs.
Wahso ASIAN $$$
( 435-615-0300; 577 Main St; mains $29-40; 5-10pm) Park City's cognoscenti flock to this modern pan-Asian phenomenon whose fine-dining dishes may include lamb vindaloo or Malaysian snapper. Expect to see and be seen.
Maxwell's PIZZERIA $-$$
(1456 New Park Blvd; pizza slices $3, mains $10-20; 11am-9pm Sun-Thu, 11am-10pm Fri & Sat) Eat with the locals at the pizza, pasta and beer joint tucked in a back corner of the stylish outdoor Redstone Mall, north of town. Huge, crispy-crusted 'Fat Boy' pizzas never linger long on the tables.
Bistro 412 FRENCH $$
( 412 Main St; mains $12-26; 11am-2:30pm & 5-10pm) The cozy dining room and French bistro fare here, including beef _Bourguignonne_ and _cassoulet_ (a hearty bean stew made with elk, sausage and lamb bacon), will keep you warm in winter. During summer months, steak _frites_ on the outdoor deck might be more appropriate.
Good Karma FUSION $-$$
(1782 Prospector Ave; breakfast $7-12, mains $10-20; 7am-10pm) Whenever possible, local and organic ingredients are used in the Indo-Persian meals with an Asian accent at Good Karma. You'll recognize the place by the Tibetan prayer flags flapping out front.
Squatters Roadhouse Grill PUB $-$$
(1900 Park Ave; burgers $9-12, mains $10-19; 8am-10pm Sun-Thu, 8am-11pm Fri & Sat) The better of the town brewpubs, as far as food goes. We love the Asiago, cheddar and Havarti mac-and-cheese. Breakfast is served until 2pm daily.
Windy Ridge Cafe AMERICAN $$
(1250 Iron Horse Dr; lunch $10-15, dinner $15-20; 11am-3pm & 5-10pm) Escape the Main St mayhem at this out-of-the-way American cafe. Across the parking lot, the bakery ( 8am-6pm) makes many of the tasty treats. Both are part of the Bill White restaurant group, which also counts Grappa (taverna Italian), Chimayo (Southwest) and Ghidotti's (fine Italian) among its numbers.
Uptown Fare CAFE $
(227 Main St; sandwiches $5-11; 11am-3pm) Comforting house-roasted turkey sandwiches and homemade soups at the hole-in-the-wall hidden below the Treasure Mountain Inn.
Lookout Cabin MODERN AMERICAN $$
(Canyons, 4000 Canyons Resort Dr; mains $10-20; 11:30am-3:30pm Dec-Mar) Gourmet lunch and aprés ski mid-mountain. Think kirsch cherry fondue and Kobe beef-turned-burger.
Zoom AMERICAN $$$
( 435-649-9108; 660 Main St; mains $20-36; 11:30am-2:30pm & 5-10pm) Robert Redford-owned restaurant in a rehabbed train depot.
Shabu FUSION $$$
( 435-645-7253; 442 Main St; small plates & rolls $10-17, mains $24-34; 11am-2:30pm, 5-11pm Thu-Tue) Hip, inventive Asian small plates and namesake _shabu shabu_ (a hotpot of flavorful broth with meat or veggies).
Wasatch Brew Pub PUB $-$$
( 250 Main St; lunch & sandwiches $7-12, dinner $10-17; 11am-10pm) Pub grub at the top of Main St.
Taste of Saigon VIETNAMESE $$
( 580 Main St; mains $10-15; 11am-3pm & 5-10pm) Reasonably priced Vietnamese dishes, even better lunch specials.
Eating Establishment AMERICAN $-$$
( 317 Main St; breakfast & sandwiches $9-12, dinner $15-20; 8am-10pm) Local institution; service can be hit-or-miss.
#### Drinking
Main St is where it's at. In winter there's action nightly; weekends are most lively off-season. For listings, see www.thisweekinparkcity.com. Several restaurants, such as Bistro 412, Easy Street, Squatters and Wasatch Brew Pub, also have good bars.
High West Distillery & Saloon BAR
( 703 Park St; 2pm-1am daily, closed Sun & Mon Apr-Jun & Sep-Dec) A former livery and Model A-era garage is now home to Park City's most happenin' nightspot. You can ski in for homemade rye whiskey at this micro distillery. What could be cooler?
Spur BAR
( 352 Main St; 5pm-1am) What an upscale Western bar should be: rustic walls, leather couches, roaring fire. Good grub, too. Live-music weekends.
Sidecar Bar BAR
( 333 Main St, 2nd fl; 5pm-1am) Local and regional bands (rock, funk, swing) play to a 20-something crowd.
No Name Saloon & Grill BAR
( 447 Main St; 11am-1am) There's a motorcycle hanging from the ceiling and Johnny Cash's 'Jackson' playing on the stereo at this memorabilia-filled bar.
O'Shucks PUB
( 427 Main St; 10am-2am) The floor crunches with peanut shells at this hard-drinkin' bar for snowboarders and skiers. Tuesdays see $3 schooners (32 ounces) of beer.
Park City Roasters CAFE
(638 Main St; 6:30am-6pm; ) This cyber coffeehouse is a cool place to hang out, sip a shade-grown brew and catch up on your news reading – online or on paper.
#### Entertainment
Symphony, chamber music, bluegrass, jazz and other musical events happen throughout summer and winter; pick up the free _This Week in Park City_ (www.parkcityweek.com).
Egyptian Theatre Company THEATER
( www.egyptiantheatrecompany.org; 328 Main St) The restored 1926 theater is a primary venue for Sundance; the rest of the year it hosts plays, musicals and concerts.
#### Shopping
The quality of stores along Main St has improved in recent years. In addition to the typical tourist Ts and schlocky souvenirs, you'll find upscale galleries and outdoor clothing brands. Park City Gallery Association (www.parkcitygalleryassociation.com) puts out a gallery guide and sponsors art walks.
Tanger Outlet MALL
(Kimball Junction, Hwy 224) Dozens of outlet and other outdoor mall shops at the junction with I-80 (exit 145).
#### Information
Main Street Visitor Center ( 435-649-7457; 528 Main St; 11am-6pm Mon-Sat, noon-6pm Sun) Small desk inside the Park City Museum downtown.
Park City Clinic ( 435-649-7640; 1665 Bonanza Dr) Urgent care and 24-hour emergency room.
Park City Magazine (www.parkcitymagazine.com) Glossy magazine with some events listings.
Park Record (www.parkrecord.com) The community newspaper for more than 130 years.
Visitor Information Center ( 435-649-6100, 800-453-1360; www.parkcityinfo.com; cnr Hwy 224 & Olympic Blvd; 9am-7pm Mon-Sat, 11am-4pm Sun Jun-Sep; hours vary Oct-May) Large office in the northern Kimball Junction area.
#### Getting There & Away
Downtown is 5 miles south of I-80 exit 145, 32 miles east of SLC and 40 miles from the airport. Hwy 190 (closed October through March) crosses over Guardsman Pass between Big Cottonwood Canyon and Park City.
Park City Transportation ( 435-649-8567, 800-637-3803; www.parkcitytransportation.com), All Resort Express ( 435-649-3999, 800-457-9457; www.allresort.com) and Powder for the People ( 435-649-6648, 888-482-7547; www.powderforthepeople.com) all run shared van service ($39 one-way) and private-charter vans (from $99 for one to three people) from Salt Lake City International Airport. The latter also has Powder Chaser ski shuttles (from $45 round-trip) that will take you from Park City to Salt Lake City resorts.
#### Getting Around
Traffic can slow you down, especially on weekends; bypass Main St by driving on Park Ave. Parking can also be challenging and meter regulations are strictly enforced. Free lots are available in Swede Alley; those by 4th and 5th Sts are especially convenient.
Better still, forgo the rental and take a shuttle from the airport. The excellent public transit system covers most of Park City, including the three ski resorts, and makes it easy not to need a car.
Park City Transit (www.parkcity.org/citydepartments/transportation) Free trolleybuses run one to six times an hour from 8am to 11pm (reduced frequency in summer). There's a downloadable route map online.
### Ogden & Around
During its heyday, historic 25th St was lined with brothels and raucous saloons; today the restored buildings house restaurants, galleries, bakeries and bars. The old town is atmospheric, but the main attraction here is 20 miles east in the Wasatch Mountains of Ogden Valley. Since skiing here is more than an hour's drive from Salt Lake City, most metro area residents head to Park City or the SLC resorts, leaving Snowbasin and Powder Mountain luxuriously empty. The villages of Huntsville and Eden, halfway between town and mountains, are nearest to the resorts.
#### Sights
Ogden Eccles Dinosaur Park MUSEUM
(www.dinosaurpark.org; 1544 E Park Blvd; adult/child $7/6; 10am-5pm Mon-Sat, noon-5pm Sun, closed Sun Nov-Mar; ) Prepare for your children to squeal as a couple of animatronic dinosaurs roar to life inside the museum at Ogden Eccles Dinosaur Park. Outside, it's like a giant playground where you can run around, under and over life-size plaster-of-Paris dinosaurs.
Motor-Vu Drive-In THEATER
(http://motorvu.com; 5368 S 1050 West; dusk Fri-Sun Mar-Nov) Kids also love piling in the car to catch a flick at this old time drive-in movie theater. There's a swap meet here on Saturday at 8am.
Union Station MUSEUM
(2501 Wall Ave; adult/child $6/4; 10am-5pm Mon-Sat) This old train houses three small museums dedicated to antique autos, natural history and firearms.
#### Activities
Snowbasin SNOW SPORTS
( 801-620-1100, 888-437-5488; www.snowbasin.com; 3925 E Snowbasin Rd, Huntsville; day lift ticket adult/child $66/40) Snowbasin hosted the 2002 Olympic downhill, and it continues to be a competitive venue today. Snowhounds are attracted to everything from gentle slow-skiing zones to wide-open groomers and boulevards, jaw-dropping steeps to gulp-and-go chutes. Snowbasin also has four terrain parks and a dedicated snow tubing lift and hill. They groom 26 miles of cross-country skiing, both classic and skating; ask about yurt camping.
The lowdown: 3000ft vertical drop, base elevation 6400ft; 3000 acres, 20% beginner, 50% intermediate, 30% expert; one tram, two gondolas, two high-speed quads, four fixed-grip chairs. The lift system is one of the most advanced in the Southwest, but for now Snowbasin remains a hidden gem with fantastic skiing, top-flight service and nary a lift line. The exposed-timber-and-glass Summit Day Lodge (accessible to nonskiers) has a massive four-sided fireplace and a deck overlooking daredevil steeps, in addition to good restaurants.
In summer, the gondola (day pass $18; 9am-6pm Sat & Sun) takes you up to Needles restaurant and hiking and mountain-biking trails; bike rentals available for $50 per day. Check online for the Sunday afternoon outdoor concert series line-up.
Powder Mountain SNOW SPORTS
( 801-745-3772; www.powdermountain.com; Rte 158, Eden; day lift ticket adult/child $59/32) If you're someone who likes to don a backpack and spend the day alone, you'll groove on Powder Mountain. They've had banner years of late, and you'll have plenty of room to roam with more than 7000 skiable acres. More than 3000 acres are lift-served by four chairs (one high speed) and three rope tows. There are two terrain parks and night skiing till 10pm. Best of all, two weeks after a storm, you'll still find powder.
The Snow Cat Safari (per day $395) accesses 3000 acres of exclusive bowls, glades and chutes for a day gliding on powder. A Lightning Ridge single Snow Cat ride-and-run costs $15. Inquire about backcountry guided tours and snow-kiting lessons. The rest of the lowdown: 3005ft vertical drop, base elevation 6895ft, 7000 skiable acres; 25% beginner, 40% intermediate, 35% advanced.
Wolf Mountain SNOW SPORTS
( 801-745-3511; www.wolfmountaineden.com; 3567Nordic Valley Way, Eden; day lift ticket adult/child $35/22; ) The old-fashioned mom-and-pop mountain. At only 1600 skiable acres and with a 1604ft vertical drop, who'd think Wolf Mountain would garner any superlatives? But since all five lifts are lit until 9pm, Wolf Mountain has some of the largest night skiing terrain in Utah. The magic carpet lifts provide good access for young'uns; 25% beginner, 50% intermediate, 25% advanced runs.
iFly EXTREME SPORTS
( 801-528-5348; http://iflyutah.com; 2261 Kiesel Ave; per flight $49; noon-10pm Mon-Sat) Take off on an indoor skydiving adventure at iFly; reservations required.
#### Sleeping
Cradled by mountains, Ogden Valley is the preferred place to stay. If you choose to stay in town, you'll have more eating and drinking options.
##### OGDEN TOWN
Of the standard chain motels near I-15, the Comfort Inn is among the newest.
Ben Lomond Historic Suite Hotel HOTEL $-$$
( 801-627-1900, 877-627-1900; www.benlomondsuites.com; 2510 Washington Blvd; r incl breakfast $79-119; ) Traditional rooms in this 1927 downtown hotel could use an update, butyou can't beat the local history connection.
Hampton Inn & Suites HOTEL $$
( 801-394-9400, 800-426-7866; 2401 Washington Blvd; r $92-159; ) Contemporary rooms; short walk to restaurants.
##### OGDEN VALLEY
There are no accommodations owned by the ski resorts, but all three have condo partners that offer ski packages; check their websites. The town of Eden is closest to Powder and Wolf Mountains; Huntsville is closest to Snowbasin. For a full lodging list, see www.ovba.org.
Jackson Fork Inn B&B $-$$
( 801-745-0051, 800-255-0672; www.jacksonforkinn.com; 7345 E 900 South, Huntsville; r/ste incl breakfast $85/150) A big ol' white barn has been turned into a simple, seven-room B&B. Downstairs there's a homey restaurant serving dinner and Sunday brunch.
Red Moose Lodge LODGE $$
( 801-745-6667, 866-996-6673; http://theredmooselodge.com; 2547 N Valley Junction Dr, Eden; r $99-129; ) This 27-room log lodge is especially kid friendly, with a game room, climbing fort, ball courts and heated pool, plus an on-site spa. In winter, take the free shuttle to ski resorts.
Atomic Chalet B&B B&B $$
( 801-745-0538; www.atomicchalet.com; 1st St, Huntsville; r incl breakfast $85-125; ) Down-to-earth and comfy, this cedar-shake cottage makes an excellent home away from home. After a day spent skiing or hiking, relax in the hot tub, watch a film from the video collection or play a game of billiards.
Snowberry Inn B&B $$
( 801-745-2634, 888-746-2634, 1315 N Hwy 158, Eden; r incl breakfast $109-238; ) Family-owned log cabin B&B with game room; no room TVs. Ski packages available.
Alaskan Inn INN $$-$$$
( 801-621-8600; 435 Ogden Canyon Rd, Ogden; cabins & ste incl breakfast $139-194; ) Luxury Western-themed suites and cabins in the picturesque canyon, just outside Ogden Valley.
#### Eating & Drinking
Look for restaurants and a handful of bars in Ogden town on historic 25th St between Union Station and Grant Ave.
##### OGDEN TOWN
Roosters 25th Street Brewing Co PUB $-$$
(253 25th St; brunch & sandwiches $8-10, mains $10-20; 11am-10pm Mon-Fri, 10am-10pm Sat & Sun) Once a house of ill repute, this great old town building is now an upscale gastro brewpub. It has a sister restaurant in Union Station, at the end of the street.
Grounds for Coffee CAFE $
(126 25th St; dishes $2-6; 6:30am-8pm Mon-Thu, 6:30am-10pm Friday & Sat, 8am-6pm Sun) Full coffee-drink menu, plus baked goods and some sandwiches, in an artsy 1800s storefront setting.
Brewski's BAR $
(244 25th St; 10am-1am) More than 20 beers on tap; live-music weekends.
##### OGDEN VALLEY
Shooting Star Saloon PUB $
(7350 E 200 South, Huntsville; burgers $5-8; noon-9pm Wed-Sat, 2-9pm Sun) Open since 1879, tiny Shooting Star is Utah's oldest continuously operating saloon. Seek this place out: the cheeseburgers – and cheap beer – are justly famous.
Eats of Eden ITALIAN $$
(2529 N Hwy 162, Eden; mains $10-16; 11:30am-9pm Tue-Sat) Munch on pizza or pasta inside the rustic restaurant, or surrounded by valley on the small patio.
Grey Cliff Lodge Restaurant AMERICAN $$-$$$
(508 Ogden Canyon, Ogden; brunch $16.50, dinner $18-30; 5-10pm Tue-Sat, 10am-2pm & 3-8pm Sun) An old-fashioned resort restaurant, it's an institution in Ogden Canyon.
Carlos & Harley's TEX-MEX $$
(5510 E 2200, Eden; mains $11-16; 11am-9pm) A lively Mexican cantina inside the old Eden General Store.
#### Information
Ogden Valley Business Association (www.ovba.org) The online lowdown on Valley activities, eateries and lodging.
Ogden Visitors Bureau ( 866-867-8824; www.ogdencvb.org; 2501 Wall Ave; 9am-5pm Mon-Fri) Town and area info.
Outdoor Information Center ( 801-625-5306; Union Station, 2501 Wall Ave 9am-5pm Mon-Fri year-round, plus 9am-5pm Sat Jun-Sep) Handles USFS and other public lands trail and campground info.
#### Getting There & Away
Greyhound ( 801-394-5573, 800-231-2222; www.greyhound.com; 2393 Wall Ave) has daily buses traveling between Ogden town and SLC ($18.50, 45 minutes), but you really need a car to get around anywhere in the Valley.
### Heber City & Midway
Twenty miles south of Park City, Heber City (population 9780) and its vast valley make an alternative base for exploring the surrounding mountains. A popular steam-powered railway runs from here. A scant 3 miles east, Midway (population 2130) is modeled after an Alpine town, with hand-painted buildings set against the slopes. Here you'll find activity-laden resorts, great for families, and a thermal crater you can swim in. Resort activities are open to all, and cross-country skiing and is close to both towns.
#### Sights & Activities
Much of the forested mountains east of the towns have hiking, biking, cross-country skiing, ATV and snowmobile trails that are part of the Uinta-Wasatch-Cache National Forest (www.fs.usda.gov).
Heber Valley Historic Railroad TRAIN RIDE
( 435-654-5601; www.hebervalleyrr.org; 450 S 600 West, Heber; 3hr adult $30-89, child $25-74) The 1904 Heber Valley Historic Railroad chugs along on scenic trips through the steep-walled Provo Canyon, as well as taking numerous themed trips.
Homestead Crater SWIMMING
( 435-654-1102; www.homesteadresort.com; Homestead Resort, 700 N Homestead Dr, Midway; admission $16; noon-8pm Mon-Thu, 10am-8pm Fri & Sat, 10am-6pm Sun) Swim in a 65ft-deep geothermal pool (90°F, or 32°C, year-round) beneath the 50ft-high walls of a limestone cone open to the sky. This is way cool. Reservations required.
Soldier Hollow ADVENTURE SPORTS
( 435-654-2002; www.soldierhollow.com; off Hwy113; day pass adult/child $18/9; 9am-4:30pm) A must-ski for cross-country aficionados, Soldier Hollow, 2 miles south of Midway, was the Nordic course used in the Olympics. Its 19 miles of stride-skiing and skating lanes are also open to snowshoeing. For nonskiers, there's a 1201ft-long snow-tubing hill (adult/child 3-6 $18/8; noon-8pm Mon-Sat, noon-4pm Sun); book in advance on weekends, since ticket sales are capped. Snow season is December through March. May through October, the resort's gorgeous 36-hole golf course, mountain biking trails and horseback riding are popular. (Equipment rentals $19 to $35 per day.)
#### Sleeping
The standard chain gang of motels are available on Main St in Heber City.
Swiss Alps Inn MOTEL $
( 435-654-0722; www.swissalpsinn.com; 167 S Main St; r $65-85; ) This independent Heber City Main St motel has huge rooms with hand-painted doors, and you get a free milkshake from the associated restaurant next door.
Homestead Resort RESORT $$
( 435-654-1102, 800-327-7220; www.homesteadresort.com; 700 N Homestead Dr, Midway; r $135-190; ) Most destination family resorts of this caliber faded into obscurity a generation ago. A collection of homey buildings and cottages gathers around the resort's village green. Activities include 18-hole golf, cycling, horseback riding, hot-spring swimming, spa-going, volleyball, shuffle board and croquet. The restaurants are good, too; some of the packages include meals.
Blue Boar Inn INN $$$
( 435-654-1400, 800-650-1400; www.theblueboarinn.com; 1235 Warm Springs Rd, Midway; r incl breakfast $175-225; ) It's as if an ornate Bavarian inn had been teleported to Utah. Everything from the hand-painted exterior to the ornately carved wooden furniture screams Teutonic.
Zermatt Resort & Spa RESORT $$$
( 866-627-1684; www.zermattresort.com; 784 West Resort Dr, Midway; r incl breakfast $175-295; ) The 'Adventure Haus' at this upscale resort not only has mountain-bike rentals; they'll arrange scenic dare-devil flights, fly-fishing lessons and boat rental on a nearby lake. Complimentary ski and golf shuttles head to Park City and Sundance.
#### Eating
Dairy Keen BURGERS $
( 435-654-5336; 199 S Main St, Heber City; burgers $3-6; 11am-9pm) Look for the miniature train that travels overhead at this local play on Dairy Queen. The ice-cream sundaes and shakes can't be beat (try boysenberry).
Snake Creek Grill AMERICAN $$
(650 W 100 South/Hwy 113, Heber City; mains $16-20; 5-10pm Thu-Sun) One of northern Utah's best restaurants looks like a saloon from an old Western. The all-American Southwest-style menu features blue-cornmeal crusted trout and finger-lickin' ribs. Halfway between downtown Heber City and Midway.
### MT TIMPANOGOS
On the north side of Provo Canyon, take the paved, 16-mile Alpine Loop Rd (Hwy 92) –an incredibly scenic, twisting road past 11,750ft Mt Timpanogos. At 6800ft, stay overnight at the Mount Timpanogos Campground ( 877-444-6777; www.reserveamerica.com; tent & RV sites $16; May-Oct). Pit toilets, water; no hookups. A trailhead leads from here into the surrounding fir tree-filled wilderness.
Spectacular, star-like helictite formations are on view at three mid-mountain caverns in Timpanogos Cave National Monument ( 801-756-5238; www.nps.gov/tica; off Hwy 92; 3 days per vehicle $6; 7am-5:30pm Jun-Aug, 8am-5pm Sep & Oct). Book ahead or get there early for a 1½-hour ranger-led tour (adult/child $7/5); they fill up. To get to the caves, you have an uphill hike that can't be done more than an hour before your tour time. Hwy 92 is closed December through March.
Blue Boar Inn INTERNATIONAL $$-$$$
( 435-654-1400, 800-650-1400; www.theblueboarinn.com; 1235 Warm Springs Rd, Midway; breakfast & sandwiches $8-11, dinner $24-28; 7am-10pm) The European-inspired experience at this inn's dining room, open tononguests, is worth the reservation you need to make.
Mountain House Grill AMERICAN $$
( 435-654-5370; 79 E Main St, Midway; mains $9-19; 7am-2:30pm) For casual all-American.
#### Information
Most of the services are in Heber City.
Heber Ranger Station ( 435-654-0470; 2460 S Hwy 40; 8am-4pm Mon-Fr) Uinta-Cache-Wasatch National Forest info.
Heber Valley Chamber of Commerce ( 435-654-3666; www.hebervalleycc.org; 475 N Main St; 8am-5pm) Pick up information about both towns here.
Sidetrack Café ( 435-654-0563; 94 S Main St; 6:30am-5pm Mon-Fri, 7:30am-5pm Sat & Sun) Log onto the internet (free with purchase) over coffee and sandwiches.
#### Getting There & Around
Hwy 190 continues over Guardsman Pass to Big Cottonwood Canyon and SLC (closed in winter).
Greyhound ( 801-394-5573, 800-231-2222; www.greyhound.com; 2393 Wall Ave) Daily buses from Ogden to SLC ($11.50, 55 minutes).
UTA ( 801-743-3882, 888-743-3882; www.rideuta.com; cnr Wall & 23rd Sts) Runs express bus service to SLC ($4, 50 minutes), with diminished frequency on weekends.
### Sundance Resort
Art and nature blend seamlessly at Sundance ( 801-225-4107, 800-892-1600; www.sundanceresort.com; 9521 Alpine Loop Rd, Provo; r $225-319 ), a magical resort-cum-artist-colony founded by Robert Redford, where bedraggled urbanites connect with the land and rediscover their creative spirits. Participate in snow sports, ride horseback, fly-fish, write, do yoga, indulge in spa treatments, climb or hike Mt Timpanogos, nosh at several wonderful eateries and then spend the night in rustic luxury. Day-trippers should ask for trail maps and activity guides at the general store ( 9am-9pm), which shoppers love for the artisan handicrafts, home furnishings and jewelry (catalog available).
Mount Timpanogos, the second-highest peak in the Wasatch, lords over the ski resort ( 801-223-4849 for reservations; day lift ticket adult/child $49/27), which is family- and newbie-friendly. The 500-skiable-acre hill is primarily an amenity for the resort, but experienced snow riders will groove on the super-steeps. The Cross Country Center ( 9am-5pm Dec-Apr) has 16 miles of groomed classic and skating lanes on all-natural snow. You can also snowshoe 6 miles of trails past frozen waterfalls (ask about nighttime owl-watching walks). The woods are a veritable fairyland.
May through September, there's lift-assist hiking and mountain biking; rental available (from $35). Sundance hosts numerous year-round cultural events, from its namesake film festival (Click here) and screenwriting and directing labs, to writers'workshops and music seminars. In summer there are outdoor films, plays, author readings and great music series at the amphitheater. Don't miss the art shack ( 10am-5pm), where you can throw pottery and make jewelry.
Lucky enough to be staying over? Rough-hewn cottage rooms are secluded, tucked among the trees on the grounds; the perfect place to honeymoon or write your next novel. Decor differs but they've all got pine walls and ever-so-comfy furnishings, plus quilts, paperback books and board games; some have kitchens. Two- to four-bedroom houses (from $1025) are also available.
Sundance's top-flight restaurant, Tree Room ( 801-223-4200; mains $25-41; 5-9pm Tue-Thu, 5-10pm Fri & Sat) is a study in rustic-mountain chic – with a big tree trunk in the middle of the room. Here the modern American menu items are as artfully presented as the chichi clientele. You'll be hard-pressed to find a better meal this side of San Francisco. For something lighter, pick up a turkey and cranberry relish panini to-go at the Deli (sandwiches $7-10; 7am-9pm) and then enjoy it on the grounds. The Foundry Grill (breakfast & sandwiches $8-16, dinner $16-31; 8-11am, 11:30am-4pm & 5-9pm Mon-Sat, 9am-2pm & 5-9pm Sun) is also available for most meals.
Built of cast-off barn wood, the centerpiece of the Owl Bar ( 5pm-11am Mon-Thu, 5pm-1am Fri, noon-1am Sat, noon-11pm Sun) is a century-old bar where the real Butch Cassidy once drank. The place looks like a Wild West roadhouse, but it's full of art freaks, mountain hipsters and local cowboys imbibing by a roaring fireplace. On Friday and Saturday there's often live music.
### Provo
The third-largest city in Utah is a conservative town with a strong Mormon influence. The most compelling reason to visit is to see Brigham Young University (BYU) on a day trip from Salt Lake City, 45 miles north. University Ave, Provo's main thoroughfare, intersects Center St in the small old downtown core. Note that the whole place pretty much shuts down on Sunday
The BYU campus (www.byu.edu) is enormous and known for its squeaky-clean student dress codes. Drive 450 East north toward the Hinckley Alumni & Visitor Center ( 801-422-4678; cnr W Campus & N Campus Drs; 8am-6pm Mon-Sat) where tours begin, by appointment. The university's what's-this-doing-here Museum of Art ( 801-378-2787; admission free; 10am-6pm Tue, Wed & Fri, 10am-9pm Mon & Thu, noon-5pm Sat) is one of the biggest in the Southwest, with a concentration on American art. Temporary exhibits are top notch. BYU sporting events take place at Lavell Edwards Stadium ( 801-422-2981; www.byutickets.com; 1700 N Canyon Rd).
You can ice skate in town at Peaks Ice Arena ( 801-377-8777; www.peaksarena.com; 100 N Seven Peaks Blvd; adult/child $6/4; Mon-Sat), where the Olympic hockey teams faced off in 2002. Free-skate hours vary.
Provo is close enough to SLC that you can easily make it in a day. If you stay over, we recommend the 1895 Hines Mansion B&B ( 801-374-8400, 800-428-5636; www.hinesmansion.com; 383 W 100 South; r incl breakfast $129-199; ). The 'Library' guest room has a 'secret passage' door to the bathroom.
### DONNY & MARIE
Well-known Mormon family the Osmonds have long called Provo, Utah, home. Seven of the nine children born to George and Olive ('Mother') Osmond participated in the family singing group 'The Osmonds' that was a sensation in the '70s. Most of the Osmond offspring have spawned large families of their own (totaling 120 descendants at last count). Pop icons Donny and Marie branched out musically, singing and hosting a live variety show. Remember 'A Little Bit Country, A Little Bit Rock 'n' Roll'?
Marie's 2007 runner-up success on the TV hit _Dancing with the Stars_ helped reignite interest in the entertaining family. Two years later, Donny trumped his sister's achievement by winning the mirror-ball trophy on the same show. In 2011 the duo celebrated the 500th performance of the new Donny & Marie show staged at the Flamingo hotel in Las Vegas.
The historic downtown has numerous little independent, ethnic restaurants; many around the intersection of Center St and University Ave. Guru's (45 E Center St; mains $6-11; 11am-9pm Mon-Sat) has an eclectic cafe menu, including rice bowls, and Gloria's Little Italy (1 E Center St; lunch $10-12.50, mains $15-19; 11am-9pm Mon-Thu, until 10pm Fri & Sat) is always popular.
Get information at the Utah Valley Visitors Bureau ( 801-851-2100; www.utahvalley.org/cvb; 111 S University Ave; 8:30am-5pm Mon-Fri, 9am-3pm Sat), inside the beautiful courthouse.
UTA ( 801-743-3882, 888-743-3882; www.rideuta.com) runs frequent express buses to SLC ($5), with diminished service Sunday.
### DINOSAUR DIAMOND
Some darn clever marketing people came up with a dual-state national scenic byway, Dinosaur Diamond (www.dinosaurdiamond.org), which aims to give Dino his due by promoting and protecting paleontology along its 512-mile suggested route in Colorado and Utah. Following their lead, here are our fossilized favorites in Utah:
Dinosaur National Monument (Vernal) Touch 150-million-year-old bones still in the ground!
Dinosaur Discovery Site (St George; Click here) Some of the most amazing dinosaur trackways ever found.
Utah Museum of Natural History (SLC; Click here) The new home for the Huntington mammoth.
Utah Field House of Natural History State Park Museum (Vernal) Still growing, but an amazing, kid-friendly Utah dinosaur museum.
Museum of Ancient Life (Lehi; Click here) Interactive exhibits provide an overview of world dinosaurs.
Cleveland-Lloyd Dinosaur Quarry (Price; Click here) Watch 'em digging up new discoveries daily.
Red Fleet State Park (Vernal) More 200-million-year-old footprints.
And just for fun:
Dinosaur Museum (Blanding; Click here) Dino movie memorabilia and models.
Ogden Eccles Dinosaur Park (Ogden; Click here) Jurassic-era playground for kids.
## NORTHEASTERN UTAH
A remote and rural area, Northeastern Utah is high wilderness terrain (much of which is more than a mile above sea level) that has traditionally attracted farmers and miners. Rising oil prices spurred oil and gas development in the rocky valleys, which in turn has led to increased services in towns like Vernal. Most travelers come to see Dinosaur National Monument, but you'll also find other dino dig sites and museums, as well as Fremont Indian rock art and ruins in the area. Up near the Wyoming border, the Uinta Mountains and Flaming Gorge attract trout fishers and wildlife lovers alike.
### Vernal & Around
The capital of self-dubbed 'Dinoland', Vernal is the closest town to Dinosaur National Monument (20 miles east). You'd never know it from the big pink allosaurus that welcomes you to town. Don't miss the great natural history museum in town.
There are a number of great drives in the area, through public lands and parks, including the road up to the gorgeous rivers and lake of Flaming Gorge, just 35 miles north. The Dinosaurland Travel Board ( 800-477-5558; www.dinoland.com; 134 W Main; 8am-5pm Mon-Fri) provides information on the entire region; pick up driving-tour brochures for area rock art and dino tracks here. The Vernal Ranger Station ( 435-789-1181; www.fs.usda.gov/ashley; 355 N Vernal Ave; 8am-5pm Mon-Fri) has details on camping and hiking in Ashley National Forest, to the north.
The informative film at the Utah Field House of Natural History State Park Museum (http://stateparks.utah.gov; 496 E Main St; 9am-5pm Mon-Sat; ) is the best all-round introduction to Utah's dinosaurs. Interactive exhibits, video clips and, of course, giant fossils are wonderfully relevant to the area. There's loads to keep the kids entertained, and the museum is still growing.
### SCENIC DRIVE: RED CLOUD LOOP
After you see the dinosaur tracks at Red Fleet State Park, continue on Hwy 191 for 21 miles north of Vernal, then take off west on Red Cloud Scenic Backway. The road starts out tame, then rises sharply up to 10,000ft in twists and turns. The one-and-a-half lane road has steep drop-offs and dramatic pine scenery amid the eastern Uinta peaks. Allow three hours to return the full 74 miles back to Vernal via Dry Fork Canyon Rd, where you can stop at the McConkie Ranch Petroglyphs.
Ten miles northeast of Vernal on Hwy 191, check out hundreds of fossilized dinosaur tracks at Red Fleet State Park ( 435-789-4432; http://stateparks.utah.gov; admission $7; 6am-10pm Apr-Oct, 8am-5pm Nov & Dec). Eleven miles northwest, the 200ft of McConkie Ranch Petroglyphs (Dry Fork Canyon Rd; by donation; dawn-dusk) are well worth checking out. Generous ranch owners built a little self-serve info shack with posted messages and a map, but be advised that the 800-year-old Fremont Indian art require some rock-scrambling to see. Being on private land has really helped; these alien-looking anthropomorphs are in much better shape than the many that have been desecrated by vandals on public lands. Follow 3000 West to the north out of Vernal. You can visit both as part of the 74-mile Red Cloud Loop. For even more rock art and ruins, we recommend the nearby Nine Mile Canyon drive.
The Green and Yampa Rivers are the main waterways in the area; both have some rapids and more genteel floats. Trips (May through September) run from $85 to $800 for one to five days. Check with Don Hatch River Expeditions ( 435-789-4316, 800-342-8243; www.donhatchrivertrips.com, 221 N 400 East) or Dinosaur Expeditions ( 800-345-7238; www.dinoadv.com).
Contemporary comforts like deluxe mattresses and flat-screen TVs come standard both in the hotel rooms at Landmark Inn & Suites ( 435-781-1800, 888-738-1800; Rte 149; r incl breakfast $69-109; ), and at the much more reasonable B&B rooms in a purpose-built house across the street. The latter is a bargain, though walls can be thin. Guests all share the buffet breakfast and fitness room at the main building. A number of new motels have popped up west of town in recent years, including Marriott Springhill Suites ( 435-781-9000, 888-287-9400; www.marriott.com; 1205 W Hwy 40; r $109-139; ), with supersized rooms, an indoor pool and outdoor sundeck. Flaming Gorge and Dinosaur National Monument both have camping.
For homemade soup, a tasty panini and a good read, stop into Backdoor Grille (87 W Main St; mains $5-8; 11am-8pm), at the rear of Bitter Creek Books. Dinosaur Brew Haus (550 E Main St; burgers $5-10; 5-10pm) serves up burgers and microbrews on tap. The hearty down-home grub at NaplesCountry Café (1010 E Hwy 40; breakfast & sandwiches $4-8, mains $9-15; 7am-10pm), east of town, includes mile-high meringue pies.
Vernal is 145 miles west of Park City and 112 miles north of Price.
### Dinosaur National Monument
Earl Douglass discovered one of the largest dinosaur fossil beds in North America here in 1909. He camped out and tenaciously protected the site until it was made a national park in 1915.
Driving in from Vernal, after about 13 miles, turn left at the Utah Welcome Center ( 800-200-1160; Hwy 40, Jensen; 9am-5pm), which can provide information on the region and the state. A further 7 miles down the road, you enter the Dinosaur Quarry (www.nps.gov/dino; per vehicle $10; 9am-5pm) section of the park.
In the early 1900s, hundreds of tons of rock was blasted away to expose the quarry. Many of the bones were only partially excavated, left half in the rock so that visitors could see how they were found – then the quarry was enclosed in a glass-sided building. Unfortunately the soil was unstable and the structure eventually became unsafe. Reopened after being closed for many years, you can once again see this marvelous site. You can also hike up to touch still-embedded, 150 million-year-old fossils on the trail. Take the free ranger-led interpretive hike, if available; you'll spot more than can easily be found on your own.
Pick up a brochure for the scenic driving tour that continues south for 13 miles past Fremont Indian rock art, ending at homesteader Josie Bassett's cabin and several trailheads. The monument straddles the Utah-Colorado state line. The Utah portion of the park contains all the fossils, but the Canyon Section Visitor Center ( 970-374-3000; www.nps.gov/dino; Dinosaur, CO; per car $10; 9am-4pm Jun-Aug, 8am-4:30pm Wed-Sun Sep & May) shows a good movie and there are pretty hikes.
Staying over? Pitch your tent at the waterfront Green River Campground (Dinosaur Quarry; campsites $12; mid-Apr–Oct); first-come, first-served. The 88 sites have access to running water (indoor plumbing and the river), but no showers. Ask about primitive camping.
If you'd rather a roof over your head, book at the comfy-cozy Jensen Inn ( 435-789-590; 5056 S 9500 East, Jensen; r incl breakfast $95-150; ), 3 miles north of the Hwy 40 turnoff on Hwy 149. Sleep in a tipi ($95) or camp ($55) on the grounds and you can still get the scrumptious home-cooked breakfast.
### Flaming Gorge National Recreation Area
Named for its fiery red sandstone canyon, Flaming Gorge provides 375 miles of shoreline around Flaming Gorge Reservoir, which straddles the Utah-Wyoming state line. As with many artificial lakes, fishing and boating are prime attractions. Various records for giant lake trout and Kokanee salmon have been set here. The area also provides plenty of hiking and camping in summer, and cross-country skiing and snowmobiling in winter. Keep an eye out for common wildlife such as moose, elk, pronghorn antelope and mule deer; you may also see bighorn sheep, black bears and mountain lions. The lake's 6040ft elevation ensures pleasantly warm but not desperately hot summers – daytime highs average about 80°F (27°C).
Information is available from www.flaminggorgecountry.com, the USFS Flaming Gorge Headquarters ( 435-784-3445; www.fs.fed.us/r4/ashley; 25 W Hwy 43, Manila; 8am-5pm Mon-Fri) and at the Flaming Gorge Dam Visitor Center ( 435-885-3135; Hwy 191; 9am-5pm May-Sep). Day use of some Flaming Gorge areas costs $5 at self-pay stations.
In Dutch John, rent a fishing, pontoon or ski boat ($110 to $280 per day) from Cedar Springs Marina ( 435-889-3795; www.cedarspringsmarina.com; off Hwy 191; Apr-Oct), 2 miles east of Flaming Gorge Dam. The best fishing is found with a guide; ask at the marina or contact Trout Creek Flies ( 435-885-3355; www.fishgreenriver.com; cnr Hwy 191 & Little Hole Rd). A guided half-day trip will cost you about $325 for two people. Aim to fly-fish late June to early July, before the river is flooded with fun floaters. Trout Creek also rents rafts and kayaks ($60 to $80 per day) and runs a floater shuttle.
Ashley National Forest (www.fs.fed.us/r4/ashley) runs more than two dozen May-to-September campgrounds in the area. The 7400ft elevation, ponderosa pine forest location and excellent clifftop overlook views of the reservoir make Canyon Rim ( 877-444-6777; www.recreation.gov; Red Canyon Rd, off Hwy 44; tent & RV sites $15) a top choice. Keep an eye out for bighorn sheep. Water; no showers or hookups.
Activities at Red Canyon Lodge ( 435-889-3759; www.redcanyonlodge.com; 790 Red Canyon Rd, Dutch John; cabins $110; closed Mon-Thu Nov-Mar) include fishing, rowing, rafting and horseback riding, among others. Its pleasantly rustic cabins have no TVs. Flaming Gorge Resort ( 435-889-3773; www.flaminggorgeresort.com; 155 Greendale/Hwy 191, Dutch John; r $110, ste $150) has similar water-based fun, and rents motel rooms and suites. Both have decent restaurants. Convenience stores in Dutch John have deli counters.
### SCENIC DRIVE: FLAMING GORGE-UINTAS SCENIC BYWAY
Heading north from Vernal, 80 miles into the northeastern Uintas Mountains, Flaming Gorge-Uintas Scenic Byway (Hwy 191) is a drive and a geology lesson all in one. As you climb up switchbacks to 8100ft, the up-tilted sedimentary layers you see represent one billion years of history. Interpretive signs explain what different colors and rock compositions indicate about the prehistoric climate in which they were laid down. It's a great route for fall color and wildlife-watching, too.
### High Uintas Wilderness Area
The Uinta Mountains are unusual in that they run east-west, unlike all other major mountain ranges in the lower 48. Several peaks rise to more than 13,000ft, including Kings (13,528ft), which is the highest point in the Southwest. The central summits lie within the High Uintas Wilderness Area (www.fs.fed.us/r4/ashley), part of Ashley National Forest, which provides 800 sq miles of hiking and horseback riding opportunities. No roads, no mountain biking and no off-road driving permitted. The reward? An incredible, remote mountain experience, one without snack bars or lodges.
### Price & San Rafael Swell
Though not the world's most interesting town in itself, Price can serve as a base for exploring backcountry dinosaur and ancient rock-art sites in the San Rafael Swell and beyond. It's en route from Green River (65 miles) to Vernal (112 miles), so a stopover is also possible. The staff at the Castle Country Travel Desk ( 800-842-0789; www.castlecountry.com; 155 E Main St; 8am-5pm Apr-Sep, 9am-5pm Mon-Sat Oct-Mar) can help you plan out your regional routes. In the same building (same hours), the College of Eastern Utah Prehistoric Museum (www.museum.ceu.edu; adult/child $5/2; 9am-5pm Mon-Sat) exhibits fossils that were discovered within two hours of the museum. Look for the Utah raptor, first identified in this part of the world.
Thirty miles south of Price you can visit an actual dinosaur dig site. More than 12,000 bones have been taken from the ground at Cleveland-Lloyd Dinosaur Quarry ( 435-636-3600; adult/child $6/2; 10am-5pm Fri & Sat, noon-5pm Sun late Mar-Oct). A dozen species of dinosaur were buried here 150 million years ago, but the large concentration of meat-eating allosaurus has helped scientists around the world draw new conclusions. Two excavations are on display and the visitor center's exhibits are quite informative. Several hikes lead off from there. Take Rte 10 south to the Elmo/Cleveland turnoff and follow signs on the dirt road.
### SCENIC DRIVE: NINE MILE CANYON
Abundant rock art is the attraction on the Nine Mile Canyon National Backcountry Byway (www.byways.org), billed as the 'longest art gallery in the world'. You can also spot Fremont granaries and structures along the canyon walls (bring binoculars). Many of the petroglyphs are easy to miss; some are on private property. Pick up a free guide at area restaurants or at the Castle Country Travel Desk in Price or the Utah Welcome Center outside Dinosaur National Monument. Allow at least three to five hours for the 70-mile unpaved ride from Wellington (on Hwy 6) to Myton (on Hwy 40). Get gas before you go: there are no services.
About 23 miles northeast along Nine Mile Canyon Byway from the Hwy 6/191 turnoff, you can stay at the simple Nine Mile Bunk & Breakfast ( 435-637-2572; www.ninemilecanyon.com; r with shared bath $70, camping cabins $55, both incl breakfast), with two big ranch house rooms on spacious grounds; plus you can stay in an old pioneer cabin or pitch a tent on site ($10). The rustic accommodations are run by a 'retired' ranching couple who are the nicest folks you'd ever want to meet. They run canyon tours (half-day from $155), too.
These southern lands between Hwys 10 and 6/24 are the canyons, arches and cliffs of the San Rafael Swell. Look for the purples, grays and greens that indicate ancient seabeds, in addition to the oxygenated oranges and reds of this anticline. The area is all BLM land where free dispersed camping and some four-wheeling is allowed. Sights include a 1200ft canyon drop at Wedge Overlook, Barrier Canyon-style pictographs at Buckhorn Wash, and a suspension footbridge. Ask for a basic map at the town visitor center or the quarry site. For more details contact the BLM Price Field Office ( 435-636-3600; www.blm.gov; 125 S 600 West; 9am-4:30pm Mon-Fri) or go online to www.emerycounty.com/travel.
The well-preserved ancient archaeological sites protected by Wilcox Ranch are now part of Range Creek Wildlife Management Area (www.wildlife.utah.gov/range_creek), east of East Carbon (25 miles southeast of Price). Since the family turned the property over to the government, the public has been allowed limited access. The best way to explore is with a full-day 4WD tour ($125 per person) run by Tavaputs Ranch ( 435-637-1236; www.tavaputsranch.com; per person incl meals $200; mid-Jun–mid-Sep). Included in the lodging price are three meals, backcountry hikes, scenic drives and wildlife tours on the 15,000-acre spread; horseback riding is $50 extra.
### STARVATION STATE PARK
No one is quite sure who did the stealing, but either trappers in the area stashed some winter stores in the mountains, or Native Americans did, and then the other group took the food. Advance planners starved when they found no tasty treats buried under the snow, or so the story goes. In all likelihood bears were to blame for the theft and the name of Starvation State Park (http://stateparks.utah.gov; Hwy 40, Duchesne; day-use $7, 6am-10pm Jun-Aug, 8am-5pm Sep-May).
Subsequent homesteaders tried to make a go of it here on the Strawberry River, but with a short growing season and frozen ground they had no better luck fending off hunger. Today the park contains a 3500-acre reservoir as well as plenty of picnickers. The 60-site Lower Beach Campground ( 800-322-3770; http://utahstateparks.reserveamerica.com; tent & RV sites with hookups $16-25; Jun-Sep) has showers andfeatures a sandy beach. Primitive camping is also available here – don't forget to bring food!.
Free camping is allowed off established roads on the San Rafael Swell BLM lands. The motels off Hwy 6/191 and on Main St aren't exactly exciting, but they are plentiful. Super 8 ( 435-637-8088, 888-288-5081; www.super8.com; 180 N Hospital Dr; r $60-80; ) has fine, basic rooms. Thirty miles south in Castle Dale, San Rafeal Swell Bed & Breakfast ( 435-381-5689; www.sanrafaelbedandbreakfast.com; 15 E 100 N; r incl breakfast $65-110; ) has more of a personal touch. Less expensive rooms share a bath; some are a bit themey.
The best place to eat in town, isn't themey. Though barely out of Price, Grogg's Pinnacle Brewing Company (1653 N Carbonville, Helper; burgers $6-10, mains $12-18; 11am-10pm) is technically in Helper. Friendly staff, tasty casual-American fare and microbrews on tap make this the place to be. Look for other eateries along Main St.
### **Understand Southwest USA**
Southwest USA Today
History
The Way of Life
Native American Southwest
Geology & The Land
Southwest Cuisine
Arts & Architecture
#
Top of section
# Southwest USA Today
### It's All Politics...
»Population of AZ, NM, UT, NV & CO: 19 million
»Regional unemployment rate June 2011: 8.9%
»US unemployment rate June 2011: 9.2%
Tourism officials in Arizona are surely not pleased by headlines in recent years. One of the biggest issues facing the state is illegal immigration. About 250,000 people crossed illegally into Arizona from Mexico in 2009. Although that was a 50% decline from a few years earlier, the State passed law SB 1070 in 2010, requiring police officers to ask for identification from anyone they suspect of being in the country illegally.
What's happening on the ground? Across the Southwest, the number of arrests for illegal border crossings has dropped. Is the ongoing recession making the US less attractive? Perhaps it's the beefed up US Border Patrol. The number of border patrol agents jumped from 10,000 in 2004 to more than 20,700 in 2010. Agents have a very visible presence in southern Arizona: there are checkpoints, and you'll likely see their green-and-white SUVs whizzing down two-lane backroads.
»Cost of marriage license in Nevada: $60
»Sprinting speed of a roadrunner: 15mph
Fiscal woes are the other political hot potato. States are slashing spending, and in Arizona and Utah state park budgets have gone under the knife. Many in Arizona are operating on a five-day schedule, closing on Tuesday and Wednesday; in Utah, state parks have cut the number of rangers. In May 2011, Nevada's unemployment rate was 12%, which was higher than the national average. Luxury condominiums in Vegas sit empty and mountain resort properties in Colorado are experiencing declines in business.
Despite state park budget woes, the Southwest's national parks are faring OK. Attendance was up in Grand Canyon National Park in 2010, and the park welcomed 4.38 million recreational visitors, making it the second-most-visited national park in the US (behind Great Smoky Mountains). Zion National Park ranked eighth.
### ...or the Weather
Although the exact causes are unclear – climate change, residential development, government policy – the Southwest has been particularly hard-hit by forest fires in recent years. The 2011 Wallow Fire was the worst in Arizona's history, burning about 538,000 acres. At about the same time, the Las Conchas Fire burned more than 244 sq miles near Los Alamos, NM. The good news? A record snowpack in western mountain ranges in early 2011 spelled w-a-t-e-r (after melting) for Nevada and Arizona, where water levels have been dropping the last 10 years. Lake Mead might swell by 40ft.
»Number of pueblos in New Mexico: 19
»Grand Canyon's widest chasm: 18 miles
»Percentage of land that is public in Utah: 70%
»Miles of railroad track on Durango to Silverton line: 45
### On the Bright Side
NASA may have wrapped up the shuttle program, but entrepreneurs like Richard Branson are looking to the stars – and taking action. Branson's Virgin Galactic is on course to send civilian 'astronauts' into space from the new Spaceport in New Mexico in the next few years. Tickets are $200,000, with a $20,000 deposit; about 430 people have signed up for a flight.
The hottest recorded temperature in Arizona was 128°F (53.5°C) at Lake Havasu City.
Not all advancements require a spaceport. On the south rim of the Grand Canyon, finishing touches have been added to the impressive new visitor center. Ecofriendly initiatives in the national park are gaining traction, including a park-and-ride shuttle from Tusayan and a bicycle rental service. Environmentally, Colorado is leading the way with its extremely progressive clean-energy standards, with legislated incentives for residents to use clean energy and significant growth in solar energy jobs.
Last but not least, New Mexico and Arizona are both celebrating 100 years of statehood in 2012.
### Dos and Don'ts
»Do tip everyone in Vegas.
»Don't smoke inside a building without asking first. Nonsmoking laws are increasingly common, and many people are strongly against secondhand smoke in their homes.
»Do leave a 15-20% tip for your waiter when served a meal.
»Don't take pictures on Native American land without first asking permission.
»Do make sure you know what time zone you're in when crossing states.
### Top Movies
127 Hours (2010) Aron Ralston's harrowing experience in Utah's red-rock country.
Thelma & Louise (1991) Dead in Dead Horse State Park? Pshaw. The duo lives to celebrate the movie's 20th anniversary in 2011.
### Greeting People
»'Hi, how are you?' is expected to receive a cheerful, 'Thanks. I'm fine.' Actual complaints are frowned upon.
»Don't be overly physical. Some Americans will hug, but many more will just shake hands. Big kisses will likely get you slapped.
### How to Speak Southwestern
adobe – building style using straw and mud (traditional) or sand and clay (modern) farolitos – Hispanic Christmas tradition; made by placing a candle inside a waxed bag lined with sand
hacienda – old Spanish colonial mansion
kiva – round-fronted adobe fireplace; once used for worship, today it's used for warmth
portales – covered porches
ristra – string of dried red chiles, often seen hanging from porches
#
Top of section
# History
History is a hands-on experience in the Southwest. Museums? Save 'em for later. First you'll want to explore the scruffy OK Corral, or climb into a lofty cliffdwelling, or simply join the congregation inside a 1700s Spanish mission. Historic spots like these are what make the region so fascinating. The land, with its mineral-rich hills and stubborn inaccessibility, is intricately tied to the regional history. Settlers were lured here for a variety of reasons: rumors of gold and copper, the possibility of religious freedom and the likelihood of unfettered adventure and self-determination.
In sun-baked Phoenix today, travelers can see the remains of canals built by the ancient Hohokam people to transport water to their fields. An ascent into Ancestral Puebloan cliffdwellings in Arizona, New Mexico or Colorado reveals the sweep of the land and the advantages of building a home far above the ground. Native American tribes eventually moved in from other regions, learning the symbols and stories of their predecessors and weaving them into their own cultural narrative.
The Spanish conquistadors, seeking the Seven Cities of Gold, left their mark on the landscape too. Their expeditions in the 1500s led to the construction of the missions, which opened the door for regional development and Western civilization – with a lot of bloodshed along the way. The Mormons arrived in 1847, building temples, orderly streets and religious outposts throughout Utah. Prospectors started towns, too, in the 19th century, and their mine shafts and old buildings are still visible in boom-and-bust towns across the region. These mining towns and the surrounding ranchland lured families seeking a better life, as well as cowboys, sheriffs and outlaws – restless, free-range men who kept upsetting the balance between chaos and civilization. Their spirit lives on today.
In the 1900s, the Southwest made its mark scientifically. The world's first atomic bomb was developed under top-secret conditions at Los Alamos: southern New Mexico was a launch pad for rockets, and the desert served as a blasting ground for the first atomic bomb in 1945 More recently, the Southwest gained fame for two historic firsts. In 1981 Sandra Day O'Connor, who grew up on an Arizona ranch, was the first woman appointed to the United States Supreme Court. In 2008, New Mexico's Bill Richardson was the first Hispanic to seek the office of President of the United States.
### PETROGLYPHS: WRITTEN ON THE LAND
Petroglyphs can be found etched into desert-varnished boulders across the Southwest. This rock art is simple yet mysterious and always leaves us wondering: who did this, and why? What were they trying to say?
Dating from at least 4000 BC to as late as the 19th century, rock art in the Southwest has been attributed to every known ancestral and modern people. In fact, one way archaeologists track the spread of ancestral cultures is by studying their distinctive rock art styles, which tend to be either abstract or representational and anthropomorphic. Representational rock art is almost always more recent, while abstract designs appear in all ages.
We can only speculate about what it means. This symbolic writing becomes obscure the moment the cultural context for the symbols is lost. 'Archaeologists believe much of the art was likely the work of shamans or elders communicating with the divine. Some of the earliest abstract designs may have been created in trance states. Certain figures and motifs seem to reflect a heavenly pantheon, while other rock art may tell stories – real or mythical – of successful hunts or battles. Some etchings may have served as simple agricultural calendars, marking the start of harvest season, for example, by the way a shadow falls across a picture.
Other images may have marked tribal territory, and some may have been nothing more than idle doodling. But no matter what the meaning, each rock-art site – whether a petroglyph (inscribed or pecked into the stone) or pictograph (painted figure) – is irreplaceable, whether as a valuable part of the human archaeological record or the continuing religious traditions and cultural patrimony of contemporary tribes.
Preserve rock-art sites for future generations by observing these rules of etiquette:
» Do not disturb or remove any artifacts or features of the site.
» Do not trace, repaint, remove graffiti or otherwise touch or apply any materials to the rock art.
» Stay back at least 10ft from all rock-art panels, using binoculars or a zoom lens for better views.
## THE FIRST AMERICANS
Archaeologists believe that the region's first inhabitants were hunters – descendants of those hardy souls who crossed the Bering Strait into North America 25,000 years ago. The population grew, however, and wild game became extinct, forcing hunters to augment their diets with berries, seeds, roots and fruits. After 3000 BC, contact with farmers in what is now central Mexico led to the beginnings of agriculture in the Southwest. Primitive corn was grown, and by 500 BC beans and squash were also cultivated. Between 300 BC and AD 100, distinct groups began to settle in villages in the Southwest.
Cliff Dwellings »
»Mesa Verde National Park, CO
»Bandelier National Monument, NM
»Gila Cliff Dwellings National Monument, NM
»Montezuma Castle National Monument, AZ
»Walnut Canyon National Monument, AZ
»Navajo Nation National Monument, AZ
## THE HOHOKAM, MOGOLLON & ANCESTRAL PUEBLOANS
By about AD 100, three dominant cultures were emerging in the Southwest: the Hohokam of the desert, the Mogollon of the central mountains and valleys, and the Ancestral Puebloans. Archaeologists originally called the Ancestral Puebloans the Anasazi, which comes from a Navajo term meaning 'ancient enemy' and has fallen out of favor.
The Hohokam lived in the deserts of Arizona from 300 BC to AD 1400, adapting to desert life by creating an incredible river-fed irrigation system. They also developed low earthen pyramids and sunken ball courts with sloped earthern walls. These oval-shaped courts, which varied in size, may have been used for organized games as well as for markets and community gatherings.
The Mogollon culture settled near the Mexican border from 200 BC to AD 1400. They lived in small communities, often elevated on isolated mesas or ridge tops, and built pit dwellings, which were simple structures of wood, shrubs and mud built over a small depression in the ground. Although they farmed, they depended more on hunting and foraging for food. Growing villages featured the kiva – a circular, underground chamber used for ceremonies and other communal purposes.
Around the 13th or 14th century, the Mogollon were likely being peacefully assimilated by the Ancestral Puebloan groups from the north. One indication of this is the beautiful black-on-white Mimbres pottery with its distinctive animal and human figures executed in a geometric style reminiscent of Puebloan ware. (The Mimbres were Mogollons who lived in a remote valley area in southwestern New Mexico between 1100 and 1150AD.) The Gila CliffDwellings in New Mexico are a late-Mogollon site with Puebloan features.
The Ancestral Puebloans inhabited the Colorado Plateau, also called the Four Corners area, which comprises parts of northeastern Arizona, northwestern New Mexico, southwestern Colorado and southeastern Utah. This culture left the Southwest's richest archaeological sites and ancient settlements, some of which are still inhabited.
Today, descendants of the Ancestral Puebloans live in Pueblo Indian communities along New Mexico's Rio Grande, and in the Acoma, Zuni and Laguna Pueblos in northwest New Mexico. The oldest links with the Ancestral Puebloans are found among the Hopi tribe of northern Arizona. The mesa-top village of Old Oraibi has been inhabited since the 1100s, making it the oldest continuously inhabited settlement in North America.
By about 1400, the Hohokam had abandoned their villages. There are many theories on this tribe's disappearance, but the most likely explanation involves a combination of factors, including drought, overhunting, conflict among groups and disease. The Mogollon people were more or less incorporated into the Ancestral Puebloans, who had also all but disappeared from their ancestral cliffdwellings at Mesa Verde in southwestern Colorado by the 1400s – their mass exodus began in the 1300s.
For more about the Native American peoples of the Southwest, see (Click here).
_Those Who Came Before_ , by Robert H and Florence C Lister, is an excellent source of information about the prehistory of the Southwest and the archaeological sites of the national parks and monuments of this area.
## THE SPANIARDS ARRIVE
Francisco Vasquez de Coronado led the first major expedition into North America in 1540. It included 300 soldiers, hundreds of Native American guides and herds of livestock. It also marked the first major violence between Spanish explorers and the native people.
The expedition's goal was the fabled, immensely rich Seven Cities of Cibola. For two years, they traveled through what is now Arizona, New Mexico and as far east as Kansas, but instead of gold and precious gems, the expedition found adobe pueblos, which they violently commandeered. During the Spaniards' first few years in northern New Mexico, they tried to subdue the Pueblos, resulting in much bloodshed. The fighting started in Acoma Pueblo, in today's New Mexico, when a Spanish contingent of 30 men led by one of Onate's nephews demanded tax payment in the form of food. The Acoma Indians responded by killing him and about half of his force. Onate retaliated with greater severity. Relations with the Native Americans, poor harvests, harsh weather and accusations of Onate's cruelty led to many desertions among the colonizers. By 1608, Onate had been recalled to Mexico. A new governor, Pedro de Peralta, was sent north to found a new capital in 1609 – Santa Fe remains the capital of New Mexico today, the oldest capital in what is now the USA.
In an attempt to link Santa Fe with the newly established port of San Francisco and to avoid Native American raids, small groups of explorers pressed into what is now Utah but were turned back by the rugged and arid terrain. The 1776 Dominguez-Escalante expedition was the first to survey Utah, but no attempt was made to settle there until the arrival of the Mormons in the 19th century.
In addition to armed conflict, Europeans introduced smallpox, measles and typhus, to which the Native Americans had no resistance, into the Southwest. Upward of half of the Pueblo populations were decimated by these diseases, shattering cultures and trade routes and proving a destructive force that far outstripped combat.
Twenty-year-old artist and vagabond Everett Ruess explored southern Utah and the Four Corners region in the early 1930s. He disappeared under mysterious circumstances outside of Escalante in November 1934. Read his evocative letters in the book Everett Ruess: A Vagabond for Beauty.
## THE LONG WALK & APACHE CONflICTS
For decades, US forces pushed west across the continent, killing or forcibly moving whole tribes of Native Americans who were in their way. The most widely known incident is the forceful relocation of many Navajo in 1864. US forces, led by Kit Carson, destroyed Navajo fields, orchards and houses, and forced the people into surrendering or withdrawing into remote parts of Canyon de Chelly in modern-day Arizona. Eventually starvation forced them out. About 9000 Navajo were rounded up and marched 400 miles east to a camp at Bosque Redondo, near Fort Sumner in New Mexico. Hundreds of Native Americans died from sickness, starvation or gunshot wounds along the way. The Navajo call this 'The Long Walk.'
The last serious conflicts were between US troops and the Apache. This was partly because raiding was the essential path to manhood for the Apache. As US forces and settlers moved into Apache land, they became obvious targets for the raids that were part of the Apache way of life. These continued under the leadership of Mangas Coloradas, Cochise, Victorio and, finally, Geronimo, who surrendered in 1886 after being promised that he and the Apache would be imprisoned for two years and then allowed to return to their homeland. As with many promises made during these years, this one, too, was broken.
Even after the wars were over, Native Americans continued to be treated like second-class citizens for many decades. Non–Native Americans used legal loopholes and technicalities to take over reservation land. Many children were removed from reservations and shipped off to boarding schools where they were taught in English and punished for speaking their own languages or behaving 'like Indians' – this practice continued into the 1930s.
From Geronimo to Zane Grey and from historical structures to Native American sites, www.arizonaheritagetraveler.org lives up to its tagline: 'Come for the scenery, stay for the stories.'
## WESTWARD HO
Nineteenth-century Southwest history is strongly linked to transportation development. During early territorial days, movement of goods and people from the East to the Southwest was very slow. Horses, mule trains and stagecoaches represented state-of-the-art transportation at the time. Major routes included the Santa Fe Trail and the Old Spanish Trail, which ran from Santa Fe into central Utah and across Nevada to Los Angeles, CA. Regular stagecoach services along the Santa Fe Trail began in 1849; the Mormon Trail reached Salt Lake City in 1847.
The arrival of more people and resources via the railroad led to further land exploration and the frequent discovery of mineral deposits. Many mining towns were founded in the 1870s and 1880s; some are now ghost towns, while others, like Tombstone, Arizona, and Silver City, New Mexico, remain active.
The cry 'Geronimo!' became popular for skydivers after a group of US Army paratroopers training in 1940 saw the movie Geronimo (1939) one night, then began shouting the great warrior's name for courage during their jumps.
## THE WILD WEST
Romanticized tales of gunslingers, cattle rustlers, outlaws and train robbers fuel Wild West legends. Good and bad guys were designations in flux –a tough outlaw in one state became a popular sheriffin another. And gunfights were more frequently the result of mundane political struggles in emerging towns than storied blood feuds. New mining towns mushroomed overnight, playing host to rowdy saloons and bordellos where miners would come to brawl, drink, gamble and be fleeced.
Legendary figures Billy the Kid and SheriffPat Garrett, both involved in the infamous Lincoln County War (Click here), were active in the late 1870s. Billy the Kid reputedly shot and killed more than 20 men in a brief career as a gunslinger – he himself was shot and killed by Garrett at the tender age of 21. In 1881, Wyatt Earp, along with his brothers Virgil and Morgan, and Doc Holliday, shot dead Billy Clanton and the McLaury brothers in a blazing gunfight at the OK Corral in Tombstone, Arizona – the showdown took less than a minute. Both sides accused the other of cattle rustling, but the real story will never be known.
Butch Cassidy and the Sundance Kid (Click here) once roamed much of Utah. Cassidy, a Mormon, robbed banks and trains with his Wild Bunch gang during the 1890s but never killed anyone.
### TOP FIVE OLD WEST SITES
» OK Corral, Tombstone, AZ Home of the famous 1881 gunfight, with the Earps and Doc Holliday facing Billy Clanton and the McLaury brothers.
» Lincoln, NM Shooting grounds of Billy the Kid; he left a still-visible bullet hole in the courthouse wall during a successful escape.
» Jerome, AZ Once known as the 'wickedest town in the old West,' it brimmed with brothels and saloons; now known for ghosts.
» Virginia City, NV Where the silver-laden Comstock Lode was struck; it's now a national historic landmark.
» Silverton, CO Old miners' spirit and railroad history with a historical downtown.
The late environ-mentalist and essayist Edward Abbey wrote that the canyon country of the Colorado Plateau once had a 'living heart' – Glen Canyon, now drowned beneath Lake Powell.
## DEPRESSION, WAR & RECOVERY
While the first half of the 20th century saw much of the USA in a major depression, the Southwest remained relatively prosperous during the Dust Bowl days.
Las Vegas came on to the scene after the completion of a railroad linking Salt Lake City and Los Angeles in 1902. It grew during the despair of the '20s and reached its first golden peak (the second came at the turn of the century) during the fabulous '50s, when mob money ran the city and all that glittered really was gold.
During the Depression, the region benefited from a number of federal employment projects, and WWII rejuvenated a demand for metals mined in the Southwest. In addition, production facilities were located in New Mexico and Arizona to protect those states from the vulnerability of attack. Migrating defense workers precipitated population booms and urbanization, which was mirrored elsewhere in the Southwest.
### GUNFIGHT AT THE OK CORRAL
Considering it's the most famous shoot-out in the history of the Wild West, we know pitifully little of what really happened on October 26, 1881, We know that Ike and Billy Clanton and their cohorts Frank and Tom McLaury belonged to a loose association of rustlers and thieves called the Cowboys. Wyatt Earp was an on-again-off-again lawman with one heck of a mustache, who was serving as a temporary deputy to his brother Virgil, Tombstone's city marshal. Their other brother, Morgan, was also a deputy. Doc Holliday, a dentist, was their good buddy. Neither Wyatt nor Doc was squeaky-clean.
Long-simmering bad blood between the Earp group and the Cowboys began to boil over just before the shoot-out. Earlier that month, Frank McLaury had threatened to kill all of the Earps. On the day of the shoot-out, the Cowboys had come to Tombstone and were apparently in violation of the law requiring them to check their weapons. Virgil was the only one of these gunslingers who wasn't itching for a showdown, preferring to keep the peace. But the situation got out of hand. As the men confronted each other on the street, shots rang out. According to lore, Wyatt shot Frank McLaury at the same time Billy Clanton shot at Wyatt. During this first exchange, Frank was hit but didn't go down and Wyatt escaped unscathed. After about 30 seconds, it was all over. Tom had been felled by the sawn-offshotgun wielded by Doc, Frank was hit again, and Billy Clanton was dropped by a shot to the chest. All three were dead. Doc had been grazed in the hip, Virgil in the calf and Morgan was hit in the back. Wyatt was untouched.
Wyatt and Doc were charged with murder but exonerated, although questions remained about who was really guilty. Soon after, a full-scale vendetta broke out between the Earps and Cowboys. Morgan was shot and killed; Virgil was attacked, lost the use of his left arm, and fled to Tucson. Wyatt and Doc, after doing some damage of their own to the Cowboy clan, moved up to Colorado, each going his own way.
The struggle for an adequate supply of water for the growing desert population marked the early years of the 20th century, resulting in federally funded dam projects such as the 1936 Hoover Dam and, in 1963, Arizona's Glen Canyon Dam and Lake Powell. Water supply continues to be a key challenge to life in this region, with 2001-02 the driest year on record. For more information, see Click here.
ANASAZI Anasazi, a Navajo word meaning 'ancient enemy,' is a term to which many modern Pueblo Indians object; it's no longer used.
## THE ATOMIC AGE
In 1943, Los Alamos, then a boys school perched on a 7400ft mesa, was chosen as the top-secret headquarters of the Manhattan Project, the code name for the research and development of the atomic bomb. The 772-acre site, accessed by two dirt roads, had no gas or oil lines and only one wire service, and it was surrounded by forest.
Isolation and security marked every aspect of life on 'the hill.' Scientists, their spouses, army members providing security, and locals serving as domestic help and manual laborers lived together in a makeshift community. They were surrounded by guards and barbed wire and unknown even to nearby Santa Fe; the residents' postal address was simply 'Box 1663, Santa Fe.'
Not only was resident movement restricted and mail censored, there was no outside contact by radio or telephone. Perhaps even more unsettling, most employee-residents had no idea why they were living in Los Alamos. Knowledge was on a 'need to know' basis; everyone knew only as much as their job required.
In just under two years, Los Alamos scientists successfully detonated the first atomic bomb at New Mexico's Trinity site, now White Sands Missile Range.
After the US detonated the atomic bomb in Japan, the secret city of Los Alamos was exposed to the public and its residents finally understood why they were there. The city continued to be clothed in secrecy, however, until 1957 when restrictions on visiting were lifted. Today, the lab is still the town's backbone, and a tourist industry embraces the town's atomic history by selling T-shirts featuring exploding bombs and bottles of La Bomba wine.
Some of the original scientists disagreed with the use of the bomb in warfare and signed a petition against it – beginning the love/hate relationship with nuclear development still in evidence in the Southwest today. Controversies continue over the locations of nuclear power plants and transportation, and disposal of nuclear waste, notably at Yucca Mountain, 90 miles from Las Vegas.
TIMELINE
AD 100
The region's dominant indigenous cultures emerge. The Hohokam settle in the desert, the Mogollon in the mountains and valleys and Ancestral Puebloans build cliff dwellings around the Four Corners.
1300s
The entire civilization of Ancestral Puebloans living in Mesa Verde, CO, leaves behind a sophisticated city of cliffdwellings, creating one of history's most enduring unsolved mysteries.
1598
A large force of Spanish explorers, led by Don Juan de Onate, stops near present-day El Paso, TX, and declares the land to the north New Mexico for Spain.
1609
Santa Fe, America's oldest capital city, is founded. The Palace of Governors is the only remaining 17th-century structure; the rest of Santa Fe was destroyed by a 1914 fire.
1682
During the Pueblo Revolt, northern New Mexico Pueblos drive out the Spanish after the latter's bloody campaign to destroy Puebloan kivas and ceremonial objects.
1846-48
The battle for the West is waged with the p>Mexican–American War. The Treaty of Guadalupe ends the fighting, and the US annexes most of Arizona and New Mexico.
1847
Mormons fleeing religious persecution arrive in Salt Lake City by wagon train; over the next 20 years more than 70,000 Mormons will escape to Utah via the Mormon Pioneer Trail.
1849
A regular stagecoach service starts along the Santa Fe Trail. The 900-mile trail will serve as the country's main shipping route until the arrival of the railroad 60 years later.
1864
Kit Carson captures
9000 Navajo and forces them to walk 400 miles to a camp near Fort Sumner. Hundreds of Native Americans die along
'The Long Walk.'
1869
One-armed Civil War veteran John Wesley
Powell leads the first Colorado River descent, a grueling 1000-mile expedition through the Grand Canyon's rapids that kills half of his men.
1881
In 1881, Wyatt Earp, along with his brothers Virgil and Morgan, and Doc Holliday, kill Billy Clanton and the McLaury brothers during the OK Corral shootout in Tombstone, AZ.
1919
The Grand Canyon becomes the USA's 15th national park. Only 44,173 people visit the park that year, compared to 4.4 million in 2010.
1931
Nevada legalizes gambling and drops the divorce residency requirement to six weeks; this, along with legalized prostitution and championship boxing, carries the state through the Great Depression.
1938
Route 66 becomes the first cross-country highway to be completely paved, including more than 750 miles across Arizona and New Mexico.
1943
High in the northern New Mexican desert, Los Alamos is chosen as the headquarters of the Manhattan Project, the code name for the research and development of the atomic bomb.
1945
The first atomic bomb is detonated in a desolate desert area in southern New Mexico that is now part of the White Sands Missile Range.
1946
The opening of the glitzy Flamingo casino in Vegas kicks offa building spree. Sin City reaches its first golden peak in the '50s.
1947
An unidentified object falls in the desert near Roswell. The government first calls it a crashed disk, but the next day calls it a weather balloon and closes offthe area.
1950
A radio game show host challenges any town to name itself after the show. Tiny Hot Springs, NM accepts the challenge and renames itself Truth or Consequences.
1957
Los Alamos opens its doors to ordinary people for the first time. The city was first exposed to the public after the atomic bomb was dropped on Japan.
1963
The controversial Glen Canyon Dam is finished and Lake Powell begins, eventually covering ancestral Indian sites and rock formations but creating 1960 miles of shoreline and a boater fantasyland.
1973
The debut of the MGM Grand in 1973 signals the dawn of the era of corporate-owned 'megaresorts' and sparks a building bonanza along the Strip that's still going on today.
1996
President Bill Clinton establishes Utah's Grand Staircase-Escalante National Monument, which is unique in allowing some uses (such as hunting and grazing by permit) usually banned in national parks.
2002
Salt Lake City hosts the Winter Olympics and becomes the most populated place to ever hold the winter games, as well as the first place women competed in bobsled racing.
2004
Sin City is back! Las Vegas enters its second golden heyday, hosting 37.5 million visitors, starting work on its latest 'megaresort' and becoming the number-one party destination.
2006
Warren Jeffs, leader of the Fundamentalist Church of the Latter Day Saints (FLDS) is charged with aggravated assaults of two under-age girls. He is serving a life-plus-20 years sentence.
2010
Arizona passes controversial legislation requiring police officers to request identification from anyone they suspect of being in the US illegally. Immigration-rights activists call for a boycott of the state.
2011
Jared Loughner is charged with shooting Arizona Congresswoman Gabrielle Giffords outside a Tucson grocery store. Giffords suffers a critical brain injury, six others are killed.
2012
New Mexico and Arizona celebrate 100 years of statehood with special events and commemorative stamps. Arizona is the last territory in the Lower 48 to earn statehood.
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# The Way of Life
Individuality is the cultural idiom of the Southwest. The identities of this region, centered on a trio of tribes – Anglo, Hispanic and Native American – are as vast and varied as the land that has shaped them. Whether your personal religion involves aliens, nuclear fission, slot machines, art or peyote, there's plenty of room for you in this harsh and ruggedly beautiful chunk of America.
Although the region's culture as a whole is united by the psychology, mythology and spirituality of its harsh, arid desert landscape, the people here are a sundry assortment of characters not so easily branded. The Southwest has long drawn stout-hearted pioneers pursuing slightly different agendas than those of the average American. Mormons arrived in the mid-1800s seeking religious freedom. Cattle barons staked their claims with barbed wire and lonely ranches, luring cowboys in the process. Old mining towns like Jerome and Bisbee in Arizona were founded by fierce individualists – gamblers, mining-company executives, storekeepers and madams. When the mining industry went bust in the 20th century, boomtowns became ghost towns for a while, before a new generation of idealistic entrepreneurs transformed them into New Age art enclaves and Old West tourist towns. Scientists flocked to the empty spaces to develop and test atomic bombs and soaring rockets.
Today, these places attract folk similar to the original white pioneers – solitary, focused and self-reliant. Artists are drawn to the Southwest's clear light, cheap housing and wide, open spaces. Collectors, in turn, follow artists and gentrify towns like Santa Fe and Taos in New Mexico, Prescott in Arizona and Durango in Colorado. Near Truth or Consequences, NM, global entrepreneur Richard Branson of Virgin Galactic is fine-tuning a commercial spacecraft that will launch paying customers into space from the scrubby desert. But not all new arrivals are Type A. There are, thank goodness, the mainstream outcasts still coming to the Southwest to 'turn on, tune in and drop out.
The Phoenix Suns protested Arizona's new immigration law in 2010 by changing the team's name on their jerseys to 'Los Suns' (that's Spanglish) for one game.
For years, these disparate individuals managed to get along with little strife. In recent years, however, the state and federal governments' very visible efforts to stop illegal immigration have destroyed the kumbaya vibe, at least in Southern Arizona. These efforts include Arizona's controversial SB 1070 – a law that requires police officers to ask for ID from anyone they suspect of being in the country illegally – and a simultaneous surge in federal border patrol agents and checkpoints. The anti-immigration rhetoric isn't common in day-today conversation, but heightened press coverage of the most vitriolic comments, coupled with the checkpoints and ever-present border patrol vehicles, do cast a pall over the otherwise sunny landscape. Fortunately, outside southern Arizona, other regions of the Southwest have retained the live-and-let-live philosophy.
## REGIONAL IDENTITY
For the most part, residents of the Southwest are more easygoing than their counterparts on the East and West Coasts. They tend to be friendlier too. Even at glitzy restaurants in the biggest cities (with the exception of Las Vegas), you'll see more jeans and cowboy boots than haute couture. Chat with a local at a low-key pub in Arizona or Colorado, and they'll likely tell you they're from somewhere else. They moved out here for the scenery, unpolluted air and slower pace of life. Folks in this region consider themselves environmentally friendly. Living a healthy lifestyle is important, and many residents like to hike, mountain bike, ski and ride the rapids. They might have money, but you won't necessarily know it. It's sort of a faux pas to flaunt your wealth.
For first-person accounts and opinion pieces about key events in Native American history, visit www.digitalhistory.uh.edu, an online 'digital' textbook compiled by the University of Houston.
Las Vegas is a different story. But a place where you can go from Paris to Egypt in less than 10 minutes can't possibly play by the rules. This is a town that's hot and knows it. The blockbuster comedy _The Hangover_ stoked its image as party central. The identity here is also a little different – there's an energy to Sin City not found elsewhere in the region. People from Vegas don't say they're from the Southwest, or even from Nevada. They say they're from Las Vegas, dammit.
If Vegas is all about flaunting one's youthful beauty, then Arizona may just be its polar opposite. In the last decade, Arizona has done a great job at competing with Florida for the retiree-paradise award – the warm weather, dry air, abundant sunshine and lots and lots of space draw more seniors with each year. You'll see villages of RV parks surrounding Phoenix and Tucson and early-bird specials are the plat du jour at many restaurants.
### WHAT'S IN A NAME?
Though the stereotypes that too often accompany racial labels are largely ignored in the Southwest, it's still a challenge for publishers to figure out the most accurate (and politically correct) term for various ethnic groups. Here's the rundown on our terminology:
»Native American After introducing themselves to one very confused Christopher Columbus, the original Americans were labeled 'Indians.' The name stuck, and 500 years later folks from Mumbai are still trying to explain that, no, they don't speak a word of Tewa. 'Native American' is recommended by every major news organization, but in the Southwest most tribal members remain comfortable with the term 'Indian.' Both terms are used in this book. However, the best term to use is always each tribe's specific name, though this can also get complicated. The name 'Navajo,' for instance, was bestowed by the Spanish; in Athabascan, Navajo refer to themselves as Diné. What to do? Simply try your best, and if corrected, respect each person's preference.
»Anglo Though 'Caucasian' is the preferred moniker (even if their ancestors hailed from nowhere near the Caucuses) and 'white' is the broadest and most useful word for European Americans, in this region the label for non-Iberian Europeans is 'Anglo' ('of England'). Even English speakers of Norwegian-Polish ancestry are Anglo around here, so get used to it.
»Hispanic The Associated Press prefers hyphens: 'Mexican-American,' 'Venezuelan- American' – and are Spanish-speaking US citizens more properly 'American- Americans'? Obviously, it's easier, if less precise, to use 'Latino' to describe people hailing from the Spanish-speaking Americas. Then add to that list 'Chicano,' 'Raza' and 'Hispano,' a de-anglicized term currently gaining popularity, and everyone's confused. But, because this region was part of Spain for 225 years and Mexico for only 25, and many folks can trace an unbroken ancestry back to Spain, 'Hispanic' ('of Spain') is the term used throughout this state and book, sprinkled with 'Spanish' and all the rest.
Colorado, Arizona and New Mexico all have large Native American and Hispanic populations, and these residents take pride in maintaining their cultural identities through preserved traditions and oral history lessons.
### POLYGAMY & THE MORMON CHURCH LISA DUNFORD
Throughout its history, Utah has been a predominately Mormon state; more than 60% of the current population has church affiliation. But as late church president Gordon Hinckley was fond of saying, the Church of Jesus Christ of Latter-Day Saints (or LDS, as the modern Mormon faith is known) has nothing to do with those practicing polygamy today.
Members of the LDS believe the Bible is the Word of God and that the _Book of Mormon_ is 'another testament of Jesus Christ,' as revealed to LDS church founder Joseph Smith. It was in the 1820s that the angel Moroni is said to have led Smith to the golden plates containing the story of a family's exodus from Jerusalem in 600 BC, and their subsequent lives, prophesies, trials, wars and visitations by Jesus Christ in the new world (Central America). Throughout his life he is said to have received revelations from God, including the 1843 visitation that revealed the righteous path of plural marriage to the prophet. Polygamy was formally established as church doctrine in 1852 by the second president, Brigham Young.
For all the impact plural marriage has had, it seems odd that the practice was officially endorsed for less than 40 years. By the 1880s US federal laws had made polygamy a crime. With the threatened seizure of church assets looming, president Wilford Woodruff received spiritual guidance and abdicated polygamy in 1890.
Today the church has more than 14 million members and a missionary outreach that spans the globe. But what happened to polygamy? Well, fundamentalist sects broke off to form their own churches almost immediately; they continue to practice today. The official Mormon church disavows any relationship to these fundamentalists, and shows every evidence of being embarrassed by the past.
Estimates for the number of people still practicing polygamy range as high as 50,000 in Utah. Some you'd never recognize; they're just large families. Others belong to isolated, cultlike groups such as the FLDS in Hildale-Colorado City on the Utah-Arizona border, which have distinct styles of dress and hair. Some of these sects have become notorious for crimes committed by some of their members.
Though polygamy itself is illegal, prosecution is rare. Without a confession or videotaped evidence, the case is hard to prove. Men typically marry only their first wife legally (subsequent wives are considered single mothers by the state, and are therefore entitled to more welfare). The larger Utah populace is deeply ambivalent about polygamy. Tens, maybe hundreds, of thousands of them wouldn't exist but for the historic practice, including me. My great-great-great grandmother, Lucy Bigelow, was a wife of Brigham Young.
## LIFESTYLE
In a region of such diversity and size, it's impossible to describe the 'typical' Southwestern home or family. What lifestyle commonalities, after all, can be seen in the New Age mystics of Sedona, the businesspeople, lounge singers and casino workers of Las Vegas and the Mormon faithful of Salt Lake City? Half the fun of touring the Southwest is comparing and contrasting all these different identities.
Utah's heavily Mormon population stresses traditional family values; drinking, smoking and premarital sex are frowned upon. You won't see much fast fashion or hear much cursing here.
Family and religion are also core values for Native Americans and Hispanics throughout the region. For the Hopi, tribal dances are such sacred events they are mostly closed to outsiders. And although many Native Americans and Hispanics are now living in urban areas, working as professionals, large family gatherings and traditional customs are still important facets of daily life. See Click here for more on contemporary Native American life.
The book _Bringing Down the House_ is a fascinating (and true) story of MIT students who broke the bank in Vegas by counting cards in the mid-'90s. The book was then made into the film 21 (2008).
Because of its favorable weather and boundless possibilities for outdoor adventures, much of the Southwest is popular with transplants from the East and West Coasts. In cities like Santa Fe, Telluride, Las Vegas, Tucson and Flagstaff, you'll find a blend of students, artists, wealthy retirees, celebrity wannabes and adventure junkies. In urban centers throughout the region (with the exception of Utah) many people consider themselves 'spiritual' rather than religious, and forgo church for Sunday brunch. Women work the same hours as men, and many children attend daycare.
With the exception of Mormon Utah, attitudes toward gays and lesbians in the Southwest are generally open, especially in major cities like Las Vegas, Santa Fe and Phoenix.
## SPORTS
Professional sports teams are based in Phoenix and Salt Lake City. The Arizona Diamondbacks of Phoenix play major league baseball from April through September; the only Southwestern major league football team, the Arizona Cardinals, play from September through December. Basketball (men play November through April) is more competitive; you can watch hoops with Salt Lake City's Utah Jazz (men) or the Phoenix Suns (men). The women's pro basketball team, Phoenix Mercury, plays June through early September.
Because pro tickets are hard to get, you'll have a better rim shot with college sports. Albuquerque teams across the board are quite popular. The University of Arizona Wildcats consistently place among the best basketball teams in the nation.
Several major league baseball teams (like the Chicago White Sox) migrate from the cold, wintry north every February and March for training seasons in warmer Arizona. They play in what is aptly referred to as the Cactus League.
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# Native American Southwest
###### Jeff Campbell
The Southwest is sometimes called 'Indian Country,' but this nickname fails to capture the diversity of the tribes that make the region their home. From the Apache to the Zuni, each tribe maintains distinctions of law, language, religion, history and custom that turn the Southwest's incomparable, seemingly borderless painted desert into a kaleidoscopic league of nations.
## THE PEOPLE
The cultural traditions and fundamental belief systems of the Southwest's tribes reflect their age-old relationship to the land, the water, the sky and the creatures that inhabit those elements. This relationship is reflected in their crafts, their dances and their architecture.
Native Americans today live incredibly diverse lives, as they inherit a legacy left by both their ancestors and the cultures that invaded from outside. Culturally, tribes grapple with dilemmas about how to prosper in contemporary America while protecting their traditions from erosion and their lands from further exploitation, and how to lift their people from poverty while maintaining their sense of identity and the sacred.
### Apache
The Southwest has three major Apache reservations: New Mexico's Jicarilla Apache Reservation and Arizona's San Carlos Apache Reservation and Fort Apache Reservation, home to the White Mountain Apache Tribe. All the Apache tribes descend from Athabascans who migrated from Canada around 1400. They were nomadic hunter-gatherers who became warlike raiders, particularly of Pueblo tribes and European settlements, and they fiercely resisted relocation to reservations.
The most famous Apache is Geronimo, a Chiricahua Apache who resisted the American takeover of Indian lands until he was finally subdued by the US Army with the help of White Mountain Apache scouts.
### Havasupai
The Havasupai Reservation abuts Arizona's Grand Canyon National Park beneath the Canyon's south rim. The tribe's one village, Supai, can only be reached by an 8-mile hike or a mule or helicopter ride from road's end at Hualapai Hilltop.
Havasupai (hah-vah- _soo_ -pie) means 'people of the blue-green water,' and tribal life has always been dominated by the Havasu Creek tributary of the Colorado River. Reliable water meant the ability to irrigate fields, which led to a season-based village lifestyle. The deep Havasu Canyon also protected them from others; this extremely peaceful people basically avoided Western contact until the 1800s. Today, the tribe relies on tourism, and Havasu Canyon's gorgeous waterfalls draw a steady stream of visitors. The tribe is related to the Hualapai.
Native American Reservations
Reservations
1 Acoma Pueblo C2
2 Cochiti Pueblo D2
3 Isleta Pueblo D2
4 Jemez Pueblo D2
5 Kaibab-Paiute Reservation A1
6 Laguna Pueblo D2
7 Nambé Pueblo C2
8 Ohkay Owingeh (San Juan) Pueblo D2
9 Picuris Pueblo D2
10 Pojoaque Pueblo D2
11 San Felipe Pueblo D2
12 San Ildefonso Pueblo D2
13 Sandia Pueblo D2
14 Santa Ana Pueblo D2
15 Santa Clara Pueblo D2
16 Santo Domingo Pueblo D2
17 Southern Ute Reservation C1
18 Taos Pueblo D1
19 Tesuque Pueblo D2
20 Ute Mountain Reservation C1
21 Zia Pueblo D2
### Hopi
The Hopi Reservation occupies more than 1.5 million acres in the middle of the Navajo Reservation. Most Hopi live in 11 villages at the base and on top of three mesas jutting from the main Black Mesa; Old Oraibi, on Third Mesa, is considered (along with Acoma Pueblo) the continent's oldest continuously inhabited settlement. Like all Pueblo peoples, the Hopi are descended from the Ancestral Puebloans (formerly known as Anasazi).
The US population in 2010 was 309 million. Native Americans/ Native Alaskans represent 0.9% of the total, which is about 2.78 million people.
Hopi ( _ho_ -pee) translates as 'peaceful ones' or 'peaceful person.' The Hopi are renowned for their traditional and deeply spiritual lifestyle. They practice an unusual, near-miraculous technique of 'dry farming'; they don't plow, but plant seeds in 'wind breaks', which protect the plants from blowing sand, and natural water catchments. Their main crop has always been corn (which is central to their creation story).
Hopi ceremonial life is complex and intensely private, and extends into all aspects of daily living. Following the 'Hopi Way' is considered essential to bringing the life-giving rains, but the Hopi also believe it fosters the well-being of the entire human race. Each person's role is determined by their clan, which is matrilineal. Even among themselves, the Hopi keep certain traditions of their individual clans private.
The Hopi are skilled artisans; they are famous for pottery, coiled baskets and silverwork, as well as for their ceremonial kachina dolls.
### Hualapai
The Hualapai Reservation occupies around a million acres along 108 miles of the Grand Canyon's south rim. Hualapai ( _wah_ -lah-pie) means 'people of the tall pines'; because this section of the Grand Canyon was not readily farmable, the Hualapai were originally seminomadic, gathering wild plants and hunting small game.
Today, forestry, cattle ranching, farming and tourism are the economic mainstays. The tribal headquarters are in Peach Springs, AZ, which was the inspiration for 'Radiator Springs' in the animated movie Cars. Hunting, fishing and rafting are the reservation's prime draws, but the Hualapai have recently added a unique tourist attraction: the Grand Canyon's Skywalk glass bridge that juts over a side canyon 4000ft (1,220m) below your feet.
_The People_ by Stephen Trimble is as comprehensive and intimate a portrait of Southwest native peoples as you'd hope to find, bursting with Native American voices and beautiful photos.
### Navajo
The Navajo Reservation, also called the Navajo Nation, is by far the largest and most populous in the US, covering 17.5 million acres (over 27,000 sq miles) in Arizona and parts of New Mexico and Utah. Using a Tewa word, the Spanish dubbed them 'Navajos' to distinguish them from their kin the Apache, but Navajo ( _nah_ -vuh-ho) call themselves the Diné (dee- _nay_ ; 'the people') and their land Dinétah.
### HOPI KACHINAS
In the Hopi religion, maintaining balance and harmony between the spirit world and our 'fourth world' is crucial, and the spirit messengers called kachinas (also spelled katsinas) play a central role. These supernatural beings are spirits of deities, animals and even deceased clan members, and they can bring rain, influence the weather, help in daily tasks and punish violators of tribal laws. They are said to live atop Southwest mountains; on the winter solstice they travel to the Hopi Pueblos, where they reside until the summer solstice.
In a series of kachina ceremonies and festivals, masked dancers impersonate the kachinas; during these rituals, it is believed the dancers are inhabited by and become the kachinas. There are hundreds of kachina spirits: some are kindly, some fearsome and dangerous, and the elaborate, fantastical costumes dancers wear evoke the mystery and religious awe of these beings. In the 1990s, to keep these sacred ceremonies from becoming trivialized as tourist spectacles, the Hopi closed most to the public.
Kachina dolls ( _tithu_ in Hopi) are brightly painted, carved wooden figures traditionally given to young Hopi girls during certain kachina festivals. The religious icons become treasured family heirlooms. The Hopi now carve some as art meant for the general public.
Nationwide, there are about 300,000 Navajo, making it the USA's second-largest tribe (after the Cherokee), and the Navajo's Athabascan tongue is the most spoken Native American language, despite its notorious complexity. In the Pacific Theater during WWII, Navajo 'code talkers' sent and received military messages in Navajo; Japan never broke the code, and the code talkers were considered essential to US victory.
For decades, traditional Navajo and Hopi have successfully thwarted US industry efforts to strip-mine sacred Big Mountain, but the fight continues. Black Mesa Indigenous Support (www.blackmesais.org) tells their story.
Like the Apache, the Navajo were feared nomads and warriors who both traded with and raided the Pueblos and who fought settlers and the US military. They also borrowed generously from other traditions: they acquired sheep and horses from the Spanish, learned pottery and weaving from the Pueblos and picked up silversmithing from Mexico. For more details about Navajo history, see Click here. Today, the Navajo are renowned for their woven rugs, pottery and inlaid silver jewelry. Their intricate sandpainting is used in healing ceremonies.
The reservation has significant mineral reserves – Black Mesa, for instance, contains the USA's largest coal deposit, perhaps 21 billion tons – and modern-day mining of coal, oil, gas and uranium has been an important, and controversial, economic resource. Mining has depleted the region's aquifer, contaminated water supplies (leading, some claim, to high cancer rates), and impacted sacred places.
Tribal headquarters are in Window Rock, AZ, and the reservation boasts numerous cultural and natural attractions, including Monument Valley, Canyon de Chelly National Monument, Navajo National Monument and Antelope Canyon.
### Pueblo
New Mexico contains 19 Pueblo reservations. Four reservations lead west from Albuquerque – Isleta, Laguna, Acoma and Zuni – and 15 Pueblos fill the Rio Grande Valley between Albuquerque and Taos: Sandia, San Felipe, Santa Ana, Zia, Jemez, Kewa Pueblo (or Santo Domingo), Cochiti, San Ildefonso, Pojoaque, Nambé, Tesuque, Santa Clara, Ohkay Owingeh (or San Juan), Picuris and Taos. For more information about the Pueblos, see www.indianpueblo.org.
These tribes are as different as they are alike. Nevertheless, the term 'Pueblo' (Spanish for 'village') is a convenient shorthand for what these tribes share: all are believed to be descended from the Ancestral Puebloans and to have inherited their architectural style and their agrarian, village-based life – often atop mesas.
Pueblos are unique among American Indians. These adobe structures can have up to five levels, connected by ladders, and are built with varying combinations of mud bricks, stones, logs and plaster. In the central plaza of each pueblo is a kiva, an underground ceremonial chamber that connects to the spirit world.
With a legacy of missionary activity, Pueblos tend to have Catholic churches, and many Pueblo Indians now hold both Christian and native religious beliefs. This unmerged, unconflicted duality is a hallmark of much of Pueblo modern life.
N Scott Momaday's Pulitzer Prize–winning _House Made of Dawn_ (1968), about a Pueblo youth, launched a wave of Native American literature.
### Other Tribes: Paiute, Ute & Tohono O'odham
#### Palute
The Kaibab-Paiute Reservation is on the Arizona–Utah border. The Kaibab ( _cay_ -bob) are a band of Southern Paiute ( _pie_ -oot) who migrated to the Colorado Plateau around 1100. They were peaceful huntergatherers who moved frequently across the arid, remote region, basing their movements on seasonal agricultural needs and animal migrations. The tribe's lifestyle changed drastically in the 1850s when Mormons began settling the region, overtaking the land for their farms and livestock. The Kaibab-Paiute Reservation, located on the Arizona Strip west of Fredonia, is next to a vitally important regional spring, one that was also important to the Mormons. Today, near the spring, their reservation runs a public campground and contains Pipe Spring National Monument; the Kaibab-Paiute worked with the National Park Service to create rich displays about Native American life. The tribe is renowned for its basketmaking.
The Indian Arts and Crafts Board (www.doi.gov /iacb) publishes a directory of Native American– owned businesses, certifies expensive craft items (always ask to see a certificate) and punishes deceptive merchants.
#### Ute
Along with the Navajo and Apache tribes, Utes helped drive the Ancestral Puebloans from the region in the 1200s. By the time of European contact, seven Ute tribes occupied most of present-day Colorado and Utah (named for the Utes). In the 16th century, Utes eagerly adopted the horse and became nomadic buff alo hunters and livestock raiders.
There are three main Ute reservations. With over 4.5 million acres, the Uintah and Ouray Reservation in northeastern Utah is the second largest in the US. Ranching and oil and gas mining are the tribe's main industries. The Ute Mountain Utes (who call themselves the Weeminuche) lead guided tours of Mancos Canyon in Ute Mountain Tribal Park; their reser vation abuts Mesa Verde National Park in southwestern Colorado. The Southern Ute Reservation relies in part on casinos for income.
#### Tohono O'odham
The Tohono O'odham Reservation is the largest of four reservations that make up the Tohono O'odham Nation in the Sonoran Desert in southern Arizona. Tohono O'odham ( _to_ -ho-no oh- _oh_ -dum) means 'desert people.' The tribe was originally seminomadic, moving between the desert and the mountains seasonally. They were famous for their calendar sticks, which were carved to mark important dates and events, and they remain well known for their baskets and pottery. Today, the tribe runs two casinos and the Mission San Xavier del Bac in southern Arizona.
## Arts
Native American art nearly always contains ceremonial purpose and religious significance; the patterns and symbols are woven with spiritual meaning that provides an intimate window into the heart of Southwest people. By purchasing arts from Native Americans themselves, visitors have a direct, positive impact on tribal economies, which depend in part on tourist dollars.
### LEGAL STATUS
Although Arizona's major tribes are 'sovereign nations' and have significant powers to run their reservations as they like, their authority – and its limitations – is granted by Congress. While they can make many of their own laws, plenty of federal laws apply on reservations, too. The tribes don't legally own their reservations – it's public land held in trust by the federal government, which has a responsibility to administer it in a way that's beneficial for the tribes. Enter the Bureau of Indian Affairs.
While Indians living on reservations have officially been American citizens since 1924, can vote in state and national elections, and serve heroically in the armed forces, they are not covered by the Bill of Rights. Instead, there's the Indian Civil Rights Act of 1968, which does grant reservation dwellers many of the same protections found in the Constitution, but not all. This is not an entirely bad thing. In some ways, it allows tribal governments to do things that federal and state government can't, which helps them create a system more attuned to their culture.
### Pottery & Basketry
Pretty much every Southwest tribe has pottery and/or basketry traditions. Originally, each tribe and even individual families maintained distinct styles, but modern potters and basketmakers readily mix, borrow and reinterpret classic designs and methods.
Pueblo pottery is perhaps most acclaimed of all. Typically, local clay determines the color, so that Zia pottery is red, Acoma white, Hopi yellow, Cochiti black and so on. Santa Clara is famous for its carved relief designs, and San Ildefonso for its black-on-black style, which was revived by world-famous potter Maria Martinez. The Navajo and Ute Mountain Utes also produce well-regarded pottery.
Pottery is nearly synonymous with village life, while more portable baskets were often preferred by nomadic peoples. Among the tribes who stand out for their exquisite basketry are the Jicarilla Apache (whose name means basketmaker), the Kaibab-Paiute, the Hualapai and the Tohono O'odham. Hopi coiled baskets, with their vivid patterns and kachina iconography, are also notable.
To learn about Navajo rugs, visit www.gonavajo.com. To see traditional weaving demonstrations, visit the Hubbell Trading Post in Ganado, AZ.
### Navajo Weaving
According to Navajo legend, Spider Woman taught humans how to weave, and she seems embodied today in the iconic sight of Navajo women patiently shuttling handspun wool on weblike looms, creating the Navajo's legendary rugs (originally blankets), so tight they held water. Preparation of the wool and sometimes the dyes is still done by hand, and finishing a rug takes months (occasionally years).
Authentic Navajo rugs are expensive, and justifiably so, ranging from hundreds to thousands of dollars. They are not average souvenirs but artworks that will last a lifetime, whether displayed on the wall or the floor. Take time to research, even a little, so you recognize when quality matches price.
### Silver & Turquoise
Jewelry Jewelry using stones and shells has always been a native tradition; silverwork did not arrive until the 1800s, along with Anglo and Mexican contact. In particular, Navajo, Hopi and Zuni became renowned for combining these materials with inlaid-turquoise silver jewelry. In addition to turquoise, jewelry often features lapis, onyx, coral, carnelian and shells.
Authentic jewelry is often stamped or marked by the artisan, and items may come with an Indian Arts and Crafts Board certificate; always ask. Price may also be an indicator: a high tab doesn't guarantee authenticity, but an absurdly low one probably signals trickery. A crash course can be had at the August Santa Fe Indian Market.
To donate to a cause, consider Black Mesa Weavers for Life and Land (www.migrations.com), which aids traditional Diné women on the Navajo Reservation to sell and market their handmade weavings.
## Etiquette
When visiting a reservation, ask about and follow any specific rules. Almost all tribes ban alcohol, and some ban pets and restrict cameras. All require permits for camping, fishing and other activities. Tribal rules may be posted at the reservation entrance, or visit the tribal office or the reservation's website (most are listed in this book).
The other thing is attitude and manner. When you visit a reservation, you are visiting a unique culture with perhaps unfamiliar customs. Be courteous, respectful and open-minded, and don't expect locals to share every detail of their lives.
Ask First, Document Later Some tribes restrict cameras and sketching entirely; others may charge a fee, or restrict them at ceremonies or in certain areas. If you want to photograph a person or their property, ask permission; a tip may or may not be expected.
Pueblos Are Not Museums At Pueblos, the incredible adobe structures are homes. Public buildings will be signed; if a building isn't signed, assume it's private. Don't climb around. Kivas are nearly always off -limits.
Ceremonies Are Not Performances Treat ceremonies like church services; watch silently and respectfully, without talking, clapping or taking pictures, and wear modest clothing. Powwows are more informal, but remember: unless they're billed as theater, ceremonies and dances are for the tribe, not you.
Privacy and Communication Many Native Americans are happy to describe their tribe's general religious beliefs, but not always or to the same degree, and details about rituals and ceremonies are often considered private. Always ask before discussing religion and respect each person's boundaries. Also, Native Americans consider it polite to listen without comment; silent listening, given and received, is another sign of respect.
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# Geology & the Land
###### David Lukas
In the Santa Catalina Mountains outside Tucson, you can ascend from searing desert to snow-blanketed fir forests within 30 miles, the ecological equivalent of driving 2000 miles from southern Arizona to Canada. Contrasts like these, often in close proximity, make the Southwest a fascinating place to explore. While everyone thinks immediately of deserts and cacti, alpine tundra and verdant marshes are also part of the landscape.
On the evening of July 5, 2011, a mile-high dust storm with an estimated 100-mile width enveloped Phoenix after reaching speeds between 50 and 60mph. Visibility dropped to between zero and a quarter mile. There were power outages, and Phoenix International Airport temporarily closed.
The desert itself is anything but monotonous; look closely and you will discover everything from fleet-footed lizards to jewel-like wildflowers. As Southwest ecowarrior Edward Abbey wrote in _Desert Solitaire: A Season in the Wilderness_ , 'The desert is a vast world, an oceanic world, as deep in its way and complex and various as the sea.' The Southwest's four distinct desert zones, each with its own unique mix of plants and animals, are superimposed on an astonishing complex of hidden canyons and towering mountains.
## THE LAND
### Geologic History
It may be hard to imagine now, but the Southwest was once inundated by a succession of seas. There is geological evidence today of deep bays, shallow mud flats and coastal dunes. During this time North America was a young continent on the move, evolving slowly and migrating northward from the southern hemisphere over millions of years. Extremely ancient rocks (among the oldest on the planet) exposed in the deep heart of the Grand Canyon show that the region was under water two billion years ago, and younger layers of rocks in southern Utah reveal that this region was continuously or periodically under water until about 60 million years ago.
Visit www.publiclands.org for a onestop summary of recreational opportunities on governmentowned land in the Southwest, regardless of managing agency. The site also has maps, a book index, links to relevant agencies and updates on current restrictions and conditions.
At the end of the Paleozoic era (about 245 million years ago), a collision of continents into a massive landmass known as Pangaea deformed the Earth's crust and produced pressures that uplifted an ancestral Rocky Mountains. Though this early mountain range lay to the east, it formed rivers and sediment deposits that began to shape the Southwest. In fact, erosion leveled the range by 240 million years ago, with much of the sediment draining westward into what we now call Utah. Around the same time, a shallow tropical sea teeming with life, including a barrier reef that would later be sculpted into Carlsbad Caverns, covered much of southern New Mexico.
For long periods of time (between episodes of being under water), much of the Southwest may have looked like northern Egypt today: floodplains and deltas surrounded by expanses of desert. A rising chain of island mountains to the west apparently blocked the supply of wet storms, creating a desert and sand dunes that piled up thousands of feet high. Now preserved as sandstone, these dunes can be seen today in the famous Navajo sandstone cliffs of Zion National Park.
_Pages of Stone: Geology of the Grand Canyon & Plateau Country National Parks & Monuments_, by Halka and Lucy Chronic, is an excellent way to understand the Southwest's diverse landscape.
## MOUNTAINS & BASINS
This sequence of oceans and sand ended around 60 million years ago as North America underwent a dramatic separation from Europe, sliding westward over a piece of the Earth's crust known as the East Pacific plate and leaving behind an ever-widening gulf that became the Atlantic Ocean. This East Pacific plate collided with, and pushed down, the North American plate. This collision, named the Laramide Orogeny, resulted in the birth of the modern Rocky Mountains and uplifted an old basin into a highland known today as the Colorado Plateau. Fragments of the East Pacific plate also attached themselves to the leading edge of the North American plate, transforming the Southwest from a coastal area to an interior region increasingly detached from the ocean.
In contrast to the compression and collision that characterized earlier events, the Earth's crust began stretching in an east–west direction about 30 million years ago. The thinner, stretched crust of New Mexico and Texas cracked along zones of weakness called faults, resulting in a rift valley where New Mexico's Rio Grande now flows. These same forces created the stepped plateaus of northern Arizona and southern Utah.
Increased pulling in the Earth's crust between 15 and eight million years ago created a much larger region of north–south cracks in western Utah, Arizona and Nevada known as the Basin and Range province. Here, parallel cracks formed hundreds of miles of valleys and mountain ranges that fill the entire region between the Sierra Nevada and the Rocky Mountains.
During the Pleistocene glacial period, large bodies of water accumulated throughout the Southwest. Utah's Great Salt Lake is the most famous remnant of these mighty Ice Age lakes. Basins with now completely dry, salt-crusted lakebeds are especially conspicuous on a drive across Nevada.
For the past several million years the dominant force in the Southwest has probably been erosion. Not only do torrential rainstorms readily tear through soft sedimentary rocks, but the rise of the Rocky Mountains also generates large powerful rivers that wind throughout the Southwest, carving mighty canyons in their wake. Nearly all of the contemporary features in the Southwest, from arches to hoodoos, are the result of weathering and erosion.
### Geographic Make Up of the Land
The Colorado Plateau is an impressive and nearly impenetrable 130,000-sq-mile tableland lurking in the corner where Colorado, Utah, Arizona and New Mexico join. Formed in an ancient basin as a remarkably coherent body of neatly layered sedimentary rocks, the plateau has remained relatively unchanged even as the lands around it were compressed, stretched and deformed by powerful forces.
The often-used term 'slickrock' refers to the fossilized surfaces of ancient sand dunes. Pioneers named it slickrock because their metal-shoed horses and ironwheeled wagons would slip on the surface.
The most powerful indicators of the plateau's long-term stability are the distinct and unique layers of sedimentary rock stacked on top of each other, with the oldest dating back two billion years. In fact, the science of stratigraphy – the reading of Earth history through its rock layers – stemmed from work at the Grand Canyon, where an astonishing set of layers have been laid bare by the Colorado River cutting across them. Throughout the Southwest, and on the Colorado Plateau in particular, layers of sedimentary rock detail a rich history of ancient oceans, coastal mudflats and arid dunes.
All other geographic features of the Southwest seem to radiate out from the plateau. To the east, running in a north–south line from Canada to Mexico, are the Rocky Mountains, the source of the mighty Colorado River, which gathers on the mountains' high slopes and cascades across the Southwest to its mouth in the Gulf of California. East of the Rocky Mountains, the eastern third of New Mexico grades into the Llano Estacado – a local version of the vast grasslands of the Great Plains.
For an insight into how indigenous peoples used this landscape, read _Wild Plants and Native Peoples of the Four Corners_ , by William Dunmire and Gail Tierney.
In Utah, a line of mountains known collectively as the Wasatch Line bisects the state nearly in half, with the eastern half on the Colorado Plateau, and the western half in the Basin and Range province. Northern Arizona is highlighted by a spectacular set of cliffs called the Mogollon Rim that run several hundred miles to form a boundary between the Colorado Plateau to the north and the highland region of central Arizona. The mountains of central Arizona decrease in elevation as you travel into the deserts of southern Arizona.
### Landscape Features
#### Red Rock Formations
A summer thunderstorm in 1998 increased the flow of Zion's Virgin River from 200 cubic ft per second to 4500, scouring out canyon walls 40ft high at its peak flow.
The Southwest is jam-packed with one of the world's greatest concentrations of remarkable rock formations. One reason for this is that the region's many sedimentary layers are so soft that rain and erosion readily carve them into fantastic shapes. But not any old rain. It has to be hard rain that is fairly sporadic because frequent rain would wash the formations away. Between rains there have to be long arid spells that keep the eroding landmarks intact.
The range of colors on rocky landscapes in the Southwest derive from the unique mineral composition of each rock type, but most visitors to the parks are content to stand on the rim of Grand Canyon or Bryce Canyon and simply watch the breathtaking play of light on the orange and red rocks.
Arches National Park has more than 2500 sandstone arches. The opening in a rock has to measure at least 3ft in order for the formation to qualify as an arch.
This combination of color and soft rock is best seen in badlands, where the rock crumbles so easily you can actually hear the hillsides sloughing away. The result is an otherworldly landscape of rounded knolls, spires and folds painted in outrageous colors. Excellent examples can be found in Arizona's Painted Desert of Petrified Forest National Park, at Utah's Capitol Reef National Park or in the Bisti Badlands south of Farmington, New Mexico.
### CRYPTOBIOTIC CRUSTS: WATCH YOUR STEP!
Cryptobiotic crusts, also known as biological soil crusts, are living crusts that cover and protect desert soils, literally gluing sand particles together so they don't blow away. Cyanobacteria, one of the Earth's oldest life forms, start the process by extending mucous-covered filaments into dry soil. Over time these filaments and the sand particles adhering to them form a thin crust that is colonized by algae, lichen, fungi and mosses. This crust plays a significant role in desert food chains, and also stores rainwater and reduces erosion.
Unfortunately, the thin crust is easily fragmented under heavy-soled boots and tires. Once broken, the crust takes 50 to 250 years to repair itself. In its absence, winds and rains erode desert soils, and much of the water that would nourish desert plants is lost. Many sites in Utah, in particular, have cryptobiotic crusts. Protect these crusts by staying on established trails.
More-elegantly sculptured and durable versions are called hoodoos. These towering, narrow pillars of rock can be found throughout the Southwest, but are magnificently showcased at Utah's Bryce Canyon National Park. Although formed in soft rock, these precarious spires differ from badlands because parallel joints in the rock create deeply divided ridges that weather into rows of pillars. Under special circumstances, sandstone may form fins and arches. Utah's Arches National Park has a remarkable concentration of these features, thought to have resulted from a massive salt deposit that was laid down by a sea 300 million years ago. Squeezed by the pressure of overlying layers, this salt body apparently domed up then collapsed, creating a matrix of rock cracked along parallel lines. Erosion along deep vertical cracks left behind fins and narrow walls of sandstone that sometimes partially collapse to create freestanding arches.
Edward Abbey shares his desert philosophy and insights in his classic _Desert Solitaire: A Season in the Wilderness_ , a must-read for desert enthusiasts and conservationists.
Streams cutting through resistant sandstone layers form natural bridges, which are similar in appearance to arches. Three examples of natural bridges can be found in Utah's Natural Bridges National Monument. These formations are the result of meandering streams that double back on themselves to cut at both sides of a rock barrier. At an early stage of development these streams could be called goosenecks as they loop across the landscape. A famous example can be found at the Goosenecks State Park in Utah.
## SANDSTONE EFFECTS
Many of the Southwest's characteristic features are sculpted in sandstone. Laid down in distinct horizontal layers, like a stack of pancakes, these rocks erode into unique formations, like flat-topped mesas. Surrounded by sheer cliffs, mesas represent a fairly advanced stage of erosion in which all of the original landscape has been stripped away except for a few scattered outposts that tower over everything else. The eerie skyline at Monument Valley on the Arizona–Utah border is a classic example.
Where sandstone layers remain fairly intact, it's possible to see details of the ancient dunes that created the sandstone. As sand dunes were blown across the landscape millions of years ago they formed fine layers of crossbedding that can still be seen in the rocks at Zion National Park. Windblown ripple marks and tracks of animals that once walked the dunes are also preserved. Modern sand dunes include the spectacular dunes at White Sands National Monument in New Mexico, where shimmering white gypsum crystals thickly blanket 275 sq miles.
Looking beneath the surface, the 85-plus caves at Carlsbad Caverns National Park in southern New Mexico are chiseled deep into a massive 240-million-year-old limestone formation that was part of a 400-milelong reef similar to the modern Great Barrier Reef of Australia.
### Geology of the Grand Canyon
Arizona's Grand Canyon is the best-known geologic feature in the Southwest and for good reason: not only does its immensity dwarf the imagination, but it also records two billion years of geologic history – a huge amount of time considering the Earth is just 4.6 billion years old. The Canyon itself, however, is young – a mere five to six million years old. Carved out by the powerful Colorado River as the land bulged upward, the 277-mile-long canyon reflects the differing hardness of the 10-plus layers of rocks in its walls. Shales, for instance, crumble easily and form slopes, while resistant limestones and sandstones form distinctive cliffs.
The North Rim of the Grand Canyon is 1200ft higher than the South Rim. The altitude of the North Rim ranges from 8000ft to 8800ft.
The layers making up the bulk of the canyon walls were laid during the Paleozoic era, 570 to 245 million years ago. These formations perch atop a group of one- to two-billion-year-old rocks lying at the bottom of the inner gorge of the canyon. Between these two distinct sets of rock is the Great Unconformity, a several-hundred-million-year gap in the geologic record where erosion erased 12,000ft of rock and left a huge mystery.
### Wildlife
The Southwest's desolate landscape doesn't mean it lacks wildlife – on the contrary. However, the plants and animals of North America's deserts are a subtle group and it takes patience to see them, so many visitors will drive through without noticing any at all. While a number of species are widespread, others have adapted to the particular requirements of their local environment and live nowhere else in the world. Deep canyons and waterless wastes limit travel and dispersal opportunities for animals and plants as well as for humans, and all life has to hunker down and plan carefully to survive.
### Animals
#### Reptiles & Amphibians
While most people expect to see snakes and lizards in a desert, it's less obvious that frogs and toads find a comfortable home here as well. But on a spring evening, many of the canyons of the Southwest reverberate with the calls of canyon tree frogs or red-spotted toads. With the rising sun, these are replaced by several dozen species of lizards and snakes that roam among rocks and shrubs. Blue-bellied fence lizards are particularly abundant in the region's parks, but visitors can always hope to encounter a rarity such as the strange and venomous 'Gila monster' lizard. Equally fascinating, if you're willing to hang around and watch for a while (but never touch or bother), are the Southwest's many colorful rattlesnakes. Quick to anger and able to deliver a painful or toxic bite, rattlesnakes are placid and retiring if left alone.
#### Birds
More than 400 species of birds can be found in the Southwest, bringing color, energy and song to every season. There are blue grosbeaks, yellow warblers and scarlet cardinals. There are massive golden eagles and tiny vibrating calliope hummingbirds. In fact, there are so many interesting birds that it's the foremost reason many people travel to the Southwest. Springtime is particularly rewarding, as songbirds arrive from their southern wintering grounds and begin singing from every nook and cranny.
One recent arrival at the Grand Canyon tops everyone's list of mustsee wildlife. With a 9ft wingspan, the California condor looks more like a prehistoric pterodactyl than any bird you've ever seen. Pushed to the brink of extinction, these unusual birds are staging a minor comeback at the Grand Canyon. After several decades in which no condors lived in the wild, a few wild pairs are now nesting on the canyon rim.
Fall provides another bird-watching highlight when sandhill cranes and snow geese travel in long skeins down the Rio Grande Valley to winter at the Bosque del Apache National Wildlife Refuge in New Mexico. The Great Salt Lake is one of North America's premier sites for migrating birds, including millions of ducks and grebes stopping each fall to feed before continuing south.
### WHAT'S THE BLM?
The Bureau of Land Management (www.blm.gov) is a Department of Energy agency that oversees more than 245 million surface acres of public land, much of it in the West. It manages its resources for a variety of uses, from energy production to cattle grazing to recreational oversight. What does that mean for you? All kinds of outdoor fun.
You'll also find both developed camping and dispersed camping. Generally, when it comes to dispersed camping on BLM land, you can camp where you want as long as your campsite is at least 900ft from a water source used by wildlife or livestock. You cannot camp in one spot for more than 14 days. Pack out what you pack in and don't leave campfires unattended. Some regions may have more specific rules, so check the state's camping requirements on the BLM website and call the appropriate district office for specifics. For developed campground information, you can also visit www.recreation.gov.
#### Mammals
The Southwest's most charismatic wildlife species were largely exterminated by the early 1900s. A combination of factors has contributed to their decline over the decades, including loss of habitat, over-hunting and oil-and-gas development. First to go was the grizzly bear. After that, herds of buffalo, howling wolves and the tropical jaguars that crossed the border out of Mexico also disappeared from the region. Prairie dogs (actually small rodents) vanished with hardly a trace, even though they once numbered in the billions.
An estimated nine million free-tailed bats once roosted in Carlsbad Caverns. Though reduced in recent years, the evening flight is still one of the premier wildlife spectacles in North America.
Like the California condor, however, some species are being reintroduced. A small group of Utah prairie dogs were successfully released in Bryce Canyon National Park in 1974. Mexican wolves were released in the midst of public controversy into the wilds of eastern Arizona in 1998.
Mule deer still roam as widely as ever, and coyote are seen and heard nearly everywhere. Small numbers of elk, pronghorn antelope and bighorn sheep dwell in their favorite habitats (forests for elk, open grasslands for pronghorns and rocky cliffs for bighorns), but it takes a lot of luck or some sharp eyes to spot them. Even fewer people will observe a mountain lion, one of the wildest and most elusive animals in North America.
### DESERT FLOWERS
Some of the Southwest's biggest wildlife surprises are the incredibly diverse flowers that appear each year in the region's deserts and mountains. These include desert flowers that start blooming in February, and late summer flowers that fill mountain meadows after the snow melts or pop out after summer thunderstorms wet the soil. Some of the largest and grandest flowers belong to the Southwest's 100 or so species of cacti; these flowers are one of the reasons collectors seek out cacti for gardens and homes. The claret-cup cacti is composed of small cylindrical segments that produce brilliant red flowers in profusion from all sides of their prickly stems. Even a 50ft-tall giant saguaro, standing like a massive column in the desert, has prolific displays of fragrant yellow flowers that grow high on the stem and can be reached only by bats.
### Plants
Although the Southwest is largely a desert region, the presence of many large mountain ranges creates a remarkable diversity of niches for plants. One way to understand the plants of this region is to understand life zones and the ways each plant thrives in its favored zone.
There are more than 100 species of cacti in the Southwest. The iconic saguaro can grow up to 50ft tall, and a fully hydrated giant saguaro can store more than a ton of water.
At the lowest elevations, generally below 4000ft, high temperatures and lack of water create a desert zone where drought-tolerant plants such as cacti, sagebrush and agave survive. Many of these species have greatly reduced leaves to reduce water loss, or they hold water (cacti, for example) to survive long hot spells.
At mid-elevations, from 4000ft to 7000ft, conditions cool a bit and more moisture is available for woody shrubs and small trees. In much of Nevada, Utah, northern Arizona and New Mexico, piñon pines and junipers blanket vast areas of low mountain slopes and hills. Both trees are short and stout to help conserve water.
Nearly pure stands of stately, fragrant ponderosa pine are the dominant tree at 7000ft on many of the West's mountain ranges. In fact, this single tree best defines the Western landscape and many animals rely on it for food and shelter; timber companies also consider it their most profitable tree. High mountain, or boreal, forests composed of spruce, fir, quaking aspen and a few other conifers are found on the highest peaks in the Southwest. This is a land of cool, moist forests and lush meadows with brilliant wildflower displays.
## ENVIRONMENTAL ISSUES
In an arid landscape like the Southwest, many of the region's most impor tant environmental issues revolve around water. Drought has so severely impacted the region that researchers were warning that 110- mile long Lake Mead has a 50% chance of running dry by 2021, leaving an estimated 12 to 36 million people in cities from Las Vegas to Los Angeles and San Diego in need of water. On the bright side, the melting of a record snowpack in western mountain ranges in 2011 pumped up water supplies in the Southwest.
Many of the Southwest's most common flowers can be found in _Canyon Country Wildflowers_ , by Damian Fagan. Chapters are arranged by the color of the flowers, including white, yellow and blue.
Construction of dams and human-made water features throughout the Southwest has radically altered the delicate balance of water that sustained life for countless millennia. Dams, for example, halt the flow of warm waters and force them to drop their rich loads of life-giving nutrients. These sediments once rebuilt floodplains, nourished myriad aquatic and riparian food chains, and sustained the life of ancient endemic fish that now flounder on the edge of extinction. In place of rich annual floods, dams now release cold waters in steady flows that favor the introduced fish and weedy plants that have overtaken the West's rivers.
In other areas, the steady draining of aquifers to provide drinking water for cows and sprawling cities is shrinking the water table and drying up unique desert springs and wetlands that countless animals once depended on during the dry season. Cows further destroy the fragile desert crust with their heavy hooves, and also graze on native grasses and herbs that are soon replaced by introduced weeds. Development is increasingly having the largest impact, as uniquely adapted habitats are bulldozed to make room for more houses.
Read Marc Reisner's Cadillac Desert: The American West and Its Disappearing Water for a thorough account of how exploding populations in the West have utilized every drop of available water.
The region's stately pine and fir forests have largely become thickets of scrawny little trees. The cutting of trees and building of roads in these environments can further dry the soil and make it harder for young trees and native flowers to thrive. Injuries to an ecosystem in an arid environment take a very long time to heal.
In the Grand Canyon in 2007 there were an estimated 70,000 commercial sightseeing flights, mostly during the summer months. Responding to a high level of visitor complaints, not to mention the fact that federal law mandates 'natural quiet' within the national-park boundaries, the park released a draft environmental impact statement (EIS) in early 2011, with public comments due at press time. A copy of the draft EIS is currently on the park's website. As drafted, the EIS allows for _more_ flights, but requires quiet technology and a move away from many sensitive cultural, natural and tourist areas.
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# Southwest Cuisine
Whoever advised 'moderation in all things' has clearly never enjoyed a streetside Sonoran dog in Tucson. A Sonoran dog 'moderated' is not a Sonoran dog at all. Same goes for a messy plate of _huevo rancheros_ at a small-town Arizona diner. Or a green chile cheeseburger at the Owl Bar Café near Socorro, NM. Food in the Southwest is a tricultural celebration not well suited for the gastronomically timid, or anyone on a diet. One or two dainty bites? Impossible! But c'mon, admit it, isn't the food part of the reason you're here?
Three ethnic groups – Mexican, cattle-country Anglo and Native American – influence Southwestern food culture. Spain and Mexico controlled territories from Texas to California well into the 19th century, and when they officially packed up, they left behind their cooking style and many of their best chefs. The American pioneers who claimed these states also contributed to the Southwest style of cooking. Much of the Southwest is cattle country, and whether you are in Phoenix, Flagstaff or Las Vegas you can expect a good steak. Native American cuisine – which goes beyond fry bread – is gaining exposure as locally grown, traditional plants and seasonings are appearing on more menus across the region.
## STAPLES & SPECIALTIES
_Huevos rancheros_ is the quintessential Southwestern breakfast; eggs prepared to order are served on top of two fried corn tortillas, loaded with beans and potatoes, sprinkled with cheese, and served swimming in chile. Breakfast burritos are built by stuffing a flour tortilla with eggs, bacon or chorizo, cheese, chile and sometimes beans.
A Southwestern lunch or dinner will probably start with a big bowl of corn chips and salsa. Almost everything comes with beans, rice and your choice of warm flour or corn tortillas, topped with chile, cheese and sometimes sour cream. Blue-corn tortillas are one colorful New Mexican contribution to the art of cooking. Guacamole is also a staple, and many restaurants will mix the avocado, lime, cilantro (coriander), tomato and onion creation right at your table!
### EATING GREEN IN THE SOUTHWEST
Numerous restaurants throughout the five-state region are dedicated to serving only organic, and when possible buying local, which helps their community self-sustain. One of the most unique, ecofriendly and wholesome eating experiences in the Four Corners can be enjoyed at Hell's Backbone Grill in Boulder, UT. It takes four hours on a lonely, potholed stretch of road to reach this super-remote foodie outpost, but those who make the drive will be rewarded. The restaurant is sustainable, growing most of its bounty on its 2-acre organic farm – the vegetables are divine. Owner Jen Spalding says her goal for the restaurant is to evoke a little bit of provincial France in off -the-grid Utah.
### Steak & Potatoes
Home, home on the range, where the ranches and the steakhouses reign supreme. Have a deep hankerin' for a juicy slab of beef with a salad, baked potato and beans? Look no further than the Southwest, where there's a steakhouse for every type of traveler. In Phoenix alone choices range from the old-school Durant's to the outdoor Greasewood Flat to the family-friendly Rawhide Western Town & Steakhouse. In Utah, the large Mormon population influences culinary options – good, old-fashioned American food like chicken, steak, potatoes, vegetables, homemade pies and ice cream prevail.
Eat Your Words
» _carne seca_ – beef that is sun-dried before cooking
» _fry bread_ – deepfried, doughy Native American bread
» _mole_ – slightly spicy chocolateflavored chile sauce
» _sopaipilla_ – deepfried puff pastry with honey
»tamale – slightly sweet corn dough wrapped in a corn husk then steamed. Often stuffed with meat
### Mexican & New Mexican Food
Mexican food is often hot and spicy, but it doesn't have to be. If you don't like spicy food, go easy on the salsa. There are some distinct regional variations in the Southwest. In Arizona, Mexican food is of the Sonoran type, with specialties such as _carne seca_ (dried beef). Meals are usually served with refried beans, rice, and flour or corn tortillas; chiles are relatively mild. Tucsonans refer to their city as the 'Mexican food capital of the universe,' which, although hotly contested by a few other places, carries a ring of truth. Colorado restaurants serve Mexican food, but they don't insist on any accolades for it.
New Mexico's food is different from, but reminiscent of, Mexican food. Pinto beans are served whole instead of refried; posole (a corn stew) may replace rice. Chiles aren't used so much as a condiment (like salsa) but more as an essential ingredient in almost every dish. _Carne adobada_ (marinated pork chunks) is a specialty.
If a restaurant references red or green chile or chile sauces on the menu, it probably serves New Mexican style dishes. The state is famous for its chile-enhanced Mexican standards. The town of Hatch, NM, is particularly known for its green chiles.
### Native American Food
Modern Native American cuisine bears little resemblance to that eaten before the Spanish conquest, but it is distinct from Southwestern cuisine. Navajo and Indian tacos – fried bread usually topped with beans, meat, tomatoes, chile and lettuce – are the most readily available. Chewy horno bread is baked in the beehive-shape outdoor adobe ovens ( _hornos_ ) using remnant heat from a fire built inside the oven, then cleared out before cooking.
Most other Native American cooking is game-based and usually involves squash and locally harvested ingredients like berries and piñon nuts. Though becoming better known, it can be difficult to find, especially in Southwestern Colorado, Utah and Las Vegas. Your best bets are festival food stands, powwows, rodeos, Pueblo feast days, casino restaurants or people's homes at the different pueblos.
Exceptions include Albuquerque's Indian Pueblo Cultural Center, the Metate Room in Southwestern Colorado, Tewa Kitchen near Taos Pueblo and the Hopi Cultural Center Restaurant & Inn on the Hopi Reservation.
John Middelkoop's documentary _Beans from God: the History of Navajo Cooking_ examines the significant role that food plays in Navajo spiritual life.
### Fruit & Vegetables
Beyond the chile pepper, Southwestern food is characterized by its use of posole, _sopaipillas_ (deep-fried puff pastry) and blue corn. Posole, Spanish for hominy, is dried or frozen kernels of corn processed in a lime solution to remove the hulls. It's served plain, along with pinto beans, as a side dish. Blue-corn tortillas have a heartier flavor than the more common yellow corn tortillas. Pinto beans, served either whole or refried, are a basic element of most New Mexican dishes.
Beans, long the staple protein of New Mexicans, come in many colors, shapes and preparations. They are usually stewed with onions, chiles and spices and served somewhat intact or refried to a creamy consistency. Avocados are a delightful staple, made into zesty guacamole. 'Guac' recipes are as closely guarded and vaunted by cooks as their bean recipes.
The folks behind the much-lauded cookies at the Jacob Lake Inn, on the road to the Grand Canyon's North Rim, say the lemonzucchini cookies have a passionate following (www.jacoblake.com).
### Nouvelle Southwestern Cuisine
An eclectic mix of Mexican and Continental (especially French) traditions began to flourish in the late 1970s and continues to grow. Try innovative combinations such as chiles stuffed with lobster or barbecued duck tacos. But don't expect any bargains here. Southwestern food is usually inexpensive, but as soon as the chef tacks on a 'nouvelle' tag, the tab soars as high as a crested butte.
Generally speaking, cities such as Phoenix, Tucson, Santa Fe and Albuquerque have the most nouvelle Southwestern restaurants.
## WINE, BEER & MARGARITAS
In the Southwest it's all about the tequila. Margaritas are the alcoholic drink of choice, and synonymous with this region, especially in heavily Hispanic New Mexico, Arizona and Southwestern Colorado. Margaritas vary in taste depending on the quality of the ingredients used, but all are made from tequila, a citrus liquor (Grand Marnier, Triple Sec or Cointreau) and either fresh squeezed lime or premixed Sweet & Sour.
Our perfect margarita includes fresh squeezed lime (say no to the ultra-sugary and high-carb packaged mix), a high-end tequila (skip the gold and go straight to silver or pure agave – we like Patron or Herrendura Silver) and Grand Marnier liquor (better than sickly sweet Triple Sec). Ask the bartender to add a splash of orange juice if your drink is too bitter or strong.
Margaritas are either served frozen, on the rocks (over ice) or straight up. Most people order them with salt. Traditional margaritas are lime flavored, but these days the popular drink comes in a rainbow of flavors – best ordered frozen.
Locally brewed beers are also popular in this region, and people like to gather after work for a drink at their local microbrewery – a pub where beer is produced in-house. Microbreweries are abundant throughout the Southwest, and many of the beers are also sold in local grocery and liquor stores. Many microbrews are considered 'big beers' – meaning they have a high alcohol content.
There are three things a good wine grape needs: lousy soil, lots of sunshine and dedicated caretakers, all of which can be found in New Mexico and Arizona. For a full run-down of New Mexico's 40+ producers, visit the New Mexico Wine Growers Association at www.nmwine.com. La Chiripada Winery, with a shop on the Taos plaza, is our choice for regional vineyards, serving a fabulous Riesling and Cabernet Sauvignon.
You can't visit Albuquerque without ordering a Frito pie – a messy concoction of corn chips, beef chile, cheese and sour cream. You can find it in restaurants and it's always served at city festivals.
In Arizona, the best-known wine region is in the southern part of the state near Patagonia. The Verde Valley between Phoenix and Flagstaff is close on Patagonia's heels in terms of quality and publicity. Tool lead singer and Jerome resident Maynard James Keenan is actively involved in producing Arizona wines, and he owns or co-owns three wineries and vineyards across the state. The Arizona Wine Growers Association (www.arizonawine.org) lists the state's wine producers.
For something nonalcoholic, you'll find delicious espresso shops in the bigger cities and sophisticated small towns; in rural Arizona or Nevada you're likely to get nothing better than stale, weak diner coffee, however. Santa Fe, Phoenix, Durango, Truth or Consequences and Tucson all have excellent coffee shops with comfortable couches for reading or studying. Basically, if the Southwestern town has a college, it will have a good coffee shop. That's a regional given.
## VEGETARIANS & VEGANS
Most metro area eateries offer at least one veggie dish, although few are devoted solely to meatless menus. These days, fortunately, almost every larger town has a natural-food grocer. You may go wanting in smaller hinterland towns, however, where beef still rules. In that case, your best bet is to assemble a picnic from the local grocery store.
'Veggie-heads' will be happiest in New Mexico and Arizona; go nuts (or more specifically, go piñon). Thanks to the area's long-standing appeal for hippie types, vegetarians and vegans will have no problem finding something delicious on most menus, even at drive-throughs and tiny dives. One potential pitfall? Traditional Southwestern cuisine uses lard in beans, tamales, _sopaipillas_ (deep-fried puff pastry) and flour (but not corn) tortillas, among other things. Be sure to ask – often, even the most authentic places have a pot of pintos simmering for vegetarians.
#
Top of section
# Arts & Architecture
Art has always been a major part of Southwest culture and one of the most compelling ways for its people to express their heritage and ideologies. The rich history and cultural texture of the Southwest is a fertile source of inspiration for artists, filmmakers, writers, photographers and musicians.
For more on the rich Native American culture, see (Click here).
Top Places for Art & Culture
»» Phoenix, AZ
»Santa Fe, NM
»Taos, NM
»Indian Pueblo Cultural Center, Albuquerque, NM
»Salt Lake City, UT
### Literature
From the classic Western novels of Zane Grey, Louis L'Amour and Larry McMurtry to contemporary writers like ecosavvy Barbara Kingsolver and Native American Louise Erdrich, authors imbue their work with the scenery and sensibility of the Southwest. Drawing from the mystical reality that is so infused in Latin literature, Southwestern style can sometimes be fantastical and absurdist, yet poignantly astute.
DH Lawrence moved to Taos in the 1920s for health reasons, and went on to write the essay 'Indians and Englishmen' and the novel _St Mawr_. Through his association with artists like Georgia O'Keeffe, he found some of the freedoms from puritanical society that he'd long sought.
Tony Hillerman, an enormously popular author from Albuquerque, wrote _Skinwalkers, People of Darkness, Skeleton Man_ and _The Sinister Pig_. His award-winning mystery novels take place on the Navajo, Hopi and Zuni Reservations.
Hunter S Thompson, who committed suicide in early 2005, wrote _Fear and Loathing in Las Vegas_ , set in the temple of American excess in the desert; it's the ultimate road-trip novel, in every sense of the word.
Edward Abbey, a curmudgeonly eco-warrior who loved the Southwest, created the thought-provoking and seminal works _Desert Solitaire_ and _The Journey Home: Some Words in Defense of the American West_. His classic _Monkey Wrench Gang_ is a fictional and comical account of real people who plan to blow up Glen Canyon Dam before it floods Glen Canyon.
John Nichols wrote _The Milagro Beanfield War_ , part of his New Mexico trilogy. It's a tale of a Western town's struggle to take back its fate from the Anglo land barons and developers. Robert Redford's movie of the novel was filmed in Truchas, NM.
Barbara Kingsolver lived for a decade in Tucson before publishing _The Bean Trees_ in 1988. Echoing her own life, it's about a young woman from rural Kentucky who moves to Tucson. Her 1990 novel, _Animal Dreams_ , gives wonderful insights into the lives of people from a small Hispanic village near the Arizona–New Mexico border and from an Indian Pueblo.
For chick lit that gives you a feel for the land, adventures and people of the Southwest, read Pam Houston's books. Her collection _Cowboys Are My Weakness_ is filled with funny, sometimes sad, stories about love in the great outdoors.
New Mexico's Green Filmmaking Initiative encourages producers to think about sustainability when creating movies and TV shows here. Visit www.nmfilm.com for resources on creating ecofriendly shoots, and the opportunity to win grants for creating green films.
### Cinema & Television
The movie business is enjoying a renaissance in the Southwest, with New Mexico as the star player. During his two terms as governor (2002–2010), Bill Richardson wooed Hollywood producers and their production teams to the state. The bait? A 25% tax rebate on production expenditures. His eff orts helped inject more than $3 billion into the economy. On television, the critically acclaimed American TV series _Breaking Bad_ is set and filmed in and around Albuquerque. Joel and Ethan Coen shot the 2007 Oscar winner _No Country for Old Men_ almost entirely around Las Vegas, NM (doubling for 1980s west Texas). The Coen brothers returned in 2010 to shoot their remake of _True Grit_ , basing their production headquarters in Santa Fe and filming on several New Mexico ranches.
Las Vegas, NV, had a starring role in 2009's blockbuster comedy _The Hangover_ , an R-rated buddy film that earned more than $467 million worldwide. A town just outside of Las Vegas is the new home of Kody Brown, his four wives and their 16 children, a polygamous family profiled in TLC's reality show _Sister Wives_. The family is currently under criminal investigation in Utah, their former home, where bigamy is a third-degree felony.
A few places have doubled as film and TV sets so often that they have come to define the American West. In addition to Utah's Monument Valley, popular destinations include Moab, for _Thelma and Louise_ (1991), Dead Horse Point State Park, also in Utah, for _Mission Impossible_ : 2 (2000), Lake Powell, Arizona, for _Planet of the Apes_ (1968) and Tombstone for the eponymous _Tombstone_ (1993). Scenes in 127 _Hours_ , about Aron Ralston's harrowing experience trapped in Blue John Canyon in Utah's Canyonlands National Park, were shot in and around the canyon.
The region also specializes in specific location shots. Snippets of _Casablanca_ (1942) were actually filmed in Flagstaff 's Hotel Monte Vista, _Butch Cassidy and the Sundance Kid_ (1969) was shot at the Utah ghost town of Grafton, and _City Slickers_ (1991) was set at Ghost Ranch in Abiquiú, NM.
### Music
The larger cities of the Southwest are the best options for classical music. Choose among Phoenix's Symphony Hall, which houses the ArizonaOpera and the Phoenix Symphony Orchestra, the famed Santa Fe Opera, the New Mexico Symphony Orchestra in Albuquerque, and the Arizona Opera Company in Tucson and Phoenix.
### EARTHSHIP ARCHITECTURE
Is that Mos Eisley Spaceport about 2 miles past the Rio Grande Gorge? No, it's the world's premier sustainable, self-sufficient community of Earthships. This environmentally friendly architectural form, pioneered in northern New Mexico, consists of auto tires packed with earth, stacked with rebar and turned into livable dwellings (http://earthship.org).
The brainchild of architect Mike Reynolds, Earthships are a form of biotecture (biology plus architecture: buildings based on biological systems of resource use and conservation) that maximizes available resources so you'll never have to be on the grid again.
Walls made of old tires are laid out for appropriate passive solar use, packed with tamped earth, and then buried on three sides for maximum insulation. The structures are outfitted with photovoltaic cells and an elaborate gray-water system that collects rain and snow, which filters through several cycles that begin in the kitchen and end in the garden.
Though the Southwest is their home, Earthships have landed in Japan, Bolivia, Scotland, Mexico and beyond, and are often organized into communities.
Nearly every major town attracts country, bluegrass and rock groups. A notable major venue is Flagstaff 's Museum Club, with a lively roster of talent. Surprisingly, Provo, UT, has a thriving indie rock scene, which offers a stark contrast to the Osmond-family image that Utah often conjures. A fabulous festival offering is Colorado's Telluride Bluegrass Festival.
Acoma Pueblo's new 40,000-sq-ft Sky City Cultural Center and Haak'u Museum http://museum acomaskycity org) showcases vibrant tribal culture ongoing since the 12th century.
Las Vegas is a mecca for entertainers of every stripe; current headliners include popular icons like Celine Dion and Barry Manilow, but for a little gritty goodness head to the Joint.
Try to catch a mariachi ensemble (they're typically dressed in ornately sequined, body-hugging costumes) at southern New Mexico's International Mariachi Festival.
### Architecture
Not surprisingly, architecture has three major cultural regional influences in the Southwest. First and foremost are the ruins of the Ancestral Puebloans – most majestically their cliff communities and Taos Pueblo. These traditional designs and examples are echoed in the Pueblo Revival style of Santa Fe's New Mexico Museum of Art and are speckled across the city and the region today.
The most traditional structures are adobe – mud mixed with straw, formed into bricks, mortared with mud and smoothed with another layer of mud. This style dominates many New Mexico cityscapes and landscapes.
Mission-style architecture of the 17th and 18th centuries, seen in religious and municipal buildings like Santa Fe's State Capitol, is characterized by red-tile roofs, ironwork and stucco walls. The domed roof and intricate designs of Arizona's Mission San Xavier del Bac embody the Spanish Colonial style.
In the 1800s Anglo settlers brought many new building techniques and developed Territorial-style architecture, which often includes porches, wood-trimmed doorways and other Victorian influences.
Master architect Frank Lloyd Wright was also a presence in the Southwest, most specifically at TaliesinWest in Scottsdale, AZ. More recently, architectural monuments along Route 66 include kitschy motels lit by neon signs that have forever transformed the concept of an American road trip.
### Painting, Sculpture & Visual Arts
The region's most famous artist is Georgia O'Keeffe (1887–1986; see Click here), whose Southwestern landscapes are seen in museums throughout the world. The minimalist paintings of Agnes Martin (1912–2004) began to be suff used with light after she moved to New Mexico. Also highly regarded is Navajo artist RC Gorman (1932–2005), known for sculptures and paintings of Navajo women. Gorman lived in Taos for many years.
Both Taos and Santa Fe, NM, have large and active artist communities considered seminal to the development of Southwestern art. Santa Fe is a particularly good stop for those looking to browse and buy art and native crafts. More than 100 galleries line the city's Canyon Rd, and Native American vendors sell high-quality jewelry and crafts beside the plaza.
The vast landscapes of the region have long appealed to large-format black-and-white photographers like Ansel Adams, whose archives are housed at the Center for Creative Photography at the University of Arizona.
For something different, pop into art galleries and museums in Las Vegas, specifically the Bellagio, which partners with museums and foundations around the world for knock-out exhibitions, and the new City Center, which hosts art by internationally renowned artists like Jenny Holzer, Maya Lin and Claes Oldenburg.
### Jewelry & Crafts
Hispanic and Native American aesthetic influences are evident in the region's pottery, paintings, weavings, jewelry, sculpture, woodcarving and leatherworking. See (Click here) for a discussion of Navajo rugs and Click here for Hopi kachina dolls. Excellent examples of Southwestern Native American art are displayed in many museums, most notably in Phoenix's Heard Museum and Santa Fe's Museum of Contemporary Native Arts. Contemporary and traditional Native American art is readily available in hundreds of galleries. For tips on buying Native American jewelry and crafts, see Click here.
The National Cowboy Poetry Gathering – the bronco of cowboy poetry events – is held in January in Elko, Nevada. Ropers and wranglers have waxed lyrical here for more than 25 years (www.westernfolklife.org).
### Kitsch & Folk Art
The Southwest is a repository for kitsch and folk art. In addition to the predictable Native American knockoff s and beaded everything (perhaps made anywhere but there), you'll find invariable UFO humor in Roswell and unexpected nuclear souvenirs at Los Alamos, both in New Mexico. Pick up an Atomic City T-shirt, emblazoned with a red and yellow exploding bomb, or a bottle of La Bomba wine.
More serious cultural artifacts fill the Museum of International Folk Art in Santa Fe.
### Dance & Theater
Native Americans have a long tradition of performing sacred dances throughout the year. Ceremonial or ritual religious dances are spiritual, reverential community occasions, and many are closed to the public. When these ceremonies are open to the public, some tribes (like the Zuni) require visitors to attend an orientation; always contact the tribes to confirm arrangements.
Social dances are typically cultural, as opposed to religious, events. They are much more relaxed and often open to the public. They occur during powwows, festivals, rodeos and other times, both on and off the reservation. Intertribal dance competitions (the lively 'powwow trail') are quite popular; the dancing may tell a story or be just for fun, to celebrate a tribe or clan gathering. The public may even be invited to join the dance.
Native Americans also perform dances strictly for the public as theater or art. Though these may lack community flavor, they are authentic and wonderful.
Classical dance options include Ballet West in Salt Lake City and Ballet Arizona in Phoenix. Dance and theater productions are flashy and elaborate in Las Vegas, where they have always been a staple of the city's entertainment platform. In Utah, Park City's George S and Dolores Doré Eccles Center for the Performing Arts hosts varied events.
### NAMPEYO
Hopi cultural expression as we think of it today owes much to a woman named Nampeyo. Born on First Mesa in 1859 or '60 to a Hopi father and Tewa mother, she learned how to work clay from her paternal grandmother. A natural, she earned the reputation as a master as a young woman, and was known for her inspired designs. Influenced by the patterns on shards of ancient pots that her husband brought to her from the ruins at Sikyatki, where he was helping with an archaeological dig, Nampeyo created a style that blended past motifs with her own artistic instincts.
At the time, pottery was a dying craft, as contact with traders enabled the Hopi to buy pre-made goods. But as Nampeyo's work began to fetch high prices and draw worldwide attention, a renaissance of Hopi arts was sparked, not only in pottery, but also in silver, woodcarving and textiles. Thanks to her influence, the tradition more than lives on – it's been taken to higher levels of artistry than at any time in the tribe's past.
### **Survival Guide**
**DIRECTORY A–Z**
Accommodations
Business Hours
Dangers & Annoyances
Discount Cards & Coupons
Electricity
Food
Gay & Lesbian Travellers
Health
Holidays
Insurance
International Visitors
Internet Access
Legal Matters
National & State Parks
Photography
Tours
Travelers with Disabilities
**TRANSPORTATION**
GETTING THERE AND AWAY
Air
Land
GETTING AROUND
Air
Bicycle
Bus
Car & Motorcycle
Motor Home (RV)
Train
# Directory A–Z
Top of section
### Accommodations
From barebones to luxurious to truly off beat, the Southwest offers a vast array of lodging options. Cookie-cutter chains line the interstates, providing a nice safety net for the less adventurous, but it's the indie-owned places that really shine. Where else but the Southwest can you sleep in a concrete wigwam or a cavern 21 stories underground? For road-trippers, the most comfortable accommodations for the lowest price are usually found in that great American invention, the mom-and-pop roadside motel.
For last-minute deals, check www.hotels.com, www.kayak.com, www.expedia.com, www.travelocity.com, www.orbitz.com, www.hotwire.com and www.priceline.com. For more on discounts, see (Click here).
Accommodations listings in this book are ordered by preference. Rates are based on standard doubleoccupancy in high season:
»$ less than $100
»$$ $100–200
»$$$ more than $200
Unless otherwise noted, breakfast is _not_ included, bathrooms are private and all lodging is open yearround. Rates generally don't include taxes, which vary considerably between towns and states. Most places are non-smoking although some national chains and local budget motels may offer smoking rooms. Ask beforehand; many places charge a fee, which can be hefty, for smoking in a non-smoking room.
As for icons, a parking icon is only used in the biggest cities. The internet icon appears where a place has computers available for public use or where an innkeeper is OK with people briefly using their personal computer. If you're carrying a laptop, look for the wi-fi icon. Child-friendly hotels now have their own icon, as do pet-friendly lodgings. The Top Choice icon indicates those accommodations that truly stand out.
High season varies depending on the region within the Southwest. In general, the peak travel season runs June through August, except in the hottest parts of Arizona, when some places slash their prices in half because it's just too darn hot. The peak travel season for southern Arizona and the ski areas of northern Utah (for different reasons) and other mountainous areas are mid-December to mid- April. Generally, we only list high-season rates. For more seasonal discussions, see (Click here).
Holidays (Click here) command premium prices. When demand peaks, and during special events no matter the time of year, book lodgings well in advance.
Note cancellation policies when booking. Many accommodations will charge a cancellation fee, or the amount of your first night's stay (in some cases the full stay), if you cancel after the stated date.
Some resorts and B&Bs have age restrictions. If you're traveling with children, inquire before making reservations.
#### B&Bs & Inns
B&Bs are a good choice for travelers looking for more personal attention and a friendly home base for regional exploration. B&Bs may not work as well for longer stays, especially if you want to cook your own meals. In smaller towns, simple guesthouses may charge $60 to $130 a night for rooms with a shared bathroom, breakfast included. Some have more charming features, such as kiva fireplaces, courtyards or lounge areas. These fancier B&Bs typically charge $125 to $195 per night with a private bathroom, although the nicest could cost more than $250 per night. Most B&Bs have fewer than 10 rooms, and many don't allow pets or young children.
#### Camping
Free dispersed camping (independent camping at non-established sites) is permitted in many backcountry areas including national forests and Bureau of Land Management (BLM) lands, and less often in national and state parks. This can be particularly helpful in the summer when every motel within 50 miles of the Grand Canyon is full. If that's the case, try Kaibab National Forest beside the southern and northern boundaries of the national park. Stake your spot among the ponderosas, taking care not to camp within a quarter-mile of any watering hole or within a mile of any developed campgrounds or administrative or recreational sites. For the latest information about how far you're allowed to drive from the nearest road to pitch camp, see the Travel Management Rule updates for Kaibab National Forest at www.fs.fed.us.
For more information about dispersed camping on BLM land see (Click here). The more developed areas (especially national parks) usually require reservations in advance. To reserve a campsite on federal lands, book through Recreation. gov ( 877-444-6777, 518-885- 3639; www.recreation.gov).
Many state parks and federal lands allow camping, sometimes free, on a first-come, first-served basis. Developed camping areas usually have toilets, water spouts, fire pits, picnic tables and even wireless internet. Some don't have access to drinking water. It is always a good idea to have a few gallons of water in your vehicle when you're out on the road. Some camping areas are open year-round, while others are open only from May through to the first snowfall – check in advance if you're planning to slumber outdoors in winter.
Basic tenting usually costs $12 to $25 a night and cabins and teepees are sometimes available too. More developed campgrounds may be geared to RV travel and cost $25 to $45 a night. For information on renting an RV, see Click here. Kampgrounds of America (KOA; 406- 248-7444; www.koa.com) is a national network of private campgrounds with tent sites averaging $30 to $32 per night plus taxes.
#### Hostels
Staying in a private double at a hostel can be a great way to save money and still have privacy (although you'll usually have to share a bathroom), while a dorm bed allows those in search of the ultimate bargain to sleep cheap under a roof. Dorms cost between $18 and $23, depending on the city and whether or not you are a Hostelling International (HI) member. A private room in a Southwestern hostel costs between $25 and $50.
Most hostels in the Southwest are run independently and are not part of Hostelling International USA ( 301- 495-1240; www.hiusa.org). They often have private or single rooms, sometimes with their own bathrooms. Kitchen, laundry, notice board and TV facilities are also typically available. Hostels.com (www.hostels.com) lists hostels throughout the world.
#### Hotels
Prices vary tremendously from season to season, and they are only an approximate guideline in this book. Rates also don't include state and local occupancy taxes, which can be as high as 14% combined. High seasons and special events (when prices may rise) are indicated in the text, but you never know when a convention may take over several hundred rooms and make beds hard to find – and raise prices. Members of the American Association of Retired Persons (AARP) and the American Automobile Association (AAA) often qualify for discounts.
#### Lodges
Normally situated within national parks, lodges are often rustic looking but are usually quite comfy inside. Rooms generally start at $100 but can easily be double that in high season. Since they represent the only option if you want to stay inside the park without camping, many are fully booked well in advance. Want a room today? Call anyway – you might be lucky and hit on a cancellation. In addition to on-site restaurants, they also offer touring services.
#### Motels
Budget motels are prevalent throughout the Southwest. In smaller towns, they will often be your only option. Many motels have at-the-door parking, with exterior room doors. These are convenient, though some folks, especially single women, may prefer the more expensive places with safer interior corridors.
Prices advertised by motels are called rack rates and are not written in stone. You may find rates as low as $35, but expect most to fall into the $50 to $75 range. If you simply ask about any specials or a reduced rate, you can often save quite a bit of money. Children are often allowed to stay free with their parents.
Motel 6 is usually the cheapest of the chains.
#### Resorts & Guest Ranches
Luxury resorts and guest ranches (often called 'dude ranches') really require a stay of several days to be appreciated and are often destinations in themselves. Start the day with a round of golf or a tennis match, then luxuriate with a massage, swimming, sunbathing and drinking. Guest ranches are even more like 'whole vacations,' with active schedules of horseback riding and maybe cattle roundups, rodeo lessons, cookouts and other Western activities like, um, hot-tubbing. When planning, be aware that ranches in the desert lowlands may close in summer, while those in the mountains may close in winter or convert into skiing centers. See the website of the Arizona Dude Ranch Association (www.azdra.com) for a helpful dude ranch comparison chart for the Grand Canyon State.
### BOOK YOUR STAY ONLINE
For more accommodations reviews by Lonely Planet authors, check out hotels.lonelyplanet.com. You'll find independent reviews, as well as recommendations on the best places to stay. Best of all, you can book online.
### Business Hours
Generally speaking, business hours are from 10am to 6pm. In large cities a few supermarkets and restaurants are open 24 hours a day. In Utah many restaurants are closed on Sunday. Unless there are variances of more than half an hour in either direction, the following are 'normal' opening hours for places reviewed in this book:
Banks 8:30am-4:40pm Mon-Thu, to 5:30pm Fridays, some open 9am-12:30pm Sat.
Bars 5pm-midnight Sun-Thu, to 2am Fri & Sat.
Government offices 9am-5pm Mon-Fri.
Post offices 9am-5pm Mon-Fri, some open 9am-noon Sat.
Restaurants Breakfast 7am-10:30am Mon-Fri; brunch 9am-2pm Sat & Sun; lunch 11:30am-2:30pm Mon-Fri; dinner 5pm-9:30pm Sun-Thu, later Fri & Sat. In larger cities and resort towns many restaurants serve at least a limited menu from open to close; in Vegas restaurants can stay open 24 hours.
Shops 10am-6pm Mon-Sat, noon-5pm Sun. Shopping malls may keep extended hours.
### Dangers & Annoyances
Southwestern cities generally have lower levels of violent crime than larger cities like New York, Los Angeles and Washington, DC. Nevertheless, violent crime is certainly present.
Take these usual precautions:
»L ock your car doors and don't leave any valuables visible. Smash-and-grab thefts can be a problem at trailhead parking lots.
»A void walking alone on empty streets or in parks at night.
»A void being in the open, especially on canyon rims or hilltops, during lightning storms.
»A void riverbeds and canyons when storm clouds gather in the distance; flash floods are deadly.
»When dust storms brew, pull off to the side of the road, turn off your lights and wait it out. They don't usually last long.
»Drivers should watch for livestock on highways and in American Indian reservations and areas marked 'Open Rangelands.'
»When camping where bears are present, place your food inside a food box (one is often provided by the campground).
»Watch where you step when you hike – particularly on hot summer afternoons and evenings, when rattlesnakes like to bask on the trail.
»Scorpions spend their days under rocks and woodpiles; use caution.
### THE SWARM
Africanized 'killer' bees have made it to southern Arizona. They've moved into the cliff dwellings at Tonto National Monument and have attacked hikers in Saguaro National Park. They're in the Phoenix area, and around Tucson, too. Each Africanized bee actually has less venom than your average honeybee, but they have very short tempers, and the real danger is the swarm factor. One sting by itself is no big deal, unless you're allergic. But because the whole swarm is easily provoked, victims may be stung a hundred times or more, which could be life-threatening to even healthy, non-bee-allergic people.
Chances are you won't run into any killer-bee colonies, but here are a few things to know. Bees are attracted to dark colors, so hike in something light. Forget the perfume, and if a bee starts 'bumping' you, it could be its way of warning you that you're getting too close to the hive. Your best move is to get away from there.
If you do attract the angry attention of a colony, RUN! Cover your face and head with your clothing, your hands, or whatever you can, and keep running. Don't flail or swat, as this will only agitate them. They should stop following you before you make it half a mile. If you can't get that far, take shelter in a building or a car or under a blanket. Don't go into the water unless you happen to have a straw in your pocket – the swarm will just hover above and wait for you to come up for air. If you do get stung by lots of bees, get medical help – and if you try to get the stingers out, scrape them away, don't pull, which will unintentionally inject more venom.
### Discount Cards & Coupons
From printable internet coupons to coupons found in tourist magazines, there are price reductions aplenty. For lodging, pick up one of the coupon books stacked outside highway visitor centers. These typically offer some of the cheapest rates out there.
#### Senior Cards
Travelers aged 50 and older can receive rate cuts and benefits at many places. Inquire about discounts at hotels, museums and restaurants before you make your reservation. US citizens aged 62 and older are eligible for the $10 Senior Pass (http://store.usgs.gov/pass), which allows lifetime entry into all national parks and discounts on some services (Golden Age Passports are still valid).
A good resource for travel bargains is the American Association of Retired Persons (AARP; 888-687- 2277; www.aarp.org), an advocacy group for Americans aged 50 years and older.
### Electricity
### Food
Eating sections are broken down into three price categories. These price estimates do not include taxes, tips or beverages.
»$ less than $10
»$$ $10–$20
»$$$ more than $20
Note that many Utah restaurants are closed on Sunday; when you find one open (even if it's not your first choice), consider yourself among the fortunate.
For details about Southwestern specialties and delicacies, see (Click here).
### Gay & Lesbian Travelers
The most visible gay communities are in major cities. Utah and southern Arizona are typically not as freewheeling as San Francisco. Gay travelers should be careful in predominantly rural areas – simply holding hands might get you assaulted.
The most active gay community in the Southwest is in Phoenix. Santa Fe and Albuquerque have active gay communities, and Las Vegas has an active gay scene. Conservative Utah has almost no visible gay life outside Salt Lake City.
Damron (www.damron.com) publishes the classic gay travel guides. OutTraveler (www.outtraveler.com) and PlanetOut (http://PlanetOut.com/travel) publish downloadable gay travel guides and articles. Another good resource is the Gay Yellow Network (www.gayyellow.com), which has listings for numerous US cities including Phoenix.
National resource numbers include the National Gay and Lesbian Task Force ( 202-393-5177 in Washington, DC; www.thetaskforce.org) and the Lambda Legal Defense Fund ( 213-382-7600 in Los Angeles; www.lambdalegal.org).
### Health
#### Altitude Sickness
Visitors from lower elevations undergo rather dramatic physiological changes as they adapt to high altitudes. Symptoms, which tend to manifest during the first day after reaching altitude, may include headache, fatigue, loss of appetite, nausea, sleeplessness, increased urination and hyperventilation due to overexertion. Symptoms normally resolve within 24 to 48 hours. The rule of thumb is, don't ascend until the symptoms descend. More severe cases may display extreme disorientation, ataxia (loss of coordination and balance), breathing problems (especially a persistent cough) and vomiting. People afflicted should descend immediately and get to a hospital.
To avoid the discomfort characterizing the milder symptoms, drink plenty of water and take it easy – at 7000ft, a pleasant walk around Santa Fe can wear you out faster than a steep hike at sea level.
#### Dehydration
Visitors to the desert may not realize how much water they're losing, as sweat evaporates almost immediately and increased urination (to help the blood process oxygen more efficiently) can go unnoticed. The prudent tourist will make sure to drink more water than usual – think a gallon (about 4L) a day if you're active. Parents can carry fruit and fruit juices to help keep kids hydrated.
Severe dehydration can easily cause disorientation and confusion, and even day hikers have got lost and died because they ignored their thirst. So bring plenty of water, even on short hikes, and drink it!
#### Heat Exhaustion & Heatstroke
Dehydration or salt deficiency can cause heat exhaustion. Take time to acclimatize to high temperatures and make sure you get enough liquids. Salt deficiency is characterized by fatigue, lethargy, headaches, giddiness and muscle cramps. Salt tablets may help. Vomiting or diarrhea can also deplete your liquid and salt levels. Anhydrotic heat exhaustion, caused by the inability to sweat, is quite rare. Unlike other forms of heat exhaustion, it may strike people who have been in a hot climate for some time, rather than newcomers. Always use water bottles on long trips. One gallon of water per person per day is recommended if hiking.
Long, continuous exposure to high temperatures can lead to the sometimes-fatal condition heatstroke, which occurs when the body's heat-regulating mechanism breaks down and the body temperature rises to dangerous levels. Hospitalization is essential for extreme cases, but meanwhile get out of the sun, remove clothing, cover the body with a wet sheet or towel and fan continually.
### Holidays
New Year's Day January 1
Martin Luther King Jr Day 3rd Monday of January
Presidents Day 3rd Monday of February
Easter March or April
Memorial Day Last Monday of May
Independence Day July 4
Labor Day 1st Monday of September
Columbus Day 2nd Monday of October
Veterans Day November 11
Thanksgiving 4th Thursday of November
Christmas Day December 25
### Insurance
It's expensive to get sick, crash a car or have things stolen from you in the US. When it comes to health care, the US has some of the finest in the world. The problem? Unless you have good insurance, it can be prohibitively expensive. It's essential to purchase travel health insurance if your regular policy doesn't cover you when you're abroad.
If your health insurance does not cover you for medical expenses abroad, consider supplemental insurance. Find out in advance if your insurance plan will make payments directly to providers or reimburse you later for overseas health expenditures.
To insure yourself from theft of items in your car, consult your homeowner's (or renter's) insurance policy before leaving home.
Worldwide travel insurance is available at www.lonelyplanet.com/travel_services. You can buy, extend and claim online anytime – even if you're already on the road.
### International Visitors
US entry requirements continue to change as the country fine-tunes its national security guidelines. All travelers should doublecheck current visa and passport regulations before coming to the USA.
#### Entering the Country
Getting into the US can be complicated. Plan ahead. For up-to-date information about visas and immigration, check with the US State Department ( 202-663-1225; www.travel.state.gov).
Apart from most Canadian citizens and those entering under the Visa Waiver Program (VWP), all foreign visitors to the US need a visa. Pursuant to VWP requirements, citizens of certain countries may enter the US for stays of 90 days or fewer without a US visa. This list is subject to continual reexamination and bureaucratic rejigging. At press time these countries included Andorra, Australia, Austria, Belgium, Brunei, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Monaco, the Netherlands, New Zealand, Norway, Portugal, San Marino, Singapore, Slovakia, Slovenia, South Korea, Spain, Sweden, Switzerland and the UK.
If you are a citizen of a VWP country you do not need a visa _only if_ you have a passport that meets current US standards _and_ you get approval from the Electronic System for Travel Authorization (ESTA) in advance. Register online with the Department of Homeland Security at https://esta.cbp.dhs.gov at least 72 hours before arrival. Canadians are currently exempt from ESTA.
Because the Department of Homeland Security is continually modifying its requirements, even travelers with visa waivers may be subject to enrollment in the US-Visit program. For most visitors (excluding, for now, most Canadian and some Mexican citizens) registration consists of having a digital photo and electronic (inkless) fingerprints taken. Contact the Department of Homeland Security (www.dhs.gov/US -visit) for current requirements.
Every foreign visitor entering the USA from abroad needs a passport. In most cases, your passport must be valid for at least another six months after you are due to leave the USA. If your passport doesn't meet current US standards you'll be turned back at the border. If your passport was issued before October 26, 2005, it must be machine readable (with two lines of letters, numbers and the repeated symbol <<< at the bottom); if it was issued between October 26, 2005 and October 25, 2006, it must be machine readable and include a digital photo on the data page or integrated chip with information from the data page; and if it was issued on or after October 26, 2006, it must be an e-Passport with a digital photo and an integrated chip containing information from the data page. Nationals from the Czech Republic, Estonia, Greece, Hungary, Latvia, Lithuania, Malta, Slovakia and South Korea must have an e-Passport.
### SOUTHWEST WITH PETS
When it comes to pet-friendly travel destinations, the Southwest is one of the best. More and more hotels accept pets these days, although some charge extra per night, others make you leave a deposit and still others have weight restrictions – less than 35lb is usually the standard. To not get hit with an extra $50 in dog-room fees, call the hotel in advance. One of the most unique pet-friendly options in the Southwest is in Santa Fe: head to the swank Ten Thousand Waves Japanese Resort & Spa (Click here).
At national parks, check first before you let your pet off the leash – many forests and park lands have restrictions on dogs. If you're planning a long day in the car, vets recommend stopping at least every two hours to let your dog pee, stretch their legs and have a long drink of water. If your dog gets nervous or nauseated in the car, it is safe and effective to give her Benadryl (or its generic equivalent) to calm her down. The vet-recommended dosage is 1mg per pound.
When stopping to eat during a downtown stroll, don't immediately tie your dog up outside the restaurant. Instead ask about the local laws.
In this guide, look for the pet-friendly icon [ ] if you're traveling with Fido and need a pet-friendly lodging.
The following websites have helpful pet-travel tips: Humane Society (www.humanesociety.org/animals/resources/tips/travelling_tips_pets_cars.html) Tips on travel with pets.
Best Friends Animal Society (www.bestfriends.org) May have you driving to Kanab just to adopt a pet, but also has a wealth of general info.
#### Money
The dollar (commonly called a buck) is divided into 100 cents. Coins come in denominations of one cent (penny), five cents (nickel), 10 cents (dime), 25 cents (quarter) and the rare 50-cent piece (half dollar). Notes come in one-, five-, 10-, 20-, 50- and 100-dollar denominations.
See the inside front cover for exchange rates and Click here for information on costs.
#### ATMS & CASH
ATMs are great for quick cash influxes and can negate the need for traveler's checks entirely, but watch out for ATM surcharges as they may charge $2 to $3 per withdrawal. Some ATMs in Vegas may charge $5 for withdrawing cash – read before you click enter.
The Cirrus and Plus systems both have extensive ATM networks that will give cash advances on major credit cards and allow cash withdrawals with affiliated ATM cards. Look for ATMs outside banks and in large grocery stores, shopping centers, convenience stores and gas stations.
To avoid possible bank holds for sums larger than the transaction, or accountdraining scams, consider paying with cash at gas stations instead of using your debit card at the pump.
#### CREDIT CARDS
Major credit cards are widely accepted throughout the Southwest, including at car-rental agencies and most hotels, restaurants, gas stations, grocery stores and tour operators.
American Express ( 800-528-4800; www.americanexpress.com)
Diners Club ( 800-234-6377; www.dinersclub.com)
Discover ( 800-347-2683; www.discover.com)
MasterCard ( 800-627-8372; www.mastercard.com)
Visa ( 800-847-2911; www.visa.com)
#### CURRENCY EXCHANGE
Banks are usually the best places to exchange currency. Most large city banks offer currency exchange, but banks in rural areas do not. Currency-exchange counters at the airports and in tourist centers typically have the worst rates; ask about fees and surcharges first. Travelex ( 877-414-6359; www.travelex.com) is a major currency-exchange company but American Express ( 800-297-2977; www.americanexpress.com) travel offices may offer better rates.
#### TRAVELER'S CHECKS
With the advent of ATMs, traveler's checks are becoming obsolete, except as a trustworthy backup. If you carry them, buy them in US dollars; local businesses may not cash them in a foreign currency. Keeping a record of the check numbers and those you have used is vital for replacing lost checks, so keep this information separate from the checks themselves. For refunds on lost or stolen checks call American Express ( 800- 221-7282) or Visa ( 800-227-6811).
#### TIPPING
Taxi drivers expect a 15% tip. Waiters and bartenders rely on tips for their livelihoods: tip $1 per drink to bartenders and 15% to 20% to waiters and waitresses unless the service is terrible (in which case a complaint to the manager is warranted) or about 20% if the service is great. Don't tip in fast-food, takeout or buffet-style restaurants where you serve yourself. Baggage carriers in airports and hotels should get $2 per bag or $5 per cart minimum. In hotels with daily housekeeping, leave a few dollars in the room for the staff for each day of your stay when you check out. In budget hotels, tips are not expected but are always appreciated.
#### Post
The US Postal Service (USPS; 800-275-8777; www.usps.gov) provides great service for the price. For 1st-class mail sent and delivered within the US, postage rates are 44¢ for letters up to 1oz (20¢ for each additional ounce) and 29¢ for standard-size postcards. If you have the correct postage, drop your mail into any blue mailbox. To send a package weighing 13oz or more, go to a post office.
International airmail rates for letters up to 1oz and postcards are 80¢ to Canada or Mexico, and 98¢ to other countries. You can have mail sent to you care of General Delivery at most big post offices in the Southwest. When you pick up your mail, bring some photo identification. General delivery mail is usually held for up to 30 days. Most hotels will also hold mail for incoming guests.
Call private shippers such as United Parcel Service (UPS; 800-742-5877; www.ups.com) and Federal Express (FedEx; 800-463-3339; www.fedex.com) to send more important or larger items.
#### Telephone
Always dial '1' before toll-free (800, 888 etc) and domestic long-distance numbers. Remember that some tollfree numbers may only work within the region or from the US mainland, for instance. But you'll only know if it works by making the call.
All phone numbers in the US consist of a threedigit area code followed by a seven-digit local number. All five Southwestern states require you to dial the full 10-digit number for all phone calls because each state has more than one area code. You will not be charged for longdistance fees when dialing locally. When calling a cell phone anywhere in the USA you need to always dial the 10-digit number; however, you do not need to dial the country code ( 1) when calling from within the United States.
Pay phones aren't as readily found at shopping centers, gas stations and other public places now that cell phones are more prevalent. But keep your eyes peeled and you'll find them. If you don't have change, you can use a calling card.
To make international calls direct, dial 011 + country code + area code + number. (An exception is to Canada, where you dial 1 + area code + number. International rates apply for Canada.)
For international operator assistance, dial 0. The operator can provide specific rate information and tell you which time periods are the cheapest for calling.
If you're calling the Southwest from abroad, the international country code for the US is 1. All calls to the Southwest are then followed by the area code and the seven-digit local number.
#### CELL PHONES
In the USA, cell phones use GSM 1900 or CDMA 800, operating on different frequencies than systems in other countries. The only foreign phones that will work in the US are tri- or quadband models. If you have one of these phones, check with your service provider about using it in the US. Make sure to ask if roaming charges apply; these will turn even local US calls into pricey international calls.
If your phone is unlocked, however, you may be able to buy a prepaid SIM card for the USA, which you can insert into your international cell phone to get a local number and voicemail.
Even though the Southwest has an extensive cellular network, you'll still find a lot of coverage holes when you're driving in the middle of nowhere. Don't take undue risks thinking you'll be able to call for help from anywhere. Once you get up into the mountains or in isolated areas, cell phone reception can be sketchy at best.
#### PHONECARDS
Private prepaid phonecards are available from convenience stores, supermarkets and pharmacies. Cards sold by major telecommunications companies such as AT&T may offer better deals than start-up companies.
### Internet Access
Public libraries in most cities and towns offer free internet access, either at computer terminals or through a wireless connection, usually for 15 minutes to an hour (a few may charge a small fee). In some cases you may need to obtain a guest pass or register. Most towns have at least one shop that offers a computer to get online, and in big cities like Phoenix, Las Vegas and Salt Lake City you'll find dozens. It generally costs $10 and up to log on, which isn't cheap – if you can bring your laptop do so, as most places that serve coffee also offer free wi-fi as long as you order a drink. Several national companies – McDonald's, Panera Bread, Barnes & Noble – are now providing free wi-fi .
When places reviewed in this book have computers available for public use, it's noted with an icon. If you're traveling with a laptop, look for the wi-fi icon.
Besides coffee shops, airports and campgrounds often offer laptop owners the chance to get online for free or a small fee. You're most likely to be charged for wi-fi usage in hotels – some places charge up to $20 per day. Check the following websites for lists of free and fee-based wi-fi hot spots nationwide: www.wififreespot.com and www.wi-fihotspotlist.com.
For a selection of useful websites about Southwest USA, see (Click here).
### Legal Matters
If you are arrested for a serious offense in the US, you are allowed to remain silent, entitled to have an attorney present during any interrogation and presumed innocent until proven guilty. You have the right to an attorney from the very first moment you are arrested. If you can't aff ord one, the state must provide one for free. All persons who are arrested are legally allowed to make one phone call. If you don't have a lawyer or family member to help you, call your embassy or consulate.
The minimum age for drinking alcoholic beverages in the US is 21; you'll need a government-issued photo ID to prove it (such as a passport or a US driver's license). Stiff fines, jail time and penalties can be incurred if you are caught driving under the influence of alcohol or providing alcohol to minors.
The legal ages for certain activities around the Southwest vary by state. For information about speed limits and other road rules, see Click here.
### National & State Parks
Before visiting any national park, check out its website, using the navigation search tool on the National Park Service (NPS) home page (www.nps.gov). On the Grand Canyon's website (www.nps.gov/grca), you can download the seasonal newspaper, _The Guide_ , for the latest information on prices, hours and ranger talks. There is a separate edition for both the North and South Rims.
At the entrance of a national or state park, be ready to hand over cash (credit cards may not always be accepted). Costs range from nothing at all to $25 per vehicle for a seven-day pass. If you're visiting several parks in the Southwest, you may save money by purchasing the America the Beautiful (http://store.usgs.gov/pass; pass $80) annual pass. It admits four adults and their children under 16 for no additional cost to all national parks and federal recreational lands for one year. US citizens and permanent residents aged 62 and older are eligible for a lifetime Senior Pass. US citizens and permanent residents with a permanent disability may qualify for a free Access Pass.
### EMERGENCIES
If you need any kind of emergency assistance, such as police, ambulance or firefighters, call 911. A few rural phones might not have this service, in which case dial 0 for the operator and ask for emergency assistance.
Due to ongoing fiscal woes, many state governments across the West and Southwest are slashing their budgets for state parks. State parks in Arizona and Utah have been particularly hard hit, and it's not yet clear which ones will ultimately survive. In Utah, funding has been cut from $12.2 million to $6.8 million in the last few years. Some state parks in Arizona are operating on a five-day schedule, closed Tuesdays and Wednesdays. Before visiting a state park, check its website to confirm its status.
### Photography
Print film can be found in drugstores and at specialty camera shops. Digital camera memory cards are available at chain retailers such as Best Buy and Target.
Furthermore, almost every town of any size has a photo shop that stocks cameras and accessories. With little eff ort you should be able to find a shop to develop your color print film in one hour, or at least on the same day. Expect to pay about $7 to process a roll of 24 color prints. One-hour processing is more expensive, usually around $12. FedEx Office is a major chain of copy shops with one-stop digital photo printing and CD-burning stations.
For information on photographing reservations and pueblos, see (Click here).
### TIPS FOR SHUTTERBUGS
»M orning and evening are the best times to shoot. The same sandstone bluff can turn four or five different hues throughout the day, and the warmest hues will be at sunset. Underexposing the shot slightly (by a halfstop or more) can bring out richer details in red tones.
»W hen shooting red rocks, a warming filter added to an SLR lens can enhance the colors of the rocks and reduce the blues of overcast or flat-light days. Achieve the same effect on any digital camera by adjusting the white balance to the automatic 'cloudy' setting (or by reducing the color temperature).
»D on't shoot into the sun or include it in the frame; shoot what the sunlight is hitting. On bright days, move your subjects into shade for close-up portraits.
»A zoom lens is extremely useful; most SLR cameras have one. Use it to isolate the central subject of your photos. A common composition mistake is to include too much landscape around the person or feature that's your main focus.
### Tours
For travelers with a limited amount of time or specialized interests, tours may be the best option. Always read the fine print; tour prices may or may not include airfare, meals, taxes and tips. Well-run Backroads, Inc ( 800-462- 2848; www.backroads.com) offers hiking and cycling trips for all ages across Arizona, New Mexico and southern Utah.
The sophisticated Washington, DC, Smithsonian Journeys ( 887-338-8687; www.smithsonianjourneys.org) organizes academically inclined, upscale tours such as Santa Fe Opera and Astronomy in Arizona.
Road Scholar ( 877- 4254-5768; www.roadscholar.org), created by Elderhostel, Inc, offers a whole host of educational programs.
For an alternative to pure tourism, look into Global Citizens Network (GCN; 612-436-8270, 800-644- 9292; www.globalcitizens.org) where socially-conscious visitors can work with the Navajo Nation in both Arizona and New Mexico.
Information about smaller site- or town-specific tour companies is sprinkled throughout the individual chapters of this guidebook.
### Travelers with Disabilities
Travel within the Southwest is getting better for people with disabilities, but it's still not easy. Public buildings are required to be wheelchair accessible and to have appropriate rest-room facilities. Public transportation services must be made accessible to all, and telephone companies have to provide relay operators for the hearing impaired. Many banks provide ATM instructions in braille, curb ramps are common, many busy intersections have audible crossing signals, and most chain hotels have suites for guests with disabilities. Still, it's best to call ahead to check.
Disabled US residents and permanent residents may be eligible for the lifetime Access Pass, a free pass to national parks and 2000 recreation areas managed by the federal government. Visit http://store.usgs.gov/pass/access.html.
For up-to-date information about wheelchair-accessible activities in Arizona, visit Accessing Arizona (www.accessingarizona.com). You'll find up-to-the-minute information about travel and accessibility issues at Rolling Rains Report (www.rollingrains.com).
Wheelchair Getaways ( main office 800-642-2042, Arizona 888-824-7413, New Mexico 505-247-2526, Las Vegas 602-494-8257; www.wheelchairgetaways.com) rents accessible vans in Phoenix, Tucson, Albuquerque, Las Vegas and Reno.
A number of organizations specialize in the needs of travelers with disabilities: Disabled Sports USA ( 301-217-0960; www.dsusa.org) Offers sports and recreation programs for those with disabilities and publishes _Challenge_ magazine.
Mobility International USA ( 541-343-1284; www.miusa.org) Advises on mobility issues, but primarily runs an educational exchange program.
Society for Accessible Travel & Hospitality (SATH; 212-447-7284; www.sath.org) Advocacy group provides general information for travelers with disabilities. Splore ( 801-484-4128; www.splore.org) Offers accessible outdoor adventure trips in Utah.
# Transport-
ation
Top of section
## GETTING THERE & AWAY
Most travelers to the Southwest arrive by air and car, with bus running a distant third place. The train service is little used but available. Major regional hubs include Las Vegas (Click here), Phoenix (Click here), Albuquerque (Click here) and Salt Lake City (Click here).
Flights, tours and rail tickets can be booked online at www.lonelyplanet.com/bookings. For information about entering the USA from overseas, see Click here.
### Air
Unless you live in or near the Southwest, flying in and renting a car is the most time-efficient option. Most domestic visitors fly into Phoenix, Las Vegas or Albuquerque. International visitors, however, usually first touch down in Los Angeles, New York, Miami, Denver or Dallas/Fort Worth before catching an onward flight to any number of destinations.
### Airports & Airlines
International visitors might consider flying into Los Angeles and driving. Los Angeles Airport (LAX; 310-646-5252; www.lawa.org/welcomeLAX.aspx) is an easy day's drive from western Arizona or southwestern Utah, via Las Vegas. The following airports are located in the Southwest.
Albuquerque International Sunport (ABQ; 505-244-7700; www.cabq.gov/airport; ) Serving Albuquerque and all of New Mexico, this is a small and friendly airport that's easy to navigate.
Denver International Airport (DEN; 303-342-2000; www.flydenver.com; ) Serving southern Colorado, Denver is only four hours from northeastern New Mexico by car.
McCarran International Airport (LAS; 702-261-5211; www.mccarran.com; ) Serves Las Vegas and southern Utah. Las Vegas is 290 miles from the South Rim of the Grand Canyon and 277 miles from the North Rim.
Salt Lake City International Airport (SLC; 801-575-2400; www.slcairport.com; ) Serving Salt Lake City and northern Utah, it's a good choice if you're headed to the North Rim of the Grand Canyon and the Arizona Strip.
Sky Harbor International Airport (PHX; 602-273-3300; www.skyharbor.com; ) Located in Phoenix, this busy airport is 220 miles from the South Rim of the Grand Canyon and 335 miles from the North Rim.
Tucson International Airport (TUS; 520-573-8100; www.tucsonairport.org; ) Serving Tucson and southern Arizona, this is a small and easily navigated airport.
### CLIMATE CHANGE & TRAVEL
Every form of transport that relies on carbon-based fuel generates CO2, the main cause of human-induced climate change. Modern travel is dependent on aeroplanes, which might use less fuel per kilometer per person than most cars but travel much greater distances. The altitude at which aircraft emit gases (including CO2) and particles also contributes to their climate change impact. Many websites offer 'carbon calculators' that allow people to estimate the carbon emissions generated by their journey and, for those who wish to do so, to off set the impact of the greenhouse gases emitted with contributions to portfolios of climate-friendly initiatives throughout the world. Lonely Planet offsets the carbon footprint of all staff and author travel.
### Land
#### Border Crossings
From Yuma, AZ (Click here), you can cross into Baja California and Mexico. Nogales, AZ, is also a prime border town. For more information about traveling south of the Southwest, pick up Lonely Planet's _Baja & Los Cabos_ and _Mexico_ guides. The biggest gateway if you're traveling in New Mexico is El Paso, TX, to reach Ciudad Juarez.
Don't forget your passport if you are crossing the border.
For information on visas, see Click here.
#### Bus
Long-distance buses can get you to major points within the region, but then you will need to rent a car (see Click here), as public transportation to the national parks, including the Grand Canyon, is nonexistent. Bus lines also don't serve many of the smaller towns, including important tourist hubs like Moab. Additionally, bus terminals are often in more dangerous areas of town. Having said that, Greyhound ( 800-231-2222; www.greyhound.com) is the main US bus system.
To save money on bus travel, plan seven days in advance, travel on weekdays, travel with a companion and avoid holiday travel. Search the internet for special deals. Students, military personnel and seniors receive discounts.
When you've graduated from Green Tortoise ( 800-867-8647; www.greentortoise.com), a rolling mosh pit of youthful sightseers, but you still want to sleep on a bus and hang with like-minded adventurers, look into Adventure Bus ( 888-737-5263; www.adventurebus.com). It specializes in travel to the Grand Canyon and the Moab area and recently added an Arizona Desert Explorer trip.
#### Car & Motorcycle
As mentioned, while the quickest way to get to the Southwest is by plane, the best way to get around is by car. Many places can only be reached by car, and it's nearly impossible to explore the national parks by bus.
Then there's the small matter of driving. If you love driving, you'll be in heaven. Of the 160,000 or so miles in the national highway system, the Southwest has more stunning miles than any other part of the country – just look at all the scenic byway signs!
Long-distance motorcycle driving is dangerous because of the fatigue factor that sets in. Please use caution during long hauls.
For more details about getting around the region by car or motorcycle, including road rules, see Click here.
#### Train
Three Amtrak ( 800-872-7245; www.amtrak.com) trains cut a swath through the Southwest, but they are not connected to one another. Use them to reach the region but not for touring around. The Southwest Chief offers a daily service between Chicago and Los Angeles, via Kansas City. Significant stations include Albuquerque, NM, and Flagstaff and Williams, AZ. As an added value, on-board guides provide commentary through national parks and Native American regions. The California Zephyr offers a daily service between Chicago and San Francisco (Emeryville) via Denver, with stops in Reno, NV and Salt Lake City, UT. The Sunset Limited runs thrice weekly from Los Angeles to New Orleans and stops in Tucson, AZ.
### CROSSING THE MEXICAN BORDER
At the time of research, the issue of crime-related violence in Mexico was front and center in the international press. Nogales, AZ, for example, is safe for travelers, but Nogales, Mexico was a major locus for the drug trade and its associated violence. As such, we cannot safely recommend crossing the border for an extended period until the security situation changes. Day trips are OK, but anything past that may be risky.
The US State Department recommends that travelers visit its website before traveling to Mexico http://travel.state.gov/travel/cis_pa_tw/cis/cis_970.html). Here you can check for travel updates and warnings and confirm the latest border crossing requirements. Before leaving, US citizens can sign up for the Smart Traveler Enrollment Program (STEP; http://travel.state.gov/travel/tips/registration/registration_4789.html) to receive email updates prior to departure.
US and Canadian citizens returning from Mexico must present a US passport or passport card, and Enhanced Driver's License or a Trusted Traveler Card (either NEXUS, SENTRI or FAST cards). US and Canadian children under the age of 16 can also enter using their birth certificate, a Consular Report of Birth Abroad, naturalization certificate or Canadian citizenship card. All other nationals must carry their passport and, if needed, visas for entering Mexico and reentering the US. Regulations change frequently, so get the latest scoop at www.cbp.gov.
Driving across the border is a serious hassle. At the border or at the checkpoint 13 miles south of it, you need to pick up a free Mexican tourist card. US or other nations' auto insurance is not valid in Mexico and we strongly suggest you buy Mexican insurance on the US side of the border. Rates range from $19 to $26 per day, depending on coverage and your car's age and model.
Book tickets in advance and look for plenty of available deals. Children, seniors and military personnel receive good discounts. Amtrak's USA Rail Pass offers coach class travel for 15 ($389), 30 ($579) and 45 ($749) days, with travel limited to 8, 12 or 18 one-way segments. Changing trains or buses completes one segment. In other words, every time you step off the train to either visit a city or to get on another Amtrak train or vehicle, you use up one of your allotted segments. Plan carefully.
It's not unusual for Amtrak trains, especially on longer routes, to run late.
### GETTING TO THE SOUTHWEST
### BY BUS
---
### FROM | ### TO | ### FARE ($)* | ### DURATION (HR)
Chicago, IL | Las Vegas, NV | 330-425 | 38-40
Dallas, TX | Albuquerque, NM | 188-259 | 13-15
Los Angeles, CA | Las Vegas, NV | 84-129 | 6
Portland, OR | Salt Lake City, UT | 194-267 | 18
*Round-trip prices
### BY CAR OR MOTORCYCLE
### FROM | ### TO | ### VIA | ### DURATION (HR)
Dallas, TX | Albuquerque, NM | I-35 & I-40 | 11½
Denver, CO | Santa Fe, NM | I-25 | 6½
Los Angeles, CA | Las Vegas, NV | I-15 | 5
San Diego, CA | Phoenix, AZ | I-8 | 7
San Francisco, CA | Santa Fe, NM | I-5 & I-40 | 19
### BY TRAIN
### FROM | ### TO | ### FARE ($)* | ### DURATION (HR)
Chicago, IL | Albuquerque, NM | 280 | 26
Chicago, IL | Salt Lake City, UT | 363 | 35
Los Angeles, CA | Flagstaff , AZ | 148 | 11
Los Angeles, CA | Tucson, AZ | 78 | 10
San Francisco, CA | Salt Lake City, UT | 180 | 18
*Round-trip prices
## GETTING AROUND
Once you reach the Southwest, traveling by car is the best way to get around and allows you to reach rural areas not served by public transportation. If you do not relish long drives, you can always take buses and trains between a limited number of major destinations and then rent a car. But that's both time-consuming and more expensive than driving yourself and stopping everywhere along the way.
### Air
Because distances between places in the Southwest are so great, regional airports are located in a number of smaller towns such as Yuma and Flagstaff (both in Arizona), and Carlsbad and Taos (both in New Mexico). But since these airports primarily serve residents and business people, and because flying between these places is quite expensive and impractical, we have focused on the major air gateways (see Click here). Still, you can find information about these smaller airports scattered throughout the regional chapters.
#### Airlines in the Southwest
Great Lakes ( 307-433-2899; www.greatlakesav.com) Direct flights between Prescott, AZ, and Los Angeles, CA, and between Farmington, CO (near Durango), and Denver, CO.
Southwest Airlines ( 800-435-9792; www.southwest.com) Major regional and budget carrier; flies to Albuquerque, NM, Tucson, AZ, Phoenix, AZ, Las Vegas, NV, Salt Lake City, UT, and El Paso, TX.
United Express ( 800-864-8331; www.united.com) Flies between Los Angeles International Airport (LAX) and Yuma, AZ.
US Airways ( 800-428-4322; www.usairways.com) Flies between Flagstaff, AZ, and Sky Harbor International Airport in Phoenix.
### Bicycle
Cycling is a cheap, convenient, healthy, environmentally sound and, above all, fun way of traveling. In the Southwest – because of altitude, distance and heat – it's also a good workout. Cyclists should carry at least a gallon of water and refill bottles at every opportunity since dehydration (Click here) is a major problem in the arid Southwest.
Airlines accept bicycles as checked luggage, but since each airline has specific requirements, it's best to contact them for details. Bicycle rentals are listed throughout this guide whenever there's a desirable place to cycle that also offers rentals. Expect to spend $25 to $50 a day for a beach cruiser or basic mountain bike. For more on cycling, see Click here. Moab (Click here) is generally considered the mountain-biking capital of the Southwest. The countryside around Sedona (Click here) is great for biking.
Cyclists are permitted on some interstates in all five Southwestern states, but typically not in urban areas or where there's no alternative route or frontage road. Check the laws and maps for each state before hopping on an interstate and, where possible, ride adjacent frontage roads instead of the freeway. On the road, cyclists are generally treated courteously by motorists. In New Mexico and in certain counties and localities in Nevada and Arizona (including Flagstaff and Tucson), helmets are required by law for those under 18. There are no requirements in Colorado and Utah, but in any case, they should be worn to reduce the risk of head injury.
Cycling has increased in popularity so much in recent years that concerns have risen over damage to the environment, especially from unchecked mountain biking. Know your environment and regulations before you ride. Bikes are restricted from entering wilderness areas and some designated trails but may be used in Bureau of Land Management (BLM) singletrack trails and National Park Service (NPS) sites, state parks, national and state forests.
### Bus
Greyhound ( 800-231-2222; www.greyhound.com) is the main carrier to and within the Southwest, operating buses several times a day along major highways between large towns. Greyhound only stops at smaller towns that happen to be along the way, in which case the 'bus terminal' is likely to be a grocery-store parking lot or something similar. In this scenario, boarding passengers usually pay the driver with exact change. To see if Greyhound serves a town, look for the blue and red Greyhound symbol. The best schedules often involve overnight routes; the best fares often require seven days' advance notice.
Greyhound no longer offers service to Santa Fe, NM. Your best bet is to ride to Albuquerque, NM, then hop onto the adjacent Rail Runner train (Click here), which takes 90 minutes to get to Santa Fe.
### Car & Motorcycle
The interstate system is thriving in the Southwest, but smaller state roads and fine scenic byways (see the regional chapters for these beauties) offer unparalleled opportunities for exploration. As for the former, I-10 runs east–west through southern Arizona, I-40 runs east–west through Arizona and central New Mexico, I-70 runs east–west through central Utah and I-80 runs east–west through northern Utah. In the north–south direction, I-15 links Las Vegas to Salt Lake City and I-25 runs through central New Mexico to Denver, CO. The oh-so-classic Route 66 more or less follows the modern-day I-40 through Arizona and New Mexico.
#### Automobile Associations
The American Automobile Association (AAA; 800-874-7532; www.aaa.com) provides members with maps and other information. Members also get discounts on car rentals, air tickets and some hotels and sightseeing attractions, as well as emergency road service and towing ( 800-222-4357). AAA has reciprocal agreements with automobile associations in other countries. Be sure to bring your membership card from your home country.
Emergency breakdown services are available 24 hours a day.
#### Driver's Licenses
Foreign visitors can legally drive a car in the USA for up to 12 months using their home country's driver's license. However, an IDP (International Driving Permit) will have more credibility with US traffic police, especially if your normal license doesn't have a photo or isn't in English. Your home country's automobile association can issue an IDP, valid for one year. Always carry your license together with the IDP.
### BUSES AROUND THE SOUTHWEST
### FROM | ### TO | ### FARE ($)* | ### DURATION (HR)
---|---|---|---
Albuquerque, NM | Salt Lake City, UT | 125-176 | 19
Las Vegas, NV | Phoenix, AZ | 45-65 | 8-9
Phoenix, AZ | Tucson, AZ | 21-28 | 38-40
Tucson, AZ | Albuquerque, NM | 99-140 | 9-14
*One-way prices
#### Fuel
Gas stations are common and many are open 24 hours a day. Small-town stations may be open only from 7am to 8pm or 9pm.
At most stations, you must pay before you pump. The more modern pumps have credit/debit card terminals built into them, so you can pay right at the pump. At more expensive, 'full service' stations, an attendant will pump your gas for you; no tip is expected.
#### Insurance
Liability insurance covers people and property that you might hit. For damage to the actual rental vehicle, a collision damage waiver (CDW) is available for about $26 to $28 per day. If you have collision coverage on your vehicle at home, it might cover damages to rental cars; inquire before departing. Additionally, some credit cards offer reimbursement coverage for collision damages when you use the card to rent a car; again, check before departing. There may be exceptions for rentals of more than 15 days or for exotic models, jeeps, vans and 4WD vehicles. Check your policy.
Note that many rental agencies stipulate that damage a car suffers while being driven on unpaved roads is not covered by the insurance they offer. Check with the agent when you make your reservation.
#### Rental
Rental cars are readily available at all airports and many downtown city locations. With advance reservations for a small car, the daily rate with unlimited mileage is about $30 to $46, though you might find lower rates. Larger companies don't require a credit card deposit, which means you can cancel without a penalty if you find a better rate. Midsize cars are often only a tad more expensive. Since deals abound and the business is competitive, it pays to shop around. Aggregator sites like www.kayak.com can provide a good cross-section of options. You can often snag great last-minute deals via the internet; rental reservations made in conjunction with an airplane ticket often yield better rates too.
Most companies require that you have a major credit card, are at least 25 years old and have a valid driver's license. Some national agencies may rent to drivers between the ages of 21 and 25 but may charge a daily fee.
If you decide to fly into one city and out of another, you may incur drop-off charges. Check the amount before finalizing your plans. Bidding for cars on Priceline (www.priceline.com) is one of the cheapest ways to hire a vehicle – you can pick the city, but not the rental company. Priceline even allows you to pick up a car in one city and drop it off in another. However, dropping off the car in another state may raise the rate.
#### Road Conditions & Hazards
Be extra defensive while driving in the Southwest. Everything from dust storms to snow to roaming livestock can make conditions dangerous. Near Flagstaff, watch for elk at sunset on I-17. The animals apparently like to soak up warmth from the blacktop (or so we heard). You don't want to hit an elk, which can weigh between 500 and 900 pounds.
Distances are great in the Southwest and there are long stretches of road without gas stations. Running out of gas on a hot and desolate stretch of highway is no fun, so pay attention to signs that caution 'Next Gas 98 Miles.'
For updates on road conditions within a state, call 511. From outside a state, try one of the following:
Arizona ( 888-411-7623; www.az511.com)
Nevada ( 877-687-6237; www.safetravelusa.com/nv)
New Mexico ( 800-432-4269; http://m.nmroads.com)
Southern Colorado ( 303-639-1111; www.cotrip.org)
Utah ( 866-511-8824; www.commuterlink.utah.gov)
### I'M JUST WORKING FOR THE BORDER PATROL...
Officers of the federal United States Border Patrol (USBP) are ubiquitous in southern Arizona. Border patrol officers are law enforcement personnel who have the ability to pull you over, ask for ID and search your car if they have reasonable cause. Be aware that there's a good chance they'll flash you to the side of the road if you're driving down back roads in a rental or out-of-state car. This is because said roads have been used to smuggle both people and drugs north from Mexico. As a result we advise you to always carry ID, including a valid tourist visa if you're a foreign citizen, and car registration (if it's a rental car, your rental contract should suffice). Be polite and they should be polite to you. Agents may ask to see inside your trunk (boot) and backseat; it's probably best to let them do so (assuming you have nothing illegal to hide).
It's almost guaranteed that you'll drive through checkpoints down here. If you've never done so before, the 'stop side' of the checkpoints is the route going from south (Mexico) to north (USA). There's a chance you'll just be waved through the checkpoint; otherwise slow down, stop, answer a few questions (regarding your citizenship and the nature of your visit) and possibly pop your trunk and roll down your windows so officers can peek inside your car. Visitors may consider the above intrusive; all we can say is grin and bear it. For better or worse, this is a reality of traveling in southern Arizona.
#### Road Rules
Driving laws are slightly different in each state, but all require the use of safety belts. In every state, children under five years of age must be placed in a child safety seat secured by proper restraints. For more details about seat belt laws for children see (Click here).
The maximum speed limit on all rural interstates is 75mph, but that drops to 65mph in urban areas in Colorado, Nevada and Utah. New Mexico allows urban interstate drivers to barrel through at 75mph. The limit for Arizona drivers in urban areas is 65mph, but lawmakers require cars to crawl through high-density areas at 55mph. On undivided highways, the speed limit range will vary from 30mph in populated areas to between 65mph and 70mph on stretches where tumbleweeds keep pace with wily coyotes.
### INSPECTION STATIONS
When entering California, agricultural inspection stations at the Arizona–California border may ask you to surrender fruit in an attempt to stop the spread of pests associated with produce.
### Motor Home (RV)
Rentals range from ultra-efficient VW campers to plush land yachts. After the size of the vehicle, consider the impact of gas prices, gas mileage, additional mileage costs, insurance and refundable deposits; these can add up quickly. It pays to shop around and read the fine print. Given the myriad permutations in rental choices, it's incredibly hard to generalize, but to get you started, you might expect a base rate for a four-person vehicle to run $1050 to $1300 weekly in the summer, plus 32¢ for each additional mile. Get out a good map and a calculator to determine if it's practical.
Before heading out, consult www.rvtravel.com for tips galore then purchase a campground guide from Woodall's (www.woodalls.com), which also has a great all-round website, or Kamp-grounds of America (KOA; 406-248-7444; www.koa.com), and hit the road.
For RV rentals contact the following:
Adventure Touring RV Rentals ( 866-457-7997; www.adventuretouring.com) Serving Los Angeles, Las Vegas, Phoenix and Salt Lake City.
Adventure on Wheels ( 800-943-3579; http://wheels9.com) Located in Las Vegas.
Cruise America ( 800-671-8042; www.cruiseamerica.com) Locations nationwide, including Las Vegas, Phoenix, Flagstaff, Tucson, Salt Lake City, Albuquerque and Colorado Springs.
### Train
Several train lines provide services using historic steam trains. Although they are mainly for sightseeing, the Williams to Grand Canyon (Click here) run is a destination in itself. More scenic train rides are located in Clarkdale, AZ (Click here), Chama, NM (Click here), Santa Fe, NM (Click here), and Durango, CO (Click here).
For info on Amtrak trains, see Click here.
## SEND US YOUR FEEDBACK
We love to hear from travell ers – your comments keep us on our toes and help make our books better. Our well- travell ed team reads every word on what you loved or loathed about this book. Although we cannot reply individually to postal submissions, we always guarantee that your feedback goes straight to the appropriate authors, in time for the next edition. Each person who sends us information is thanked in the next edition – and the most useful submissions are rewarded with a free book.
Visit www.lonelyplanet.com/contact to submit your updates and suggestions or to ask for help. Our award-winning website also features inspirational travel stories, news and discussions.
Note: We may edit, reproduce and incorporate your comments in Lonely Planet products such as guidebooks, websites and digital products, so let us know if you don't want your comments reproduced or your name acknowledged. For a copy of our privacy policy visit www.lonelyplanet.com/privacy.
## OUR READERS
Many thanks to the travellers who used the last edition and wrote to us with helpful hints, useful advice and interesting anecdotes:
Melissa Bazley, John Bennett, Eleanor Butler, Kim Dorin, Tony Fox, Jaclyn Gingrich, Giovanni Govoni, Duncan Grant, Mandeep Gulati, Arnaud Kaelbel, Marijn Kastelein, Tamara Kozak, Michael McMillan, Carsten Menke, Leah Moore, Janét Moyle, Michael Nicholas, Melanie Nisbet, Dale Parriott, Francesca Pittoni, Charlotte Pothuizen, Ulrich Raich, Ann & Bill Stoughton, Emanuela Tasinato, Silke Warmer, Madeleine Wasser
## AUTHOR THANKS
#### Amy C Balfour
Thank you Suki and the Southwest team for top-notch editing and mapping. Big cheers to my super-helpful co-authors Lisa, Michael, Sarah and Carolyn. Many thanks to Deb Corcoran, Tucson's greatest docent, and Judy Hellmich-Bryan, who provided the latest news for Grand Canyon National Park. A special shout out to Lucy, Michael, Madeline, Claire and Clay Gordon for their hospitality and Phoenix insights, thanks Rob Hill and a toast to Mark Baker and Bisbee's in-the-know barflies. Ninette Crunkleton and Melissa Peeler, thanks for the Arizona leads!
#### Michael Benanav
Thank you, Whitney George, in Ruidoso, for a great story about one Mike the Midget and a mysterious village beneath Bonita Lake. This summer, a huge thanks goes to the firefighters around the state. And to Kelly and Luke, thanks for always letting me go – and for always welcoming me back!
#### Sarah Chandler
My trusty co-pilot, the intrepid Jennifer Christensen, deserves serious props for remaining calm during flat tires, blizzards and a losing streak in the smoky blackjack room of the Hotel Nevada. Vek Neal and Todd Rice, thanks for being my partners in crime as we rocked out from the Double Down to the Bellagio: having that much fun is probably illegal, even in Nevada. Finally, to Jack and everyone at the Hard Rock, thanks for showing me how the locals brave Vegas nightlife (fearlessly, of course).
#### Lisa Dunford
I always meet so many kindred spirits on the Utah road. Thanks go to Nan Johnson, Peggy Egan, Trista Rayner, Nicole Muraro, David Belz, Jessica Kunzer, Lisa Varga and Ty Markham, among others. I very much enjoyed talking to you all. Thanks, too, to the many park rangers I met, for the ever-helpful job they do.
#### Carolyn McCarthy
Sincere gratitude goes out to all those who contributed to this book. An exceptionally snowy spring made it a challenge. Thanks also to Louise, Conan, Anne and the Cameron Johns family for their thoughtful hospitality. Richard proved adept at attacking the snowy passes and the all-American breakfasts. Finally, virtual microbrews go out to Melissa and the Fruita crowd for shoring me up in the home stretch.
## ACKNOWLEDGMENTS
Climate map data adapted from Peel MC, Finlayson BL & McMahon TA (2007) 'Updated World Map of the Köppen-Geiger Climate Classification', _Hydrology and Earth System Sciences,_ 11, 1633–44.
Cover photograph: Balanced Rock, Arches National Park, Utah, Andrew Marshall & Leanne Walker/LPI.
Many of the images in this guide are available for licensing from Lonely Planet Images: www.lonelyplanetimages.com.
## THIS BOOK
This 6th edition of Southwest USA was researched and written by a fabulous author team (see Our Writers), with Amy C Balfour coordinating. Wendy Yanagihara and Jennifer Denniston contributed to the Grand Canyon section. Beth Kohn wrote the Reno text. The Native American chapter was based on text by Jeff Campbell. The Travel with Children was based on text by Jennifer Denniston.
This guidebook was commissioned in Lonely Planet's Oakland office, laid out by Cambridge Publishing Management, UK, and produced by the following:
Commissioning Editors Suki Gear
Coordinating Editors Karen Beaulah, Asha Ioculari
Coordinating Cartographer Eve Kelly
Coordinating Layout Designer Paul Queripel
Managing Editors Helen Christinis, Kirsten Rawlings
Managing Cartographers Alison Lyall, Shahara Ahmed
Senior Cartographer Anita Banh
Managing Layout Designer Chris Girdler
Assisting Editors Elin Berglund, Kathryn Glendenning, Michala Green, Briohny Hooper, Amy Karafin, Hazel Meek, Emma Sangster, Ceinwen Sinclair, Helen Yeates
Assisting Cartographers Ildiko Bogdanovits, Julie Dodkins, Joelene Kowalski, Sophie Reed, Brendan Streager
Assisting Layout Designer Julie Crane
Cover Research Naomi Parker
Internal Image Research Sabrina Dalbesio
Color Designer Tim Newton
Indexer Marie Lorimer
Thanks to Lucy Birchley, Seviora Citra, Ryan Evans, Jane Hart, Yvonne Kirk, Susan Paterson, Trent Paton, Angela Tinson, Gerard Walker
####
Ebook thanks to
Ross Butler, John Carney, Hunor Csutoros, Samantha Curcio, Mark Germanchis, Liz Heynes, Matt Langley, Chris Lee Ack, Nic Lehman, Corine Liang, Ross Macaw, Douglas McClurg, Piers Pickard, Lachlan Ross, the team at Textech
# OUR STORY
A beat-up old car, a few dollars in the pocket and a sense of adventure. In 1972 that's all Tony and Maureen Wheeler needed for the trip of a lifetime – across Europe and Asia overland to Australia. It took several months, and at the end – broke but inspired – they sat at their kitchen table writing and stapling together their first travel guide, _Across Asia on the Cheap_. Within a week they'd sold 1500 copies. Lonely Planet was born.
Today, Lonely Planet has offices in Melbourne, London and Oakland, with more than 600 staff and writers. We share Tony's belief that 'a great guidebook should do three things: inform, educate and amuse'.
# Our Writers
### Amy C Balfour
Amy has hiked, biked, skied and gambled her way across the Southwest, finding herself returning again and again to Flagstaff , Monument Valley and, always, the Grand Canyon. On this trip she fell hard for Bisbee and Chiricahua National Monument. When she's not daydreaming about red rocks and green chile cheeseburgers, she's writing about food, travel and the outdoors. Amy has authored or co-authored 11 guidebooks for Lonely Planet, including _Los Angeles Encounter, California, Hawaii and Arizona_.
### Michael Benanav
Michael came to New Mexico in 1992 and quickly fell under its spell; soon after, he moved to a rural village in the Sangre de Cristo foothills, where he still lives. A veteran international traveler, he can't imagine a better place to come home to after a trip. Aside from his work for LP, he's authored two non-fiction books and writes and photographs for magazines and newspapers. His website is www.michaelbenanav.com.
### Sarah Chandler
Long enamored of Sin City's gritty enchantments, Sarah jumped at the chance to sharpen her blackjack skills while delving into the atomic and alien mysteries of rural Nevada. In Vegas, Sarah learned the secret art of bypassing velvet ropes, bounced from buffets to pool parties, and explored the seedy vintage glamour of downtown. Sarah is currently based between the US and Amsterdam, where she works as a writer, actor, and lecturer at Amsterdam University College. When in doubt, she always doubles down.
### Lisa Dunford
As one of the possibly thousands of descendants of Brigham Young, Lisa was first drawn to Utah by ancestry. But it's the incredible red rocks that keep her coming back. Driving the remote backroads outside Bluff , she was once again reminded how here the earth seems at its most elemental. Before becoming a freelance Lonely Planet author 10 years ago, Lisa was a newspaper editor and writer in South Texas. Lisa co-authored Lonely Planet's _Zion & Bryce Canyon_
### Carolyn McCarthy
Author Carolyn McCarthy was introduced to southern Colorado as a university freshman, when a freak blizzard stranded her orientation group in tents at 12,000ft in the Sangre de Cristo range. With sagebrush, powdery peaks and Spanish lore, the region soon became a favorite. In the last seven years she has contributed to more than a dozen Lonely Planet titles. She has also written for _National Geographic, Outside_ and _Lonely Planet Magazine_ , among other publications. You can follow her Americas blog at www.carolynswildblueyonder.blogspot.com.
### Contributing Authors
Jeff Campbell has been a travel writer for Lonely Planet since 2000. He was the coordinating author of three editions of USA, as well as editions of _Southwest USA, Zion & Bryce National Parks, Hawaii, Florida_, and _Mid-Atlantic Trips_ , and he's been a contributor on other titles. He wishes that he called the Southwest home, but next best is meeting and writing about those who do.
David Lukas is a professional naturalist whose travels and writing take him around the American West and further afield. He has contributed environment and wildlife chapters to about 20 Lonely Planet guides. David's favorite Southwest moment was getting up to watch sunrise on the magnificent hoodoos at Bryce Canyon (don't miss it!).
Published by Lonely Planet Publications Pty Ltd
ABN 36 005 607 983
6th edition – June 2012
ISBN 978 1 74321 075 8
© Lonely Planet 2012 Photographs © as indicated 2012
All rights reserved. No part of this publication may be sold or hired without the written permission of the publisher. Lonely Planet and the Lonely Planet logo are trademarks of Lonely Planet and are registered in the US Patent and Trademark Office and in other countries. Lonely Planet does not allow its name or logo to be appropriated by commercial establishments, such as retailers, restaurants or hotels. Please let us know of any misuses: lonelyplanet.com/ip.
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Qatar Airways announces $69 million revenue loss this year
The boycott locked Qatar Airways out of the airspace of Bahrain, Egypt, Saudi Arabia and the United Arab Emirates, forcing the airline to take longer flights consuming more jet fuel, raising expenses.
Source: Associated Press
Last update: 19 September 2018 | 11:38
In this Jan. 15, 2015, file photo, a Qatar Airways jet arriving from Doha, Qatar, approaches the gate at the airport in Frankfurt, Germany. (AP Photo)
DUBAI, United Arab Emirates: Qatar Airways suffered a $69 million loss this fiscal year, an over $800 million swing from the year before that the long-haul carrier blamed on the ongoing boycott of Doha by four Arab nations.
The loss by the flagship carrier shows the challenges still facing Qatar, a small, energy-rich nation that juts out like a thumb on the Arabian Peninsula. However, the airline struck a defiant tone while releasing its results for the fiscal year that ended March 31.
"This turbulent year has inevitably had an impact on our financial results, which reflect the negative effect the illegal blockade has had on our airline," Qatar Airways CEO Akbar al-Baker said in a statement Tuesday.
"However, I am pleased to say ... the impact has been minimized - and has certainly not been as negative as our neighboring countries may have hoped for," he added.
The Doha-based airline reported revenue of $11.5 billion in 2018. It also adjusted its profit in 2017 to $766 million off revenue of $10.7 billion, a result that didn't include the effect of the boycott that began June 5, 2017.
The boycott locked Qatar Airways out of the airspace of Bahrain, Egypt, Saudi Arabia and the United Arab Emirates, forcing the airline to take longer flights consuming more jet fuel, raising expenses. The carrier said 18 routes were "closed due to the illegal blockade."
Boycotting nations say the crisis stems from Qatar's support for extremist groups in the region, charges denied by Doha. Their demands include Qatar limiting diplomatic ties to Iran, shutting down the state-funded Al-Jazeera satellite news network and other media outlets, and severing ties to all "terrorist organizations," including the Muslim Brotherhood and Lebanon's Hezbollah.
Mediation by Kuwait and the United States has failed to stop the boycott. America relies on Qatar's massive al-Udeid Air Base to host the forward headquarters of the U.S. military's Central Command.
Also, Qatar's vast natural gas reserves have so far insulated the nation. Work there continues ahead of Doha hosting the 2022 FIFA World Cup soccer tournament. Meanwhile, Qatar Airways continues to compete with the region's other marquee long-haul carriers, Dubai-based Emirates and Abu Dhabi-based Etihad, in connecting the East and West.
All-Afghan peace summit agreed upon, but on Taliban terms
Platini arrested as part of 2022 World Cup investigation
QNTC launches biggest 'Summer in Qatar' program yet with various experiences for all
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Where's my damn money
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Hezbollah and the Stockholm Syndrome
Trending on An-Nahar
Turkey: EU sanctions over gas drilling 'worthless'
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Finding healing through comedy
Danielle Perez lost her feet in a tragic accident. Despite her challenges, the comedian just wants to make people laugh.
Updated: Mar 25, 2018 10:33 PM
Danielle Perez has been carried on stage, Cleopatra-style.
"Comedy happens in very cool places. And nowhere cool is accessible," said Perez, who uses a wheelchair.
Once she's up there, though, the 33-year-old comedian feels right at home.
"It feels so powerful to be on stage," she said. "Life is hard for everyone. To participate in something that makes people laugh -- there's nothing like it."
But life for Perez wasn't always funny. Growing up in Los Angeles, she struggled with depression and eating disorders. Then, Perez moved to San Francisco to attend San Francisco State University, where a tragic accident changed her life.
Before that, she was living a glamorous urban lifestyle, "running around the hills of San Francisco in 3-inch-high heels and drinking cosmopolitans."
One day, Perez was crossing the street to catch a Muni streetcar. She suddenly found herself in the streetcar's path. It didn't stop.
"By the time it stopped, the wheels were above my legs," she said.
When two firefighters arrived, they started asking her questions.
" 'Can you feel your hands? Can you feel your shoulders?' Once they got to my feet, I started to freak out a little bit because I couldn't feel them," she said.
The impact also shattered her pelvis and ruptured her bladder. When she woke up in the hospital, her mother was sitting next to her.
"The first words she said to me were, 'Danielle, you don't have any feet.' "
Adjusting to life in a wheelchair
Perez was 20 years old. Her legs were amputated below the knee, and she spent the next month recovering in the hospital.
"I was in such denial about the reality. I just wanted to go and hang out with my friends. I just wanted to be normal," she recalled.
At first, that denial helped Perez move forward.
"It allowed me to get out of the house, learn how to drive," she said. "But it also delayed that healing process of knowing that people are gonna treat you differently. And some things are going to be harder."
Like wearing prosthetics. Perez had trouble using them after having skin grafts on her legs.
"I got very depressed after that, and I gained a lot of weight."
Making people laugh
But three years ago, she found healing in an unlikely place: a comedy club. Her best friend's roommate was a standup comedian. Perez and her friend started going to his shows.
"By the third one, I was like, 'I could do this,' " she said. "It's that insane hubris that every person who starts standup comedy has to have. Where you think, 'Oh, that's not hard.' "
Perez took a comedy class and started going to open mics.
"I went to my first open mic at this crappy little Hollywood coffee shop, and people laughed at my jokes. And I just fell in love with it."
Perez uses her experiences as material for her comedy routines.
"It's about my life, my family, my friends, dating," she said. "I talk about the accident. I talk about my depression. ... We are all complex people, so when people see that and relate to it, it's great."
When she performs her comedy routine, she doesn't care about what people think of her.
"When I go on stage, I'm just worried about 'are these jokes funny?' not 'what do they think about my disability?' " she said.
'The Price Is Right'
In 2015, Perez was thrust into the spotlight after she appeared on an episode of "The Price Is Right." Her prizes: a treadmill and a walk-in sauna.
"If you're having a crazy reaction to that, that's also the reaction the Internet had, because that video went viral," she said.
She was interviewed by news networks around the world and appeared as a guest on "Jimmy Kimmel Live!"
"People keep asking me what I'm gonna do with (the treadmill). And I said, 'I guess I'll just do what everyone else does and just use it as a piece of furniture,' " she told Kimmel.
That exposure helped Perez get her name out and build a fan base. "At shows, people are like, 'Oh, it's that girl from "The Price Is Right." ' "
Now, Perez performs in comedy clubs all over Los Angeles. She's come a long way since that accident 13 years ago.
"Standup comedy has helped me heal because it's really given me purpose," she said. "What I try to convey is that it's OK to be yourself."
She lost her feet in an accident. Now, her standup comedy helps her heal
Anxiety sufferers find relief with comedy improv class
'Game Night' serves up a comedy winner
Mae West: A 'History of Comedy' pioneer
Stand-up comedy still scares 'Insecure' actress
Survivors of sex trafficking find healing in cooking class
The healing power of horses
Boy healing after heart transplant
For Golden Globes, comedy can be a joke
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,123
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The Mantra of Vision: An Overview of Sri Aurobindo's Aesthetics
S. Murali (Author)
Synopsis There are certainly several critical works available which deal with the poetics/aesthetic theories of Sri Aurobindo. In The Mantra of Vision – An Overview of Sri Aurobindo's Aesthetics, the author has taken a holistic attitude and stresses on the two aspects of Sri Aurobindo's darsana – the Mantra and Vision – and centralises on his spiritual aesthetics. The first chapter examines the premises of Sri Aurobindo's aesthetics and is concerned mainly with his spiritually as the dominant motivating force of his life and work. Chapter 2 deals mainly with his theory of poetry while Chapter 3 focuses attention on what Sri Aurobindo had designated as "overhead poetry" and the author has taken recourse to ancient Indian psychology and philosophy, largely from Vedas and Upanishads to corroborate the idea of the aesthetics. Chapter 4 is a close study of the poetics of the mantra relating to the sphota sastra. Chapter 5 deals with Sri Aurobindo's poetry. The Sixth chapter centralizes on Savitri and the author has shown that it was the culmination of Aurobindo's poetic career in which he achieved an integration of gnosis and praxis. This book would be of interest to the general readers as well as scholars / students of Indian aesthetics.
S. Murali
S. Murali is a poet, painter and critic-a specialist in Indian aesthetics. He received his Ph.D. from the University of Kerala (1990) and is a scholar of repute deeply concerned with indigenous values and essential issues. His book The Mantra of Vision: An Overview of Sri Aurobindo's Aesthetics (1997) has come to be recognised as a valuable contribution to the study of Indian poetics and comparative aesthetics. He has also authored a collection of poems and sketches-Night Heron (1998). He is a well known painter and his works have gone on display at several exhibitions in India and abroad. His publications include poems, translations and essays on art, literature and ideas in journals of international repute. He has as much involvement with nature and environment as with poetry and painting. At present Dr. Murali and painting. At present Dr. Murali teaches in the Department of English, University College, Trivandrum, Kerala.
Figuring the Female: Women's Discourse, Art and Literature
Tradition and Terrain: Aesthetic Continuities
South Indian Studies
The Hastigiri Mahatmyam of Vedantadesika
Brihad Indrajaal: Mantra Tantra & Yantra
The Supreme Yoga: Yoga Vasistha
The Compassionate Mother: The Oldest Biography of Sri Sarada Devi by Brahmachari Akshaychaitanya
Title The Mantra of Vision: An Overview of Sri Aurobindo's Aesthetics
Author S. Murali
Publisher B.R. Publishing Corporation
length xiv+253p., Notes & References; Bibliography; Index; 23cm.
Subjects Health, Mind & Body > Philosophy
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,768
|
Q: get website root in dev and prod without hard-coding anything My dev server is http://localhost/mygreatapp and my production server is http://www.myawesomesite.com but maybe someday it will migrate to http://www.myawesomesite.com/mygreatapp
In these cases mygreatapp is a virtual directory.
I would like a php function to return the correct website roots without having to hard-code anything (e.g., mygreatapp), regardless if it's off the default website or a virtual directory. In either case, that's where all the relative paths to the files begins.
I have looked at the similar questions and not found a solution that does not involve hard-coding, which would then involve having to update the value for each environment, painful and error prone.
A: This will get my by for now, but I'll need to adjust it if I go into a subfolder on a linux machine.
public static function WebRoot(){
$virtualdir = '';
if(isset($_SERVER['APPL_MD_PATH'])){
$virtualdir = substr($_SERVER['APPL_MD_PATH'], strpos($_SERVER['APPL_MD_PATH'], '/ROOT/') + strlen('/ROOT/'));
}
return 'https://'.$_SERVER['SERVER_NAME'].'/'.$virtualdir.'/';
}
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,235
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\section{Introduction}
As the remnants of some of the oldest stars in the galaxy, cool white dwarfs offer an
independent method for dating different Galactic populations and constraining their star
formation history \citep{winget87,liebert88}. The current best estimates for the ages of the
Galactic thin and thick discs are $8 \pm 1.5$ Gyr \citep{leggett98,harris06} and $\geq10$ Gyr
\citep{gianninas15}, respectively. Extended \textit{Hubble Space Telescope} observing campaigns
on 47 Tuc, M4, and NGC 6397 revealed the end of the white dwarf cooling sequence in these globular
clusters \citep{hansen04,hansen07,kalirai12b}, which reveal an age spread of 11 to 13 Gyr for the
Galactic halo \citep{campos15}.
Field white dwarfs provide additional and superior information on the age and age spread of the
Galactic disc and halo. Recent large scale surveys such as the Sloan Digital Sky Survey (SDSS) have found many cool field
white dwarfs \citep{gates04,harris06,harris08,kilic06,kilic10b,vidrih07,tremblay14,gianninas15}. These stars are
far closer and brighter than those found in globular clusters, allowing for relatively easy optical and infrared
observations in multiple bands from ground-based telescopes. Modeling the spectral energy distributions (SEDs)
of these white dwarfs provides excellent constraints on their atmospheric composition and cooling ages and
gives us an alternate method for calibrating the white dwarf cooling sequences of globular clusters.
However, there are only a handful of nearby halo white dwarfs currently known.
\citet{kalirai12a} use four field white dwarfs with halo kinematics to derive an age of $11.4 \pm 0.7$ Gyr for the
inner halo. These four stars are warm enough to show Balmer absorption lines, which enable precise constraints
on their surface gravity, mass, temperature, and cooling ages. The SPY project (ESO SN Ia Progenitor
Survey) found 12 halo members with ages consistent with a halo age $\approx 11$ Gyr in a sample of 634 DA white dwarfs. These
have accurate radial velocities determined from Balmer absorption lines, allowing for the determination of accurate 3D space
velocities \citep{pauli03,pauli06,richter07}. Similarly, \citet{kilic12} use optical and infrared photometry and parallax
observations of two cool white dwarfs with halo kinematics, WD 0346+246 and SDSS J110217.48+411315.4 to derive an age of
11.0-11.5 Gyr for the local halo.
Ongoing and future photometric and astrometric surveys like the Panoramic Survey Telescope \& Rapid Response System
\citep{tonry12}, Palomar Transient Factory \citep{rau09}, the Large Synoptic
Survey Telescope and the \textit{GAIA} mission will significantly increase the number of field white dwarfs known.
Previously, \citet{liebert07} performed a targeted proper motion survey for identifying thick disc and halo
white dwarfs in the solar neighborhood. \citet{munn14} present the proper motion catalog from this survey,
which includes $\approx 3100$ square degrees of sky observed at the Steward Observatory Bok 90 inch telescope
and the U.S. Naval Observatory Flagstaff Station 1.3 m telescope. \citet{kilic10a} presented three halo
white dwarf candidates identified in this survey, with ages of 10-11 Gyr. Here we present follow-up observations
and model atmosphere analysis of 54 additional high proper motion white dwarfs identified in this survey.
We find seven new ultracool ($T_{\rm eff}<4000$ K) white dwarfs and three new halo white dwarf candidates.
We discuss the details of our observations in Section \ref{sec:obs}, and the model atmosphere fits in Section
\ref{sec:phot}. We present the kinematic analysis of our sample in Section \ref{sec:kinematics}, and conclude
in Section \ref{sec:con}.
\section{Target Selection and Observations}
\label{sec:obs}
\subsection{The Reduced Proper Motion Diagram}
Reduced proper motion is defined as $H = m + 5 \log{\mu} + 5$ (where $\mu$ is the proper motion and m is the apparent magnitude), which is equivalent to $M + 5 \log{V_{\rm tan}} - 3.379$.
Hence, reduced proper motion can be used to identify samples with similar kinematics, like the disc or halo white
dwarf population. \citet{kilic06,kilic10b} demonstrate that the reduced proper motion diagram provides a clean
sample of white dwarfs, with contamination rates of 1\% from halo subdwarfs. Figure \ref{fig:rpm} displays the
reduced proper motion diagram for a portion of the sky covered by the \citet{munn14} proper motion survey.
Going from left to right, three distinct populations of objects are clearly visible in this diagram;
white dwarfs, halo subdwarfs, and disc dwarfs. The solid lines show the predicted evolutionary sequences
for $\log{g}=8$ white dwarfs with $V_{\rm tan}=40$ and 150 km s$^{-1}$. The model colors become redder until the white
dwarfs become cool enough to show infrared absorption due to molecular hydrogen \citep{hansen98}.
We selected targets for follow-up spectroscopy and near-infrared photometry based on their reduced proper motion
and colors. To find the elusive halo white dwarfs and other white dwarfs with high tangential velocities, we
targeted objects with $H_g>21$ mag and below the $V_{\rm tan}=40$ km s$^{-1}$\ line.
\begin{figure}
\includegraphics[width = 9cm]{fig.nsfrpm.ps}
\caption{The reduced proper motion diagram for a portion of the \citet{munn14} proper motion
survey. White dwarf evolutionary tracks for tangential velocities of 40 and 150 km s$^{-1}$\ are shown as solid
lines. Filled circles mark spectroscopically confirmed white dwarfs with $H_g>21$ mag and triangles show
our targets with SWIRC near-infrared photometry, but with no follow-up spectroscopy.}
\label{fig:rpm}
\end{figure}
\subsection{Optical Spectroscopy}
We obtained follow-up optical spectroscopy of 32 white dwarf candidates at the 6.5 m MMT telescope
equipped with the Blue Channel Spectrograph \citep{schmidt89} on UT 2009 June 18-23 and 2009 November 19-20.
We used a $1\farcs25$ slit and the 500 line mm$^{-1}$ grating in first order to obtain
spectra over the range 3660-6800 \AA{} and with a resolving power of R = 1200.
We obtained all spectra at the parallactic angle and acquired He-Ar-Ne comparison lamp
exposures for wavelength calibration. We use observations of the cool white dwarf G24-9
for flux calibration.
Out of the 32 candidates with spectra, only two (SDSS J024416.07-090919.7 and
J172431.61+261543.1) are metal-poor halo subdwarfs. The remaining objects are confirmed to
be DA, DC, or DZ white dwarfs. This relatively small (2 out of 32) contamination rate from
subdwarfs demonstrates that our white dwarf sample is relatively clean.
Figure \ref{fig:DA} shows the spectra for the five DA WDs in our sample. Two of the DAs,
J1513+4743 and J1624+4156, are warm enough ($T_{\rm eff}\approx 5900$ K) to show H$\alpha$
and a few of the higher order Balmer lines, while the remaining three DAs only show H$\alpha$,
which implies effective temperatures near 5000 K.
\begin{figure}
\includegraphics[width = 9cm]{DA.ps}
\caption{Optical spectra for the five DA WDs in our sample. The dotted line marks H$\alpha$.}
\label{fig:DA}
\end{figure}
Figure \ref{fig:DC} shows the MMT spectra for the 24 DC white dwarfs in our sample, including
the three cool DCs presented in \citet{kilic10a}. All of these 24 targets have featureless
spectra that are rising toward the infrared, indicating temperatures below 5000 K.
\begin{figure}
\includegraphics[width = 9cm]{DC1.ps}
\includegraphics[width = 9cm]{DC2.ps}
\caption{Optical spectra for 24 DC WDs in our sample.}
\label{fig:DC}
\end{figure}
\subsection{Near-Infrared Photometry}
We obtained J- and H-band imaging observations of 40 of our targets using the Smithsonian Widefield Infrared Camera
\citep[SWIRC,][]{brown08} on the MMT
on UT 2011 March 23-24. SWIRC has a $5.12 \times 5.12$ arcmin field of view at a resolution of $0\farcs15$ per pixel.
We observed each target on a dozen or more dither positions, and obtained dark frames and
sky flats each evening. We used the SWIRC data reduction pipeline to perform
dark correction, flat-fielding, and sky subtraction, and to produce a combined image for each field in each filter.
We use the 2MASS stars in the SWIRC field of view for photometric and astrometric calibration.
In addition, near-infrared photometry for two more targets, J0040+1458 and J1649+2932, are available from the
UKIRT Infrared Deep Sky Survey \citep[UKIDSS,][]{lawrence07} Large Area Survey.
Table \ref{tab:phot} presents the \textit{ugriz} and \textit{JH} photometry for our sample
of 57 targets with follow-up spectroscopy and/or near-infrared photometry.
Figure \ref{fig:color} presents optical and infrared color-color diagrams for the same stars,
along with the predicted colors of pure H and pure He atmosphere white dwarfs. The differences
between these models are relatively minor in the optical color-color diagrams, except for the
ultracool white dwarfs with $T_{\rm eff}<4000$ K. The pure H
models predict the colors to get redder until the onset of the Collision Induced Absorption (CIA)
due to molecular hydrogen, which leads to a blue hook feature. This transition occurs at 3750 K
for the $r-i$ color, whereas it occurs at 4500 K for the $r-H$ color. The colors for our
sample of 57 stars, including the targets with and without follow-up spectroscopy, are consistent
with the white dwarf model colors within the errors. The majority of the targets with $g-r\geq1.0$ mag
($T_{\rm eff}\leq4250$ K) show bluer $r-H$ colors than the pure He model sequence, indicating
that the coolest white dwarfs in our sample have H-rich atmospheres.
\begin{figure}
\includegraphics[angle=-90,width = 9cm]{fig.nsfcolor.ps}
\caption{Color-color diagrams for our sample of 57 white dwarf candidates.
Solid and dashed lines show the predicted colors for pure H ($T_{\rm eff} \geq 2500$ K)
and pure He atmosphere ($T_{\rm eff} \geq 3500$ K) white dwarfs with $\log{g}= 8$
\citep{bergeron95}, respectively.}
\label{fig:color}
\end{figure}
We use the SWIRC astrometry to verify the proper motion measurements from our optical
imaging survey. Given the relatively small field of view of the SWIRC camera and the limited
number of 2MASS stars available in each field, the astrometric precision is significantly worse
in the SWIRC images compared to the Bok 90 inch and USNO 1.3m optical data. We find that the proper
motion measurements from the SWIRC data are on average $54\pm44$ mas yr$^{-1}$ higher. Nevertheless,
all but one of our targets, J1513+4743, have SWIRC-SDSS proper motion measurements consistent with the
proper motion measurements from our optical data within 3$\sigma$. J1513+4743 is spectroscopically
confirmed to be a DA white dwarf. Hence, the contamination rate of our sample of 57 stars by objects
with incorrectly measured proper motions should be relatively small.
\begin{table*}
\centering
\scriptsize
\caption{Optical and Near-Infrared Photometry of White Dwarf Candidates}
\label{tab:phot}
\begin{tabular}{lccccccc}
\hline
SDSS & \textit{u} & \textit{g} & \textit{r} & \textit{i} & \textit{z} & \textit{J} & \textit{H} \\ \hline
J213730.86+105041.5 & 23.30 $\pm$ 0.54 & 21.77 $\pm$ 0.06 & 20.51 $\pm$ 0.03 & 20.01 $\pm$ 0.03 & 19.73 $\pm$ 0.08 & 19.21 $\pm$ 0.10 & 19.25 $\pm$ 0.18 \\
J214538.16+110626.6 & 23.72 $\pm$ 0.52 & 21.49 $\pm$ 0.04 & 20.22 $\pm$ 0.02 & 19.77 $\pm$ 0.02 & 19.61 $\pm$ 0.05 & 18.87 $\pm$ 0.07 & 19.00 $\pm$ 0.10 \\
J214538.60+110619.1 & 23.47 $\pm$ 0.45 & 21.01 $\pm$ 0.03 & 19.93 $\pm$ 0.02 & 19.49 $\pm$ 0.02 & 19.29 $\pm$ 0.04 & 18.54 $\pm$ 0.06 & 19.31 $\pm$ 0.06 \\
J004022.47+145835.0 & 22.23 $\pm$ 0.23 & 20.56 $\pm$ 0.03 & 19.83 $\pm$ 0.02 & 19.53 $\pm$ 0.03 & 19.43 $\pm$ 0.06 & 18.60 $\pm$ 0.10 & 18.39 $\pm$ 0.12 \\
J004725.61$-$085223.9 & 25.78 $\pm$ 0.74 & 21.65 $\pm$ 0.06 & 20.67 $\pm$ 0.04 & 20.29 $\pm$ 0.05 & 20.17 $\pm$ 0.15 & \dots & \dots \\
J010838.42$-$095415.7 & 24.07 $\pm$ 1.04 & 21.56 $\pm$ 0.06 & 20.61 $\pm$ 0.04 & 20.20 $\pm$ 0.04 & 19.98 $\pm$ 0.13 & \dots & \dots \\
J014749.07$-$093537.4 & 22.98 $\pm$ 0.53 & 21.64 $\pm$ 0.07 & 20.70 $\pm$ 0.04 & 20.44 $\pm$ 0.05 & 20.39 $\pm$ 0.24 & \dots & \dots \\
J073417.76+372842.6 & 24.01 $\pm$ 0.74 & 21.88 $\pm$ 0.07 & 20.95 $\pm$ 0.05 & 20.57 $\pm$ 0.04 & 20.44 $\pm$ 0.14 & 19.59 $\pm$ 0.09 & 20.08 $\pm$ 0.17 \\
J074942.95+294716.7 & 22.45 $\pm$ 0.26 & 20.80 $\pm$ 0.03 & 19.95 $\pm$ 0.02 & 19.64 $\pm$ 0.03 & 19.49 $\pm$ 0.06 & 18.56 $\pm$ 0.04 & 18.37 $\pm$ 0.05 \\
J080505.26+273557.2 & 23.73 $\pm$ 0.62 & 21.52 $\pm$ 0.06 & 20.59 $\pm$ 0.03 & 20.25 $\pm$ 0.03 & 20.28 $\pm$ 0.12 & 19.05 $\pm$ 0.06 & 19.16 $\pm$ 0.06 \\
J080545.80+374720.4 & 23.87 $\pm$ 0.64 & 21.12 $\pm$ 0.04 & 20.39 $\pm$ 0.03 & 20.08 $\pm$ 0.03 & 19.87 $\pm$ 0.10 & 19.13 $\pm$ 0.05 & 18.86 $\pm$ 0.06 \\
J081140.07+384202.2 & 23.87 $\pm$ 0.69 & 21.89 $\pm$ 0.07 & 20.84 $\pm$ 0.04 & 20.55 $\pm$ 0.04 & 20.30 $\pm$ 0.11 & 19.50 $\pm$ 0.06 & 19.24 $\pm$ 0.08 \\
J081735.51+310625.5 & 22.39 $\pm$ 0.23 & 20.52 $\pm$ 0.03 & 19.50 $\pm$ 0.02 & 19.14 $\pm$ 0.02 & 18.89 $\pm$ 0.03 & 18.14 $\pm$ 0.03 & 17.84 $\pm$ 0.04 \\
J082035.23+390419.9 & 22.72 $\pm$ 0.32 & 22.01 $\pm$ 0.07 & 20.86 $\pm$ 0.04 & 20.53 $\pm$ 0.04 & 20.29 $\pm$ 0.09 & 19.31 $\pm$ 0.05 & 19.49 $\pm$ 0.10 \\
J082255.41+390302.7 & 23.16 $\pm$ 0.34 & 21.87 $\pm$ 0.05 & 20.90 $\pm$ 0.04 & 20.49 $\pm$ 0.03 & 20.37 $\pm$ 0.11 & 19.19 $\pm$ 0.06 & 19.24 $\pm$ 0.08 \\
J082842.31+352729.5 & 21.43 $\pm$ 0.09 & 19.84 $\pm$ 0.02 & 19.06 $\pm$ 0.02 & 18.73 $\pm$ 0.02 & 18.69 $\pm$ 0.03 & 17.88 $\pm$ 0.03 & 17.47 $\pm$ 0.04 \\
J084802.30+420429.7 & 22.92 $\pm$ 0.37 & 21.72 $\pm$ 0.06 & 20.79 $\pm$ 0.04 & 20.53 $\pm$ 0.05 & 20.41 $\pm$ 0.14 & 19.63 $\pm$ 0.06 & 19.29 $\pm$ 0.08 \\
J085441.14+390700.1 & 22.87 $\pm$ 0.28 & 21.22 $\pm$ 0.03 & 20.40 $\pm$ 0.03 & 20.12 $\pm$ 0.03 & 20.03 $\pm$ 0.08 & 19.17 $\pm$ 0.04 & 18.83 $\pm$ 0.06 \\
J091035.82+374454.8 & 23.85 $\pm$ 0.63 & 21.79 $\pm$ 0.06 & 20.53 $\pm$ 0.03 & 19.95 $\pm$ 0.03 & 19.64 $\pm$ 0.07 & 18.95 $\pm$ 0.04 & 18.80 $\pm$ 0.05 \\
J091823.08+502826.4 & 22.60 $\pm$ 0.26 & 20.72 $\pm$ 0.03 & 19.87 $\pm$ 0.02 & 19.62 $\pm$ 0.02 & 19.47 $\pm$ 0.06 & 18.67 $\pm$ 0.04 & 18.38 $\pm$ 0.04 \\
J092716.99+485233.3 & 22.96 $\pm$ 0.30 & 20.65 $\pm$ 0.02 & 19.59 $\pm$ 0.02 & 19.17 $\pm$ 0.03 & 19.11 $\pm$ 0.05 & 19.12 $\pm$ 0.06 & 19.60 $\pm$ 0.14 \\
J100953.03+534732.9 & 23.82 $\pm$ 0.84 & 21.82 $\pm$ 0.07 & 20.75 $\pm$ 0.04 & 20.40 $\pm$ 0.04 & 19.86 $\pm$ 0.10 & 19.09 $\pm$ 0.06 & 18.92 $\pm$ 0.07 \\
J102417.17+492011.3 & 22.83 $\pm$ 0.29 & 21.59 $\pm$ 0.06 & 20.70 $\pm$ 0.03 & 20.42 $\pm$ 0.04 & 20.15 $\pm$ 0.10 & 19.46 $\pm$ 0.08 & 18.89 $\pm$ 0.10 \\
J105652.84+504321.3 & 23.56 $\pm$ 0.56 & 21.40 $\pm$ 0.04 & 20.37 $\pm$ 0.03 & 19.99 $\pm$ 0.03 & 19.79 $\pm$ 0.08 & 19.05 $\pm$ 0.04 & 18.78 $\pm$ 0.05 \\
J110105.01+485437.9 & 23.00 $\pm$ 0.51 & 20.88 $\pm$ 0.04 & 19.92 $\pm$ 0.05 & 19.68 $\pm$ 0.03 & 19.67 $\pm$ 0.09 & 18.75 $\pm$ 0.04 & 18.50 $\pm$ 0.05 \\
J114558.52+563806.8 & 23.08 $\pm$ 0.52 & 21.73 $\pm$ 0.06 & 20.93 $\pm$ 0.06 & 20.62 $\pm$ 0.06 & 20.26 $\pm$ 0.15 & 19.64 $\pm$ 0.08 & 19.35 $\pm$ 0.07 \\
J120514.49+550217.2 & 22.84 $\pm$ 0.43 & 21.31 $\pm$ 0.04 & 20.37 $\pm$ 0.03 & 20.00 $\pm$ 0.03 & 19.88 $\pm$ 0.10 & 18.94 $\pm$ 0.05 & 18.68 $\pm$ 0.04 \\
J132358.81+022342.2 & 23.10 $\pm$ 0.46 & 21.88 $\pm$ 0.07 & 20.91 $\pm$ 0.04 & 20.60 $\pm$ 0.05 & 20.52 $\pm$ 0.16 & 19.43 $\pm$ 0.07 & 19.37 $\pm$ 0.07 \\
J133309.98+494227.2 & 24.03 $\pm$ 0.78 & 21.15 $\pm$ 0.04 & 20.23 $\pm$ 0.03 & 19.86 $\pm$ 0.04 & 19.60 $\pm$ 0.06 & 18.79 $\pm$ 0.04 & 18.60 $\pm$ 0.04 \\
J140907.89$-$010036.9 & 22.94 $\pm$ 0.28 & 21.64 $\pm$ 0.06 & 20.58 $\pm$ 0.03 & 20.18 $\pm$ 0.03 & 19.97 $\pm$ 0.10 & 19.12 $\pm$ 0.06 & 19.06 $\pm$ 0.06 \\
J142136.69+035612.4 & 24.39 $\pm$ 0.97 & 21.89 $\pm$ 0.08 & 20.82 $\pm$ 0.05 & 20.43 $\pm$ 0.04 & 20.23 $\pm$ 0.16 & 19.19 $\pm$ 0.06 & 19.04 $\pm$ 0.07 \\
J143400.55+534525.2 & 22.95 $\pm$ 0.44 & 21.20 $\pm$ 0.04 & 20.28 $\pm$ 0.03 & 19.89 $\pm$ 0.03 & 19.62 $\pm$ 0.07 & 18.99 $\pm$ 0.06 & 18.64 $\pm$ 0.06 \\
J144417.48+602555.1 & 23.73 $\pm$ 0.61 & 21.62 $\pm$ 0.05 & 20.65 $\pm$ 0.03 & 20.42 $\pm$ 0.04 & 20.52 $\pm$ 0.13 & 19.50 $\pm$ 0.07 & 19.09 $\pm$ 0.10 \\
J144606.46+025811.5 & 23.70 $\pm$ 0.85 & 21.72 $\pm$ 0.12 & 20.64 $\pm$ 0.07 & 20.33 $\pm$ 0.06 & 30.02 $\pm$ 0.12 & 19.03 $\pm$ 0.06 & 18.92 $\pm$ 0.09 \\
J150904.50+540825.2 & 24.60 $\pm$ 1.03 & 21.97 $\pm$ 0.08 & 20.94 $\pm$ 0.05 & 20.49 $\pm$ 0.05 & 20.17 $\pm$ 0.13 & 19.31 $\pm$ 0.07 & 19.13 $\pm$ 0.08 \\
J151319.26+502318.6 & 23.39 $\pm$ 0.44 & 21.96 $\pm$ 0.07 & 20.70 $\pm$ 0.03 & 20.30 $\pm$ 0.03 & 19.93 $\pm$ 0.07 & 18.85 $\pm$ 0.05 & 19.30 $\pm$ 0.08 \\
J151321.20+474324.2 & 20.82 $\pm$ 0.06 & 19.92 $\pm$ 0.03 & 19.63 $\pm$ 0.02 & 19.42 $\pm$ 0.02 & 19.41 $\pm$ 0.06 & 18.62 $\pm$ 0.05 & 18.55 $\pm$ 0.21 \\
J151555.53+593045.3 & 25.19 $\pm$ 0.86 & 21.96 $\pm$ 0.06 & 20.78 $\pm$ 0.03 & 20.34 $\pm$ 0.04 & 20.24 $\pm$ 0.09 & 19.40 $\pm$ 0.08 & 19.66 $\pm$ 0.10 \\
J153300.94$-$001212.2 & 23.65 $\pm$ 0.59 & 22.05 $\pm$ 0.07 & 20.89 $\pm$ 0.04 & 20.46 $\pm$ 0.04 & 20.16 $\pm$ 0.12 & 19.24 $\pm$ 0.07 & 19.07 $\pm$ 0.09 \\
J153432.25+562455.7 & 21.76 $\pm$ 0.14 & 20.26 $\pm$ 0.02 & 19.62 $\pm$ 0.02 & 19.36 $\pm$ 0.03 & 19.28 $\pm$ 0.05 & \dots & \dots \\
J155243.40+463819.4 & 21.53 $\pm$ 0.11 & 20.09 $\pm$ 0.02 & 19.50 $\pm$ 0.02 & 19.31 $\pm$ 0.02 & 19.28 $\pm$ 0.05 & \dots & \dots \\
J155501.57+494056.4 & 25.76 $\pm$ 0.64 & 21.84 $\pm$ 0.08 & 20.77 $\pm$ 0.04 & 20.46 $\pm$ 0.05 & 20.30 $\pm$ 0.16 & 19.29 $\pm$ 0.07 & 19.23 $\pm$ 0.07 \\
J160125.48+412014.1 & 21.20 $\pm$ 0.07 & 19.28 $\pm$ 0.02 & 18.44 $\pm$ 0.02 & 18.15 $\pm$ 0.02 & 18.08 $\pm$ 0.02 & \dots & \dots \\
J160130.82+420427.6 & 24.19 $\pm$ 0.98 & 21.65 $\pm$ 0.06 & 20.71 $\pm$ 0.04 & 20.37 $\pm$ 0.04 & 20.37 $\pm$ 0.17 & 19.29 $\pm$ 0.07 & 19.01 $\pm$ 0.09 \\
J160424.38+392330.5 & 21.88 $\pm$ 0.20 & 20.51 $\pm$ 0.03 & 19.87 $\pm$ 0.02 & 19.67 $\pm$ 0.03 & 19.44 $\pm$ 0.07 & \dots & \dots \\
J162417.93+415656.6 & 21.21 $\pm$ 0.09 & 20.18 $\pm$ 0.02 & 19.84 $\pm$ 0.02 & 19.69 $\pm$ 0.03 & 19.62 $\pm$ 0.07 & \dots & \dots \\
J162724.57+372643.1 & 21.78 $\pm$ 0.10 & 19.80 $\pm$ 0.02 & 18.94 $\pm$ 0.02 & 18.64 $\pm$ 0.01 & 18.53 $\pm$ 0.03 & 17.60 $\pm$ 0.03 & 17.39 $\pm$ 0.03 \\
J164358.79+443855.4 & 21.42 $\pm$ 0.10 & 19.84 $\pm$ 0.02 & 19.11 $\pm$ 0.02 & 18.88 $\pm$ 0.01 & 18.81 $\pm$ 0.04 & 17.91 $\pm$ 0.03 & 17.63 $\pm$ 0.03 \\
J164745.45+394638.6 & 24.56 $\pm$ 1.09 & 21.55 $\pm$ 0.05 & 20.30 $\pm$ 0.03 & 19.89 $\pm$ 0.03 & 19.84 $\pm$ 0.08 & 18.91 $\pm$ 0.05 & 18.60 $\pm$ 0.05 \\
J164931.91+293247.7 & 22.19 $\pm$ 0.15 & 20.61 $\pm$ 0.03 & 19.90 $\pm$ 0.02 & 19.63 $\pm$ 0.02 & 19.51 $\pm$ 0.08 & 18.62 $\pm$ 0.06 & 18.52 $\pm$ 0.11 \\
J165723.84+263843.5 & 24.80 $\pm$ 0.80 & 21.33 $\pm$ 0.04 & 20.28 $\pm$ 0.03 & 19.99 $\pm$ 0.03 & 19.77 $\pm$ 0.10 & 19.24 $\pm$ 0.08 & 19.20 $\pm$ 0.10 \\
J171135.27+294046.0 & 23.00 $\pm$ 0.33 & 21.11 $\pm$ 0.03 & 20.37 $\pm$ 0.03 & 19.96 $\pm$ 0.02 & 19.85 $\pm$ 0.07 & 18.73 $\pm$ 0.05 & 18.41 $\pm$ 0.07\\
J171543.76+260016.9 & 22.82 $\pm$ 0.40 & 21.25 $\pm$ 0.04 & 20.45 $\pm$ 0.03 & 20.06 $\pm$ 0.03 & 19.91 $\pm$ 0.10 & 18.81 $\pm$ 0.07 & 18.27 $\pm$ 0.04 \\
J212739.00+103655.1 & 22.77 $\pm$ 0.41 & 21.67 $\pm$ 0.06 & 20.71 $\pm$ 0.04 & 20.35 $\pm$ 0.04 & 20.11 $\pm$ 0.13 & \dots & \dots \\
J223038.21+141505.7 & 21.86 $\pm$ 0.15 & 20.37 $\pm$ 0.03 & 19.87 $\pm$ 0.02 & 19.64 $\pm$ 0.02 & 19.60 $\pm$ 0.07 & \dots & \dots \\
J231617.67$-$104411.0 & 23.41 $\pm$ 0.67 & 21.98 $\pm$ 0.09 & 20.99 $\pm$ 0.05 & 20.56 $\pm$ 0.05 & 20.34 $\pm$ 0.14 & \dots & \dots \\
J232018.23$-$084516.7 & 25.55 $\pm$ 0.95 & 21.63 $\pm$ 0.07 & 20.57 $\pm$ 0.04 & 20.20 $\pm$ 0.05 & 19.97 $\pm$ 0.15 & \dots & \dots\\
\hline
\end{tabular}
\end{table*}
\section{Photometric Analysis}
\label{sec:phot}
\subsection{Model Atmospheres}
Our model atmospheres come from the LTE model atmosphere code described in \citet{bergeron95}
and references within, along with the recent improvements in the calculations for the Stark
broadening of hydrogen lines discussed in \citet{tremblay09}. We follow the method of \citet{holberg06} and
convert the observed magnitudes into fluxes, and use a nonlinear least-squares method to fit the resulting
SEDs to predictions from model atmospheres. Given that all our targets appear to be within 150 pc, we do not
correct for extinction. We consider only the temperature and the solid angle $\pi(R/D)^{2}$, where $R$ is the
radius of the white dwarf and $D$ is its distance from Earth, as free parameters. Convection is modeled by the
ML/$\alpha$ = 0.7 prescription of mixing length theory. For a more detailed discussion of our fitting technique,
see \citet{bergeron01b}; for details of our helium-atmosphere models, see \citet{bergeron11}. Since we do not have
parallax measurements for our objects, we assume a surface gravity of $\log{g}=8$. This is appropriate, as the
white dwarf mass distribution in the Solar neighborhood peaks at about 0.6 $M_{\odot}$ \citep{tremblay13}. We
discuss the effects of this choice in Section \ref{sec:kinematics}.
Below about 5000 K, H$\alpha$ is not visible. However, the presence of hydrogen can still be seen in
the blue from the red wing of Ly$\alpha$ absorption \citep{kowalski06}, and in the infrared from CIA due to molecular hydrogen.
Cool white dwarfs with pure helium atmospheres are not subject to these opacities, so their SEDs should
appear similar to a blackbody. Because of this, atmospheric composition can still be determined from
ultraviolet and near-infrared data. Table \ref{tab:wd} presents the best-fit atmospheric compositions,
temperatures, distances, and cooling ages for our targets, as well as their proper motions and tangential velocities.
Below, we discuss the pure H, pure He, and mixed H/He atmosphere targets separately, and highlight the most interesting
objects in the sample.
\begin{table*}
\centering
\scriptsize
\caption{Physical Parameters of our White Dwarf Sample. Source of the optical spectroscopic observations: (1) This paper, (2) \citet{kilic10b}, and (3) \citet{kilic10a}.}
\label{tab:wd}
\begin{tabular}{lccclrrrrr}
\hline
Object & Spectral & Source & Composition & $T_{\rm eff}$ & $d$ & Cooling Age & $\mu_{RA}$ & $\mu_{Dec}$ & $V_{tan}$ \\
(SDSS) & Type & & (log He/H) & (K) & (pc) & (Gyr) & (mas yr$^{-1}$) & (mas yr$^{-1}$) & (km s$^{-1}$) \\
\hline
J2137+1050 & DC & 2 & H & 3670 $\pm$ 160 & 75 & 9.8 & $-$228.9 & $-$473.6 & 187.1 \\
J2145+1106N & DC & 2 & H & 3720 $\pm$ 110 & 68 & 9.7 & 191.9 & $-$366.9 & 134.4 \\
J2145+1106S & DC & 2 & H & 3960 $\pm$ 100 & 65 & 9.1 & 185.9 & $-$367.7 & 126.5 \\
J0040+1458 & DC & 1 & He & 4890 $\pm$ 90 & 94 & 6.3 & 128.1 & 18.5 & 57.6 \\
J0047$-$0852 & DC & 1 & H & 3140 $\pm$ 160 & 68 & 11.0 & 211 & $-$27.2 & 69.0 \\
& & & He & 3920 $\pm$ 120 & 79 & 8.5 & & & 79.2 \\
J0108$-$0954 & DC & 1 & H & 3630 $\pm$ 520 & 77 & 9.9 & $-$70.1 & $-$183.9 & 72.1 \\
& & & He & 4360 $\pm$ 150 & 100 & 7.5 & & & 93.6 \\
J0147$-$0935 & DC & 1 & H & 4300 $\pm$ 320 & 108 & 8.2 & 211.5 & $-$26.4 & 109.0 \\
& & & He & 4640 $\pm$ 190 & 126 & 6.9 & & & 127.3 \\
J0734+3728 & DC & 1 & H & 3700 $\pm$ 140 & 94 & 9.8 & $-$3.5 & $-$114 & 50.5 \\
J0749+2947 &\dots & \dots & He & 4690 $\pm$ 60 & 90 & 6.7 & 216.1 & $-$133.9 & 108.9 \\
J0805+2735 &\dots & \dots & H & 4130 $\pm$ 120 & 94 & 8.7 & 68.1 & $-$215.9 & 101.1 \\
J0805+3747 &\dots & \dots & He & 4820 $\pm$ 80 & 118 & 6.4 & $-$91.8 & $-$135.5 & 91.4 \\
J0811+3842 & DC & 1 & He & 4570 $\pm$ 110 & 131 & 7.0 & 99.3 & $-$147.4 & 110.1 \\
J0817+3106 &\dots & \dots & He & 4510 $\pm$ 50 & 67 & 7.1 & 231.4 & $-$93.8 & 79.8 \\
J0820+3904 & DC & 1 & H & 4050 $\pm$ 150 & 104 & 8.9 & $-$172 & $-$129 & 106.0 \\
J0822+3903 & DC & 1 & H & 4190 $\pm$ 150 & 109 & 8.5 & 274.2 & $-$316.5 & 216.5 \\
J0828+3527 & DC & 3 & He & 4840 $\pm$ 60 & 65 & 6.4 & $-$13.1 & $-$161 & 49.9 \\
J0848+4204 &\dots & \dots & He & 4820 $\pm$ 120 & 146 & 6.4 & $-$137.8 & $-$32.5 & 97.9 \\
J0854+3907 &\dots & \dots & He & 4810 $\pm$ 80 & 119 & 6.5 & $-$29.9 & $-$162.1 & 93.2 \\
J0910+3744 & DC & 1 & $-$3.69 & 3450 $\pm$ 190 & 63 & 9.5 & $-$143.6 & $-$91.7 & 50.7 \\
J0918+5028 &\dots & \dots & He & 4810 $\pm$ 70 & 94 & 6.5 & $-$108.2 & $-$185.9 & 96.3 \\
J0927+4852 &\dots & \dots & 6.33 & 3210 $\pm$ 90 & 42 & 9.9 & 216.5 & $-$70.1 & 45.4 \\
J1009+5347 &\dots & \dots & He & 4290 $\pm$ 100 & 104 & 7.7 & $-$120.1 & $-$254.3 & 138.2 \\
J1024+4920 &\dots & \dots & He & 4680 $\pm$ 120 & 128 & 6.8 & $-$80.1 & $-$391.8 & 242.1 \\
J1056+5043 &\dots & \dots & He & 4560 $\pm$ 70 & 104 & 7.0 & $-$36.7 & $-$119.7 & 61.7 \\
J1101+4854 &\dots & \dots & He & 4770 $\pm$ 80 & 97 & 6.6 & 73.9 & $-$196.1 & 96.8 \\
J1145+5638 &\dots & \dots & He & 4780 $\pm$ 120 & 148 & 6.5 & $-$127 & $-$114.3 & 119.8 \\
J1205+5502 &\dots & \dots & He & 4560 $\pm$ 70 & 102 & 7.0 & $-$23.4 & $-$311.8 & 151.2 \\
J1323+0223 &\dots & \dots & H & 4250 $\pm$ 170 & 116 & 8.4 & $-$112.2 & $-$50.6 & 67.5 \\
J1333+4942 &\dots & \dots & He & 4550 $\pm$ 60 & 95 & 7.0 & $-$174.7 & $-$0.9 & 79.0 \\
J1409$-$0100 &\dots & \dots & H & 4090 $\pm$ 120 & 92 & 8.8 & $-$125.2 & 75.8 & 63.7 \\
J1421+0356 &\dots & \dots & He & 4340 $\pm$ 100 & 111 & 7.5 & $-$156.2 & $-$15 & 82.3 \\
J1434+5345 &\dots & \dots & He & 4600 $\pm$ 70 & 100 & 7.0 & $-$143 & 136.6 & 93.5 \\
J1444+6025 &\dots & \dots & He & 4730 $\pm$ 100 & 132 & 6.6 & $-$18.1 & $-$134.3 & 85.1 \\
J1446+0258 &\dots & \dots & He & 4360 $\pm$ 140 & 104 & 7.5 & $-$196.2 & 43.2 & 99.5 \\
J1509+5408 &\dots & \dots & He & 4320 $\pm$ 110 & 114 & 7.6 & 13.3 & $-$135.7 & 73.9 \\
J1513+5023 &\dots & \dots & -3.22 & 3860 $\pm$ 180 & 86 & 8.7 & $-$98.6 & $-$49.4 & 45.0 \\
J1513+4743 & DA & 1 & H & 5960 $\pm$ 120 & 124 & 2.3 & $-$500.8 & $-$147.1 & 305.9 \\
J1515+5930 &\dots & \dots & H & 3700 $\pm$ 120 & 87 & 9.8 & $-$74.6 & 90.4 & 48.5 \\
J1533$-$0012 &\dots & \dots & He & 4240 $\pm$ 100 & 107 & 7.8 & $-$44.2 & $-$140.2 & 74.7 \\
J1534+5624 & DC & 1 & H & 4900 $\pm$ 120 & 84 & 6.2 & $-$140.3 & 119.5 & 73.2 \\
& & & He & 5050$_{-70}^{+120}$ & 93 & 5.7 & & & 81.0 \\
J1552+4638 & DA & 1 & H & 5100$_{-100}^{+120}$ & 88 & 5.2 & $-$48.7 & $-$181.5 & 78.1 \\
J1555+4940 & DC & 1 & -3.16 & 3910 $\pm$ 180 & 94 & 8.5 & 27.1 & $-$127.1 & 57.6 \\
J1601+4120 & DC & 1 & H & 4080 $\pm$ 120 & 36 & 8.8 & 74.8 & $-$228.7 & 40.6 \\
& & & He & 4610 $\pm$ 60 & 44 & 6.9 & & & 50.5 \\
J1601+4204 &\dots & \dots & He & 4540 $\pm$ 110 & 119 & 7.1 & $-$111.1 & 70.9 & 74.1 \\
J1604+3923 & DA & 1 & H & 5010 $\pm$ 140 & 99 & 5.6 & 15.3 & $-$152.1 & 72.0 \\
J1624+4156 & DA & 1 & H & 5840 $\pm$ 150 & 133 & 2.4 & 27.7 & $-$194.1 & 123.6 \\
J1627+3726 & DC & 3 & He & 4650 $\pm$ 50 & 57 & 6.8 & $-$24.1 & $-$169.3 & 46.0 \\
J1643+4438 & DC & 1 & He & $4910 _{-40}^{+60}$ & 70 & 6.2 & 42.8 & $-$197.7 & 66.8 \\
J1647+3946 & DC & 1 & He & 4360 $\pm$ 70 & 91 & 7.5 & $-$114.3 & $-$111.8 & 69.3 \\
J1649+2932 & DC & 1 & He & 4930 $\pm$ 80 & 99 & 6.2 & 121.3 & 16.1 & 57.6 \\
J1657+2638 & DC & 1 & H & 3550 $\pm$ 100 & 67 & 10.1 & $-$73.3 & $-$104.6 & 40.3 \\
J1711+2940 & DC & 1 & He & 4550 $\pm$ 70 & 97 & 7.1 & 57.7 & $-$165.8 & 80.7 \\
J1715+2600 & DC & 1 & He & 4310 $\pm$ 80 & 88 & 7.6 & $-$34.3 & $-$162.2 & 69.5 \\
J2127+1036 & DC & 1 & H & 3970 $\pm$ 370 & 93 & 9.1 & $-$112.5 & $-$65.9 & 57.5 \\
& & & He & 4470 $\pm$ 160 & 113 & 7.2 & & & 69.7 \\
J2230+1415 & DA & 1 & H & 5210 $\pm$ 140 & 107 & 4.6 & $-$18.3 & $-$142.3 & 72.7 \\
J2316$-$1044 & DC & 1 & H & 3670 $\pm$ 790 & 93 & 9.8 & 237.7 & $-$72 & 109.7 \\
& & & He & 4310 $\pm$ 200 & 115 & 7.6 & & & 136.0 \\
J2320$-$0845 & DC & 1 & H & 3240 $\pm$ 190 & 67 & 10.8 & 166.7 & 20.3 & 53.3 \\
& & & He & 4010 $\pm$ 130 & 80 & 8.3 & & & 63.7 \\
\hline
\end{tabular}
\end{table*}
\subsection{Pure H Solutions}
Of our 57 targets, only 45 have the near-infrared data that are needed to observe the CIA that allows us
to detect the presence of hydrogen. Of these 45 objects, twelve have SEDs best fit by pure hydrogen models.
Figure \ref{fig:pure_h} shows the SEDs and our model fits for four of these objects (full sample is available online). We show the photometric data as error bars and the best-fit model
fluxes for pure H and pure He composition as filled and open circles, respectively.
\begin{figure*}
\includegraphics[angle=-90,width = 14cm]{H_ex.ps}
\caption{Fits to the SEDs for four of our WDs with pure H atmospheres (full sample available online). Filled circles are pure H models, and open circles are pure He models (included for comparison).}
\label{fig:pure_h}
\end{figure*}
J1513+4743 is the only DA white dwarf in our sample with near-infrared photometry available (the four
other DAs are discussed in Section \ref{sec:nonIR}), and the pure H model is a better fit to the SED
than the pure He model. For the remaining objects, we chose the composition based on the solution that
best fits the SED. Our sample includes three previously published H-atmosphere DC white dwarfs: J2137+1050,
J2145+1106N, and J2145+1106S \citep{kilic10a}. Our temperature estimates of $3670\pm 160$, $3720\pm110$, and
$3960\pm100$ K, respectively agree with the previously published values of 3780, 3730 K, and 4110 K \citep{kilic10a}
within the errors.
With the exception of the DA WD J1513+4743, all of the remaining 11 objects that are best explained by pure H
atmosphere models have $T_{\rm eff} \leq 4250$ K. These objects appear significantly fainter in the $H-$band
than expected from the blackbody-like SEDs of pure He atmosphere white dwarfs, indicating that they have H-rich
atmospheres. In addition to the previously published J2137+1050 and J2145+1106N \citep{kilic10a}, we identify
three new white dwarfs with $T_{\rm eff}\leq3700$ K; namely J0734+3728, J1515+5930, and J1657+2638.
The latter is the coolest white dwarf known ($T_{\rm eff} = 3550 \pm 100$ K) with an SED that is matched
relatively well by a pure H atmosphere model. The implied cooling age for such a cool white dwarf is
10.1 Gyr assuming an average mass, $\log{g}=8$, white dwarf.
\subsection{Pure He Solutions}
For our remaining 33 objects with infrared data, 29 show no evidence of CIA and are best fit by
pure He atmosphere models. Figure \ref{fig:pure_he} shows the SEDs for a sample of these targets. All 29 of these
objects have $T_{\rm eff}$ in the range $4240-4930$ K. Nine stars have optical spectra available, and
all nine are DC white dwarfs.
\begin{figure*}
\includegraphics[angle=-90,width = 14cm]{He_ex.ps}
\caption{Fits to the SEDs for four of our WDs with pure He atmospheres (full sample available online). Filled circles are pure H models (included for comparison), and open circles are pure He models.}
\label{fig:pure_he}
\end{figure*}
The differences between the pure H and pure He
model fits are relatively small in this temperature range, and additional $K-$band photometry would be
useful to confirm the atmospheric composition for these stars. However, \citet{bergeron01a} and \citet{kilic10b}
also find an overabundance of pure He atmosphere white dwarfs in the temperature range 4500-5000 K.
\citet{kilic10b} discuss a few potential problems that could lead to misclassification of spectral types
for these stars, including problems with the CIA calculations, or small shifts in the $ugriz$ or $JH$
photometric calibration.
\subsection{Mixed Atmosphere Solutions}
The last four targets with infrared data (J0910+3744, J0927+4852, J1513+4743, and J1555+4940) have SEDs
that are inconsistent with either a pure H or pure He atmosphere solution. We fit the SEDs of these stars
with a mixed H/He atmosphere model. The mixed models allow for significant $H_2$-He CIA at higher temperatures
than seen for $H_2$-$H_2$, as CIA becomes an effective opacity source at higher temperatures in cool He-rich
white dwarfs due to lower opacities and higher atmospheric pressures \citep{bergeron02}.
Figure \ref{fig:mixed} shows our mixed H/He atmosphere model fits for these four objects.
The models yield $\log{(He/H)}$ of $-3.7, 6.3, -3.2$, and $-3.2$ and temperatures of 3450, 3210, 3860,
and 3910 K, respectively. Note that these models predict CIA absorption features around 0.8 and 1.1$\mu$m
that are never observed in cool white dwarfs. Hence, the temperature and composition estimates for such
infrared-faint stars is problematic \citep[see the discussion in][]{kilic10b,gianninas15}.
\begin{figure*}
\includegraphics[width = 8cm]{J0910.ps}
\includegraphics[width = 8cm]{J0927.ps}
\includegraphics[width = 8cm]{J1513.ps}
\includegraphics[width = 8cm]{J1555.ps}
\caption{Fits to the SEDs of the four white dwarfs best fit by mixed atmosphere models.}
\label{fig:mixed}
\end{figure*}
The coolest object among these four stars, J0927+4852 appears to be similar to WD0346+246.
\citet{oppenheimer01} originally found a $T_{\rm eff} = 3750$ K and $\log{(He/H)}$ = 6.4 for
WD0346+246, for an assumed surface gravity of $\log{g}=8$. However, \citet{bergeron01a} showed that such a
He-rich atmosphere would require accretion rates from the interstellar medium too low to be
realistic. With the addition of parallax observations to constrain the distance, they estimated
a more realistic solution with $T_{\rm eff} = 3780$ K, $\log{(He/H)}=1.3$, and $\log{g}=8.34$.
A re-analysis by \citet{kilic12} that include the red wing of the Ly$\alpha$ opacity indicate
a similar solution with $T_{\rm eff} = 3650$ K, $\log{(He/H)}=-0.4$, and $\log{g}=8.3$.
Adopting a similar $\log{g}$ value for J0927+4852 would yield a $T_{\rm eff}$ of 3730 K and $\log{(He/H)}$ of 0.3.
This exercise shows the problems with constraining the atmospheric composition of ultracool white dwarfs, and
the need for parallax observations to derive accurate parameters for such white dwarfs.
Regardless of these issues, all four mixed atmosphere white dwarfs appear to be ultracool ($T_{\rm eff}<4000$ K),
bringing the total number of ultracool white dwarfs in our sample to ten.
\subsection{Targets without Infrared Data}
\label{sec:nonIR}
There are twelve spectroscopically confirmed white dwarfs in our sample that lack infrared photometry.
Figure \ref{fig:non-ir} displays the SEDs along with the pure H and pure He model fits for a subsample of these objects.
The spectra of four of these objects; J1552+4638, J1604+3923, J1624+4156, and J2230+1415 confirm that they
are DA white dwarfs, and the pure H models reproduce the SEDs and spectra reasonably well. This brings our
final number of pure H solutions to sixteen stars.
\begin{figure*}
\includegraphics[angle=-90,width = 14cm]{nonIR_ex.ps}
\caption{Fits to the SEDs for a sample of our WD lacking IR data (full sample available online). Filled circles are pure H models, and open circles are pure He models. As can be seen, no model is clearly better.}
\label{fig:non-ir}
\end{figure*}
The remaining eight objects without infrared data are confirmed to be DC white dwarfs. For the most part, the
pure H and pure He models are nearly indistinguishable in the optical for these objects and we cannot
determine their composition. Table \ref{tab:wd} shows the results for both pure H and pure He solutions
for these objects.
All of these targets have SEDs rising toward 1$\mu$m, hence the lack of infrared data
limits the precision of these temperature measurements. However, given the lack of He
atmosphere white dwarfs below 4240 K, we do not expect J0047$-$0852 and J2320$-$0845 to
have pure He atmospheres, and if they were to have pure H atmospheres, they would be the
coolest white dwarfs in our sample, with $T_{\rm eff}$ of $3140 \pm 160$ K and $3240 \pm 190$
K respectively. J0108$-$0954, J2127+1036, and J2316$-$1044 are also potentially ultracool objects
if the pure H solution is correct, which would bring the total number of ultracool white dwarf
candidates in our sample to fifteen. Without infrared data, however, we cannot rule out
the pure He solution, or the possibility of a mixed H/He atmosphere for J0047$-$0852 and J2320$-$0845.
\section{Kinematic Membership}
\label{sec:kinematics}
The estimated temperatures for our targets yield white dwarf cooling ages between 5 and 10 Gyr,
with the only notable exceptions being J1513+4743 and J1624+4156, which have cooling ages of 2.3
and 2.4 Gyr respectively. Eight objects have cooling ages longer than 9 Gyr, with the oldest
being J1657+2638 at 10.1 Gyr. However, in order to associate a white dwarf with the thick disc or
halo, it is important to determine the total stellar age \citep{bergeron05}. The main-sequence
lifetime of the $\approx 2 M_{\odot}$ progenitor of a $0.6 M_{\odot}$ white dwarf is 1.0-1.3 Gyr;
therefore, the total ages of our objects on average range from 6 to 11 Gyr, with J1513+4743 and
J1624+4156 having total ages between 3.3 and 3.7 Gyr.
Figure \ref{fig:UVW} shows U versus V (bottom) and W versus V (top) velocities of our objects
(assuming a radial velocity of 0 km s$^{-1}$and calculated using the prescription of \citet{johnson87}),
as well as the 3$\sigma$ ellipsoids of the halo, thick disc, and thin disc populations \citep{chiba00}.
The filled, open, and red circles represent the objects best fit by pure H, pure He, and mixed H/He
atmosphere models, respectively. For the eight objects with undetermined compositions, velocities were
calculated assuming the pure H solution for simplicity. The choice of the pure H or pure He solution
has a negligible effect on the final UVW velocities (see Table \ref{tab:wd}).
\begin{figure}
\includegraphics[scale=0.425,bb=30 167 592 679]{plotWV.ps}
\includegraphics[scale=0.425,bb=30 117 592 679]{plotUV.ps}
\caption{Plots of W vs. V (top) and U vs. V (bottom) velocity distributions for our sample of H-rich (black dots), He-rich (white dots), and mixed (red) WDs. Also plotted are the 3$\sigma$ ellipsoids for the Galactic thin disc (dotted), thick disc (dashed), and stellar halo populations (solid).}
\label{fig:UVW}
\end{figure}
J2137+1050 shows velocities inconsistent with thick disc objects in U, consistent with the analysis in \citet{kilic10a},
while the results for the J2145+1106 common-proper motion binary are consistent to 2$\sigma$, but not 3$\sigma$. In addition,
three other targets in our sample show velocities inconsistent with thick disc objects: J0822+3903, J1024+4920, and
J1513+4743, with cooling ages of 8.5, 6.8, and 2.3 Gyr respectively. The Toomre diagram for our targets is shown in
Figure \ref{fig:toomre}, with thin disc and thick disc boundaries from \citet{fuhrmann04}; the differentiation between our halo
candidates and the rest of our sample is clearer here than in Figure \ref{fig:UVW}.
\begin{figure*}
\includegraphics[angle=-90,width = 14cm]{toomre.ps}
\caption{Toomre diagram for our 57 targets. Symbols have the same meaning as Figure \ref{fig:UVW}. Thin disc (dotted) and thick disc (dashed) boundaries taken from \citet{fuhrmann04}.}
\label{fig:toomre}
\end{figure*}
The total main-sequence + white dwarf cooling ages of these objects are relatively young for halo objects,
but without parallax measurements, we cannot constrain their masses, velocities, and cooling ages precisely. For example,
if these objects have $M\approx0.53M_{\odot}$ \citep{bergeron01a}, the progenitor mass would be closer to $1M_{\odot}$ and
their main-sequence lifetimes would be on the order of 10 Gyr, making them excellent candidates for membership in the halo.
A lower surface gravity would also imply a larger and more distant white dwarf, and UVW velocities that are even more inconsistent
with the thick disc population. Conversely, for $\log{g} = 8.5$ white dwarfs, the cooling ages would range from 5 to 11
Gyr, and the UVW velocities of our halo white dwarf candidates would remain inconsistent with thick disc objects.
Interestingly, with the exception of the three previously published white dwarfs (J2137+1050 and J2145+1106 binary),
none of our objects with cooling ages above 9 Gyr have UVW velocities inconsistent with the thick disc, nor do they
show the high tangential velocities expected for halo objects. In fact, the highest tangential velocity for these
objects is 72 km s$^{-1}$. Assuming these objects really do belong to the thick disc gives a thick disc age of
$\approx$11 Gyr.
Our assumption of zero radial velocity has a negligible effect on our results \citep[see the discussion in][]{kilic10a}.
The UVW velocities of our halo white dwarf candidates remain inconsistent with the 3$\sigma$ distribution for the thick
disc for positive and negative radial velocities up to 100 km s$^{-1}$ (though J0822+3903 only remains inconsistent in both U and
W for radial velocities between -90 and 30 km s$^{-1}$).
\section{Conclusions}
\label{sec:con}
We present follow-up optical spectroscopy and/or near-infrared photometry of 57 cool white dwarf candidates
identified from a $\approx3100$ square degree proper motion survey described by \citet{munn14}. Thirty one
of our candidates are spectroscopically confirmed to be white dwarfs, including 5 DA and 26 DC white dwarfs.
The remaining targets have proper
motion measurements from both optical and infrared observations that are consistent within the errors. The
optical and near-infrared colors for these targets are also consistent with the predictions from the white
dwarf model atmospheres. Hence, the contamination from subdwarfs should be negligible for this sample of
57 stars.
We perform a model atmosphere analysis of these 57 objects using $ugriz$ and $JH$ photometry.
The best-fit models have 29 pure He atmosphere white dwarfs with $T_{\rm eff}=4240-4930$ K, 16 pure
H atmospheres with $T_{\rm eff}=3550-5960$ K, and 4 mixed H/He atmospheres with $T_{\rm eff}=3210-3910$ K.
Eight of our targets lack the near-infrared data necessary to differentiate between the pure H and pure He solutions.
Our sample contains ten ultracool white dwarf candidates, with another five potential candidates that currently
lack near-infrared data. All of the ultracool white dwarfs have hydrogen-rich atmospheres. J1657+2638 is
the most interesting with $T_{\rm eff} = 3550 \pm 100$ K and an SED that is reproduced fairly well by
a pure H atmosphere. For an average mass of 0.6 $M_{\odot}$, J1657+2638 would be an $\approx$11 Gyr old
(main-sequence + cooling age) white dwarf at a distance of 67 pc. The implied tangential velocity of 40 km s$^{-1}$
demonstrates that J1657+2638 belongs to the Galactic thick disc.
Our sample contains three new halo white dwarf candidates. All three have high tangential velocities and
UVW velocities inconsistent with the Galactic thick disc. The oldest halo white dwarf candidate
is J0822+3903 with a cooling age of 8.5 Gyr. However, without trigonometric parallax observations, we cannot
accurately constrain the distances, masses, and ages of our white dwarfs.
Our current sample of cool field halo white dwarfs is limited by a lack of deep proper motion surveys. Ongoing
and future large scale surveys such as \textit{GAIA} and \textit{LSST} will find a significant number of cool
white dwarfs, including halo white dwarfs, in the solar neighborhood. With $g-$band magnitudes of 20$-$22, we
expect parallax errors from \textit{GAIA} to range from about 400$-$1200 $\mu$as
\footnote{http://www.cosmos.esa.int/web/gaia/science-performance}, corresponding to uncertainties of $\approx 20$
per cent in both mass and cooling age for the majority of our targets. In addition, \textit{GAIA} will reveal the
brighter population of halo white dwarfs near the Sun.
\section*{Acknowledgements}
We gratefully acknowledge the support of the NSF and
NASA under grants AST-1312678 and NNX14AF65G, respectively.
|
{
"redpajama_set_name": "RedPajamaArXiv"
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Before the era of internet business in Indonesia, internet connections could only be found at a few leading universities. By using UUCP, university servers in Indonesia exchange information with other university servers in the world through their respective gateways. In 1994, the internet business in Indonesia was started, marked by the granting of an internet service provider (ISP) company license issued by the Indonesian government to PT. Rahajasa Media Internet or RADNET.
Usage
Based on OpenSignal in November 2016, there were only 58.8% of internet users in Indonesia who received 4G LTE signal, and received only HSPA+ signal or lower the rest of the time, ranking Indonesia 51st in the world. The download speed using 4G LTE in Indonesia was only an average of 8.79Mbit/s (ranked 74th in the world).
Based on the Indonesia Internet Service Providers Association, in mid-2016, there were 132.7 million internet users, representing more than half of the Indonesian population. Only 3% of users are 50 years old or over, but surprisingly 100% in the 10–14 age bracket. Users on the island of Java dominated (65%), followed by Sumatra with 15.7 million users. Almost 90% of users were employees and students. Almost all of the users knew about e-commerce, but only 10.4 million users used the internet for transactions. Almost 70% of the users used their mobile phones for access.
According to eMarketer in 2014, Indonesia had 83.7 million users (in sixth place behind Japan), but Indonesia was predicted to surpass Japan in 2017, due to the slower growth rate in Japan compared to Indonesia.
According to Akamai Technologies, Indonesia, with nine connections to undersea cables, had in Q1 2014 an average Internet connection speed of 2.4 Mbit/s, which was an increase of 55% from the previous year. Just 6.6% of homes had access to 4 Mbit/s or higher speed connections. However, in Q4 2014, the average internet connection speed was 1.9Mbit/s or dropped about 50% from Q3 2014 with 3.7Mbit/s.
Based on the Indonesia Internet Service Providers Association, in Q4 2013, there were 71.19 million Internet users in Indonesia or about 28% of Indonesia's population. According to Cisco's Visual Networking Index, in 2013, Indonesia had the world's second-fastest growth of IP traffic and has become an "Internet of Everything" country.
Based on Communication Ministry data, at the end of June 2011, there were 45 million Internet users in Indonesia, of which 64% or 28 million users are between the ages of 15 to 19.
July 2011: Based on Nielsen's survey, 48% of Internet users in Indonesia used mobile phones for access, whereas another 13% used other handheld multimedia devices. It represents the highest dependence on mobile internet access in Southeast Asia, although Indonesia has the lowest level of overall internet penetration in the region with only 21% of Indonesians aged between 15 and 49 using the Internet.
According to a survey conducted by the Association of Internet Service Providers in Indonesia, the number of internet users in Indonesia reached 171.17 million at the beginning of 2019. The Indonesian government is eager to complete the Palapa Ring project, an undersea fiber-optic cable network across the country to offer affordable and faster internet access. It is expected to be fully completed by August 2019. The project comprises three sections – the west, central and east – that would span around 13,000 kilometers. It aims to expand domestic broadband service nationwide, particularly in the remote rural regions. The project is estimated to cost Rp 1.38 trillion (US$97.74 million) and would provide 4G access with speeds of up to 30 Mbit/s. In addition to connecting all of Indonesia in the telecommunications network, the Palapa Ring development is intended to reduce the gap in telecommunications services between Java and other regions in Indonesia.
May 2011: Based on TNS research, Indonesia has the world's second-largest number of Facebook users and the third-largest number of Twitter users. Eighty-seven percent of Indonesians have social networking site accounts, but only 14% access the sites daily, far below the global average of 46% due to access from old phones or inconvenient internet cafes. In line with the increase of cheap Android smartphones recently, there is the possibility that Indonesian internet user activity will increase as well.
Based on the Yahoo Net Index survey released in July 2011, the internet in Indonesia still ranks second after television in terms of media usage. Eighty-nine per cent of users were connected to social network, 72% used the internet for web browsing, and 61% read the news.
Indonesian Internet service providers (ISPs) offer service on PT Telkom's ADSL network. ADSL customers usually receive two separates bills, one for the ADSL line charges to PT Telkom and another for Internet service charges to the ISP.
Mobile internet & telecommunications
All of the GSM major cellular telecommunication providers offer 3G, 3.5G HSDPA and 4G LTE, which cover cities and countrysides. They include Indosat, Telkomsel, Excelcomindo (XL) and 3. The usage of CDMA EV-DO has been phased out as the last provider, Smartfren, pulled its support in 2017 and converted to LTE-A. In 2016, almost all CDMA providers in Indonesia moved to either GSM or 4G LTE service such as Smartfren.
Due to COVID-19, Indonesia is adapting to digital transformation faster than predicted. The country is one of the striving mobile markets, underpinned by strong economic fundamentals, hence fast developing. With the population of the country, Indonesia is among the biggest market especially for smartphones along with China and India. 4G in Indonesia will continue to be the main network for mobile internet in Indonesia as 3G gradually resides over the years. The country is predicted by GSM Association to launch the new 5G network for commercial usage by 2022 and forecasted to have more than 20 million 5G connections by 2025.
Telkomsel launched 5G on 27 May 2021 in Jakarta and 8 other cities. Indosat have been given a permit to operate 5G networks, and will roll out 5G in four cities in Java and Sulawesi. Smartfren is currently testing mmWave 5G in its office.
Censorship
Internet filtering in Indonesia was deemed "substantial" in the social arena, "selective" in the political and internet tools arenas, and there was no evidence of filtering in the conflict/security arena by the OpenNet Initiative in 2011 based on testing done during 2009 and 2010. Testing also showed that Internet filtering in Indonesia is unsystematic and inconsistent, illustrated by the differences found in the level of filtering between ISPs.
Cyber army
As of 29 May 2013, the Indonesian Defence Ministry has proposed plans for creating a cyber army in order to protect the state's portals and websites. Though no law has yet been created in order to maintain and establish the cyber army, the ministry is seeking talented Internet security specialists who, upon hiring, would be trained in information technology and use methods to defend against cyber-attacks.
Domestic domain
Upon learning that about 80% of local internet traffic went abroad, the government began to encourage Indonesian institutions, business people and the public in general to use domestic domains. In mid-April 2015, there were about 20,000 .id domains and about 47,000 .co.id domains. The government targeted one million domestic domains with funding of Rp 50 billion ($3.85 million). Some users with non-domestic domains also possess domestic domains and redirect searches from its non-domestic domains to domestic domains.
See also
Communications in Indonesia
Indonesia Internet Exchange
References
Further reading
External links
APJII Indonesian ISP Association
Department of Transportation: Departemen Perhubungan - Wireless Frequency regulator
Department of Communication and Informatics: Departemen Komunikasi dan Informasi
Internet companies in Indonesia
|
{
"redpajama_set_name": "RedPajamaWikipedia"
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**CONTENTS**
_Foreword_
1The Sea Monster
2Diving for Seahorses in February
3The Skydiver's Final Thoughts
4In the Cuckoo's Nest
5The Big Taxi Experiment and a Rather Extraordinary Game of Chess
6The Elephant's Graveyard
7The Seeds of Svalbard
_Notes_
_Recipe for Good Memories (Acknowledgments)_
**FOREWORD**
**_Sam Kean_**
IN ONE OF Plutarch's _Lives_ , he mentions an old philosophical conundrum now called the Ship of Theseus Paradox. After slaying the minotaur in the labyrinth, the Greek hero Theseus sails home, and the people of Athens are so overjoyed that they preserve his ship as a memorial. Being a material object, however, the ship shows some wear and tear as the years pass, and every so often the caretakers have to replace a piece of it—a board here, a plank there. Eventually, after several centuries, they've replaced every last original piece of wood. So is it still the same ship now that it was at the beginning?
You can ask a similar question about our own bodies. We're three-fourths water, molecules of which cycle into and out of us in a constant flow, never sticking around long. And because our DNA and other biomolecules break down, we swap in new parts all the time to repair them. Skin cells get recycled every few weeks, blood cells every few months, liver cells every two years. Even bone experiences constant turnover. Over the course of a decade or so, every last atom in your body gets replaced. So are you still _you_ at the end?
Most of us feel, intuitively, that we do remain the same person from decade to decade. But how can that be if our bodies aren't the same? Why do we feel this continuity so strongly? One big reason is because of our memories. The bio-bits come and go, but the pattern of information coursing through our brains remains largely consistent. In a fundamental way, then, we _are_ our memories.
Yet, few of us really understand how memory works. We rely on misleading analogies or folk theories, or we simply remain oblivious and take it all for granted: memories bubble up so easily inside us, so effortlessly, that we rarely pause to consider just what a miracle they are.
Well, no more. After reading _Adventures in Memory_ , you'll fully appreciate what a complex, beautiful, and intricate thing memory is. Indeed, in the hands of Hilde and Ylva Østby, memory is more than a simple repository of our selves. It's a creative force—something dynamic that actively shapes our thinking. It has all the rich, layered complexity of human beings themselves.
What makes the book unique is the double-barreled perspective the Østby sisters bring. Unlike, say, electrons or black holes, memory is both an objective and a subjective phenomenon. We need to understand the neurotransmitters and electrical firing patterns involved, but memory is a _lived_ thing too. We need both sides—in other words, the literary and the scientific—to make sense of memory. It's therefore reassuring to know that Hilde Østby is a novelist and her sister Ylva a neuroscientist. Imagine if another sibling pair—William James the famous psychologist and Henry James the brilliant novelist—had combined forces, and you can see what a valuable perspective this combination provides.
We usually think about science as ultra-rational, but it's an intensely human activity as well. And it's especially important to see that human side when studying memory, since it does influence our sense of self so profoundly. In exploring how memory works, then, _Adventures in Memory_ is really a dive into your innermost self—the most intimate aspects of your being. And when you surface from this dive, you'll never see the world, or your own self, in quite the same way again.
SAM KEAN, author of _Caesar's Last Breath_ and _The Tale of the Dueling Neurosurgeons_
— 1 —
**THE SEA MONSTER**
**_Or: The discovery of the hippocampus_**
Your memory is a monster; _you_ forget— _it_ doesn't. It simply files things away. It keeps things for you, or hides things from you—and summons them to your recall with a will of its own. You think you have a memory; but it has you!
**JOHN IRVING _, A Prayer for Owen Meany_**
AT THE BOTTOM of the ocean, tail curled around seagrass, the male seahorse sways back and forth in the current. He may be tiny and mysterious, but no ocean creature compares to him. The only male in the animal kingdom to become pregnant, he stands on guard, carrying his eggs in his pouch until they hatch and the fry swim away into the open sea.
But let's back up: this isn't a book about seahorses. To find our real subject, we must rise out of the depths and journey back 450 years.
The year is 1564. We're in Bologna, Italy, a city full of elegant brick buildings and shady, vine-covered walkways. Here, at the world's first proper university, Dr. Julius Caesar Arantius bends over a beautiful object. Well, beautiful might be an exaggeration, if you're not already deeply, passionately involved in its study. It's a human brain. Rather gray and unassuming, and on loan from a nearby mortuary. Students surround the doctor, clustered on benches throughout the theater, following his work intently, as though he and the organ in front of him are the two leads in a drama. Arantius leans over the brain and slices through its outer layers, studying each fraction of an inch with extreme interest, hoping to understand what it does. His disregard for religious authority is clear in the gusto with which he approaches his dissection because, until shortly before that time, the scientific study of human corpses had been strictly forbidden.
The doctor cuts further into the object, examining what's inside. And then, deep within the brain, buried in the temporal lobe, he finds something very interesting. Something small, curled up into itself. It looks, he thinks, a bit like a silkworm. The upper classes of the Italian Renaissance loved silk, a luxurious and exotic fabric that arrived in Venice via the Silk Road from China; by extension, they loved silkworms too. Intrigued, Arantius looks closer, making some careful cuts, and pries the little worm loose, liberating it from the rest of the brain.
This is the moment at which modern memory research was born, the precise moment that memory, as a concept, moved from the mythological world into the physical one. However, back then, on that particular day in sixteenth-century Bologna, life goes on in the markets as usual; people carry wine and truffles and pasta below the city's famous pergolas and ancient red brick towers, oblivious to the hugely important discovery in their midst.
Arantius turns over what he has dug out of the brain and places it on the table before him, considering what it might be. That's it! Rather than a silkworm, perhaps it is a tiny seahorse? Yes, indeed. With its head nodding forward and its tail curling up, it does look like a seahorse, the tiny distinctive fish living in shallow ocean waters between the tropics and England. And so he names it: _hippocampus_ , meaning "horse sea monster" in Latin. It also shares its name with a mythological creature—half horse, half fish—said to wreak havoc in the waters around ancient Greece.
By the light of a tallow candle perched on an autopsy table, Julius Caesar Arantius couldn't tell what this little part of the brain actually did. All he could do was give it a name. Hundreds of years passed before we fully understood the significance of what this Italian doctor held in his hands, and you might guess that it has something to do with memory. After all, memory is the subject of this book.
The world beneath the sea and the one in our brain are profoundly different, of course, but there are many similarities between the seahorse and the hippocampus. Just as the male seahorse carries his eggs in his pouch until it's safe for the fry to be on their own, the seahorse of the _brain_ also carries something: our memories. It watches over them and nurtures them until they are strong enough to make it on their own. The hippocampus is the womb that carries our memories.
No one knew how crucial the hippocampus was to memory until 1953, but there was endless speculation about where memories were stored in the brain. One popular early belief was that our thoughts flowed through the liquid inside our skulls, but that theory was long gone by 1953. By then, the prevailing thought was that memories were created and stored throughout the brain. But then something happened to sink this theory once and for all, an incident that was tragic for one man, fortunate for the rest of us. An unsuccessful experimental surgery was the key to understanding Julius Caesar Arantius's earlier discovery.
IF HENRY MOLAISON had lived in modern times, his treatment would have been very different. Henry suffered from severe epilepsy, and several times a day—or sometimes several times an hour—he had small absence seizures (also known as petit mal seizures), in which he would black out for a few seconds at a time. At least once a week he'd suffer a major convulsive seizure (or a grand mal seizure), in which he'd completely lose consciousness and his body would shake violently for several minutes. The medicines he was prescribed only made things worse and resulted in more seizures. In 1953, at age twenty-seven, he sought treatment from a surgeon, William Beecher Scoville, who proposed an operation unthinkable by today's standards.
Dr. Scoville didn't have the benefit of hindsight. He was inspired by reports of a Canadian surgeon who'd removed the hippocampus on one side in several patients in order to cure their epilepsy, and he believed that if he removed the hippocampi from both sides of Henry's brain, then the treatment would be twice as effective. Henry listened to his doctor. After a lifetime of crippling epilepsy, he was desperate, and he agreed to the operation. Unwittingly, Henry Molaison had signed up to become the most important subject in the history of memory research.
When Henry woke up after the surgery, doctors found that he had no memory of the last two or three years; in fact, he couldn't retain anything beyond what was present within his short-term memory. The nurses had to show him the way to the bathroom every time he needed to go. He had to be constantly reminded of where he was, because he forgot as soon as he thought of something else. He had lost his ability to form new memories.
For the remaining fifty-five years of his life, Henry lived literally in the moment. He couldn't remember what he'd done half an hour ago, or the joke he'd told a minute earlier. He couldn't remember what he'd eaten for lunch and had no idea how old he really was, until he looked in the mirror and saw gray hairs. He had to guess what season it was when looking out the window. Since he couldn't remember new information, he couldn't manage his money, diet, or household chores, so he lived at home with his parents. In spite of this, he was usually calm and content. But sometimes, things would upset him—like the death of his father.
Each morning, Henry woke up with no recollection of his grief, but every time he rose, he made an alarming discovery: the valuable weapons collection normally hanging on the wall was missing. He understood there was something wrong—the weapons were gone—and concluded that the house had been burgled and the weapons stolen. The truth was that his uncle had inherited the collection. But there was no use explaining that this was due to his father's death, as the next morning he would conclude, all over again, that he'd been burgled. Finally, his uncle had to return the weapons collection. Eventually, Henry appeared to get used to the fact that his father didn't come home anymore and, to some degree, understood that he was gone.
Scoville's surgery on Henry was an experiment, but no one at the time could have anticipated the consequences. In fact, Scoville had already performed the operation on dozens of other patients. None had shown any obvious signs of memory loss. But there was a catch: every patient in this group had been acutely schizophrenic, paranoid, or psychotic. Their behavior was already abnormal, so any memory problems were blamed on their psychosis. Incidentally, they were no less schizophrenic after the surgery. But this was the era when lobotomies were in fashion, and Scoville believed he could improve this procedure by removing the hippocampi rather than following the classic approach of removing parts of the brain's frontal lobe. Exactly why he believed this is another story. _Our_ story centers on the consequences of his famous surgery on Henry Molaison. But there were also consequences for Scoville, who was deeply concerned about the results of the surgery. In a scientific paper he cowrote with Canadian neuropsychologist Brenda Milner in 1957, he confessed to his mistake. In the years after the article was published, Milner endeavored to find out more about how Henry's memory was damaged. She believed that together, she and Henry would be able to explain to the world how human memory functions.
What could be learned about memory by studying Henry Molaison? Simply talking to him revealed some basics about the structure of memory; he was quite capable of sticking to the topic of conversation, as long as his thoughts didn't wander and he didn't become distracted by something around him. This meant that he had normal _short-term_ memory. Short-term memory is what we remember _in the moment_. Before our experiences become _permanent_ memories, they spend time in short-term memory. When we look up a phone number, we remember the number for a short while before we dial it. The same happens when we learn a new word or somebody's name. These things remain in our memories for no more than a few seconds, or as long as we keep thinking about them. Sometimes, items that pass through short-term memory are picked up for long-term storing. In this case, all that remained was Henry's short-term memory, but he learned how to use it in ingenious ways. During one study, examining his ability to perceive time, a researcher told him that she would leave the room, and that when she returned, she would ask him how long he thought she'd been gone. He suspected that he wouldn't be able to do this, so he did something clever; he looked at the wall clock (something the researcher hadn't noticed) and memorized the time by silently repeating it to himself, over and over again, until she returned. When she came back, he looked at the clock again to calculate how long she'd been gone. Since he'd focused on this one task during the test, he was able to keep the information in his short-term memory. Henry knew that he was participating in an experiment. But he couldn't remember the researcher or her name.
Luckily, Henry enjoyed mental challenges; he always had a crossword with him and happily solved puzzles, which made him a willing participant in Brenda Milner's experiments. In one example, she gave him a small maze, in which he had to negotiate steps through a grid to find an exit. After 226 attempts, he still couldn't do it. But since he had no recollection of all his previous attempts, he happily carried on trying.
Another time, Milner asked him to draw a star while looking only at a reflection of his hand in a mirror. For anyone, this is a difficult task, because when you're watching a mirror image, you tend to move the pencil in the wrong direction when you get to a corner of the star. But with practice you can improve. It's a way of learning, of remembering, that helps you perform a task better the next time. But unlike remembering _events_ you have experienced, or figuring out a maze, this kind of memory doesn't involve conscious thought. It's like riding a bicycle; you never remember that you have to move your feet a certain way, or tilt your body to keep your balance; it becomes second nature. Each time Henry repeated the mirror drawing task, he too improved. As with people with intact hippocampi, he eventually mastered the mirror star test. His final, almost perfectly drawn star surprised him, because he had no knowledge of the previous attempts that had helped him to gradually improve.
"That's strange. I thought it would be difficult, but it looks as though I've done it rather well," he said, astounded.
Brenda Milner was also astounded. She'd made a crucial discovery about long-term memory: that it consists of different, separate storage areas. In learning tasks that are not based on conscious memories, but rather on procedural memories (the body's memory of how to do something), the hippocampus is not involved. If it were, Henry wouldn't have done so well.
IN LATER YEARS, Suzanne Corkin, a student of Brenda Milner's who became a neuroscientist, took over the work of researching Henry Molaison's memory. Corkin and Henry's partnership lasted for more than forty years, and in a way continued past his death. But though the two saw each other frequently, and to her he was like an old friend, _she_ was new to him every time they met. When she asked him if he knew who she was, he replied that there was something familiar about her. He would guess that she was perhaps an old schoolmate. He may have wanted to be polite, but perhaps there was a remnant of something like a memory in his brain, which gave him a feeling of recognition, without knowing where it came from.
Henry reaffirmed that we possess a short-term memory, something he still had, and a long-term memory, which he had only half of—the part involving unconscious learning, otherwise known as _procedural memory_. What he was missing was the ability to store memories that can be consciously recalled: facts about the world and himself, called _semantic memories_ , and all the experiences that would normally become part of his personal memory album, called _episodic memories_.
The modern theory of memory—based in part on Henry Molaison—suggests that previously stored memories are separate from new memories waiting to be let in. Henry did have memories from before his surgery. He remembered who he was and where he came from. He remembered events from his childhood and youth. But the three years leading up to the surgery were completely gone. This meant that memories could not be stored in the hippocampus, or at least not _only_ there. Anyway, it is unlikely that there could be room for all of life's experiences in such a tiny, fragile structure deep inside our brain. The role of the hippocampus must be to hold on to memories while they are maturing, before they are properly stored elsewhere in the brain—in the cerebral cortex, the outer layer enveloping the brain. It's logical to think this process may take about three years, since Henry couldn't remember the three years prior to his unfortunate surgery.
As Henry was living life from one minute to the next, in the safety of his mother's house, the continual experiments turned him into something of a memory celebrity. Fortunately, researchers kept his identity hidden until after his death. If they hadn't, he would have been vulnerable to overenthusiastic researchers and journalists. He was known only by his initials, and to this day, memory researchers around the world refer to him only as H.M.
Henry contributed his life to research—or at least the memories of his life. He took part in one experiment after the other, so researchers could document how memory works. Although he remembered very little after the surgery, he had memories of conversations with his doctor from several years prior to the surgery. This meant he understood that something had gone wrong—maybe with the surgery. This is why he repeatedly told the researchers that he wanted to help prevent the same thing from happening to others. "It's a funny thing—you just live and learn. I'm living, and you're learning," he said.
Another important consequence of the research on Henry was that no one _was_ ever operated on in the same way again. Scoville quit removing both hippocampi from his patients, whether they suffered from epilepsy or schizophrenia. Surgery to cure epilepsy did continue, however, and is still carried out today. If a patient has a certain type of epilepsy, originating in the area of the hippocampus, it can sometimes be remedied by removing one of the seahorses. The other one is left intact, so new memories still have at least one entrance into long-term memory.
For those of us whose brains are pretty much intact, it's easy to take memory for granted. It's easy to think, "I'm sure I'll remember this, I won't need to write it down." All the special moments in our lives will remain with us as memories, won't they? We like to imagine memory as a hard drive filled with film clips from our lives that we can watch whenever we want to. That's not how it works, though. When we're driving to the store or sitting around the dinner table with good friends and family, how can we be sure those precise moments will be remembered? Will those memories be useful or important in the future? Our memories do take good care of certain moments, of course: birthdays, weddings, a first kiss, the first time we score in soccer. But all the other moments—what happens to them? We spring-clean our brains now and then, throw out the clutter, and keep some things for safekeeping. This is a good thing, because if we had to remember every single moment of our lives, we wouldn't be able to do much more than reminisce. When would we have time to live?
Some of us, however, store more than others: meet Solomon, the man who was unable to forget anything at all!
Solomon Shereshevsky worked as a Russian newspaper journalist in the 1920s. There, he annoyed his editor by never taking notes when he was given an assignment. The editor distributed the stories for the day, and while the other reporters eagerly wrote down what they needed to know to get to work, Solomon just sat there, as if he couldn't care less.
"Haven't you got anything of what I said?" the chief editor would ask.
But Solomon had gotten all of it: every address mentioned, every name, what the issue was. He could repeat it all back to his editor, every last detail. "Isn't this the way it is for everyone?" he thought. He found it odd that others had to take notes. To him, it was natural that everything he heard, he remembered. Solomon's editor sent him to see an expert. In the office of neuropsychologist Alexander Luria, Solomon was—like Henry Molaison—exposed to a battery of tests. How much was it possible for a human being to remember?
An almost limitless amount, as it turned out. At least it was difficult to find limits for Solomon's memory. The psychologist showed him long lists of nonsense words and he could regurgitate them in perfect order, even backward and diagonally. He memorized poetry in other languages, tables of numbers, and advanced math in the blink of an eye. When Solomon met Luria again, seventeen years later, he could still repeat the same lists he had seen that time many years ago.
Solomon eventually quit his job at the newspaper and launched a new career as a mnemonist, a memory artist. He appeared onstage and memorized endless lists of numbers or words provided by the audience. Then he repeated them perfectly, to everyone's amazement. But contrary to what you may think, an amazing memory—the kind so good we dream of having it ourselves—didn't make Solomon rich, nor did it make him powerful or particularly happy. He jumped from job to job and finally died alone in 1958, without friends or family by his side.
Solomon Shereshevsky's astonishing memory was partly due to something called synesthesia. This is a condition in which all sensations are accompanied by another sensation, such as sight, sound, smell, or taste. Solomon suffered from an extreme form of synesthesia. Everything he experienced was accompanied by impressions of bright colors, strong tastes, or special images. Hearing certain words would conjure distinct pictures, even tastes and smells. Certain voices evoked strong visual impressions. Once, when he was buying an ice cream at a kiosk, he recoiled in disgust because the seller's voice made him see a billowing storm of black coal and ashes. These profound sensations made his memories latch on far stronger than a regular person's. It was said that he couldn't get rid of a memory—not even a meaningless list of numbers—unless he made a conscious effort to remove it.
Solomon was special. Almost no one remembers things as well as he did. Compared with his, the memory of an average person is a mere joke. But would you really want to be able to remember not only your parents' phone number and the bus schedule from elementary school, but all phone numbers and bus schedules you have ever encountered?
Exactly fifty years after Solomon passed away, eighty-two-year-old Henry Molaison also died. The difference between these two exceptional men is not only that one of them had a vast trove of memories while the other couldn't remember a thing. The fifty years between them also made a difference in terms of how their memories were researched. While we know a lot about Henry's brain, we know nothing about Solomon's. We don't know if he had an extra large—or in any other way different—hippocampus. Meanwhile, Henry Molaison is still, even after his death, contributing to science. In his will, he bequeathed his brain to research, and the researcher who worked most closely with him for the last forty years of his life, neuroscientist Suzanne Corkin, planned to give her subject an afterlife in her field. After Henry's death on December 2, 2008, Corkin worked together with a large team of physicians and researchers to make his brain work for posterity. First, researchers at Harvard scanned the brain with a magnetic resonance imaging (MRI) machine in Boston. Then, Corkin placed Henry's brain in a cooler and handed it over to brain researcher Jacopo Annese, who took it on a plane bound for San Diego. Annese's Brain Observatory stores the donated brains of deceased people so they can be used in various avenues of research, including on Alzheimer's and normal aging. There, Annese's team was ready and waiting to cut Henry's brain into slices, thin as strands of hair. "We believe that the enormous attention that was devoted to patient H.M. when he was living and generously served as a keen research subject ought to be matched by a similarly involved study of his brain," Jacopo Annese said.
Henry's brain needed special attention. No other brain at the Brain Observatory had received as much scientific attention as his. The team photographed every single one of the 2,401 slices of Henry's brain and stored them both in formaldehyde and as digital files. They spent fifty-three hours doing so, and Annese didn't sleep until he was sure that all the pieces of this exceptional brain were securely preserved. Thanks to his work, researchers can now study the exact location where Scoville made his mistake and speculate about which of the remaining areas, near the hippocampus, helped Henry remember the few things which he occasionally and surprisingly did remember. In May 2016, Corkin passed away at age seventy-nine, and her brain is now in the safekeeping of other brain researchers. It contains no unusual surgical scars but houses decades of memories of her special contributions to research.
Henry Molaison's legacy was an entirely new field of research. Now the hippocampus has a definite place in our memory. And during the past fifty years, memory research has become more and more focused on mapping memories all the way down to the cellular level.
"I believe that we will achieve the goal of explaining memory in the brain within my lifetime," says one of the leading memory researchers in the world, Eleanor Maguire, professor at University College London and Wellcome Trust Centre for Neuroimaging. Her research, which focuses on the hippocampus, has allowed her to "see" memories. In one experiment, she told test subjects to think of a certain memory while she watched, through an MRI machine, the patterns that lit up their hippocampus. When they thought of other specific memories, different patterns became visible.
"Your experiences are taken into the brain. After that, the experience is taken apart and stored away in little pieces in the brain's neocortex. Every time you recollect it, it is brought back to life. The hippocampus is critical to reconstructing the memory in your mind's eye, enabling you to relive it once more," says Maguire.
Memory research is also, in a sense, a process whereby small pieces are assembled into a larger puzzle. Memories cannot be seen, per se. No one can retrieve a memory and put it under the microscope. That's also why it took so long for memory to move from being strictly a philosophical and literary topic to being the object of scientific examination. Psychology is a relatively new academic discipline, and so the scientific study of memory has a shorter history than that of many other subjects. But when memory researchers started piecing together human memory, they gave us a picture of an amazing inner world. They worked tirelessly with lists of words, meaningless shapes, staged bank robberies, life stories, puppet shows, and strings of numbers, all to reveal the truth about memory by using the brains of the people who volunteered to be guinea pigs.
Some of you will probably argue that it's meaningless to measure something so abstract, a thing that exists only for the individual who owns the memory. How will we be able to reduce the evocative descriptions of memories in Marcel Proust's seven volumes of _In Search of Lost Time_ into figures and scientific graphs?
To capture unique human experiences and turn them into science, isn't that a paradox? Like putting a seahorse in a glass of formaldehyde hoping to preserve its beauty and essence forever?
There are, however, many good arguments for why memory research is necessary. Turning memory into something concrete and measurable helps us compare memory in the healthy and in those with diseases, and it can help people with memory problems. It contributes to our understanding of how the brain works, which in turn may help find the solution to major medical issues of our time, such as Alzheimer's, epilepsy, and depression.
Some 140 years of measuring memory has not solved all its riddles—far from it. Disagreements come and go on the memory battleground. One longstanding dispute is referred to as the "memory wars." One side maintains that, in extreme situations, memory will behave differently, producing things like repression and dissociation. The other side maintains that memory always behaves the same way, only much more strongly in extreme situations. Another hot issue is the possibility of memory training: Is it like strengthening a muscle—that is, it gets better with repetition—or can you use strategies and techniques to improve existing ability? And what exactly _is_ memory? Even this is being debated in minute, technical detail in scientific papers—debates punctuated by indignant letters to the editors of scientific journals—while researchers try to gain ground in the scientific community. It's almost like an election campaign in slow motion, or a TV debate spread out over fifty or a hundred years.
There's even discord over the hippocampus. Two camps face each other. One rigidly believes that the role of the hippocampus is simply to consolidate memories into the rest of the brain. As time passes—sometimes with the help of a good night's sleep—memories attach themselves to more robust cortical networks, while the seahorse slowly and carefully lets go of the memories it has been tending. The other camp argues that this is too simple. This group adamantly insists that the seahorse holds on to memories, especially the personal, vivid sort that we remember in something resembling a personal memory theater, at the same time as they are also stored deeper in the cortex. Every time we recall a memory, they say, the hippocampus is involved and "overwrites" the original memory, each time with a slightly new interpretation or reconstruction.
In the same way as the seahorse's ocean ecosystem is important to understanding its existence, the hippocampus's brain ecosystem is important to understanding how memory is kept and recalled. In the past few years, people have been paying more attention to how the hippocampus interacts with the rest of the brain. Memories play out in physical networks, where different parts of the brain move as in a synchronized dance. It's visible with modern MRI methods. William James, one of the fathers of psychology, understood it already in 1890:
"What memory goes with is, on the contrary, a very complex representation, that of the fact to be recalled plus its associates, the whole forming one object,... known in one integral pulse of consciousness... and demanding probably a vastly more intricate brain-process than that on which any simple sensorial image depends."
In other words, each memory consists of different bits and pieces brought together in one unified wave of consciousness. Each part of the memory originates in a different part of the brain, where it first made a sensory impact. To make the whole thing feel like one experience, one unique memory, requires intricate brain interaction. William James didn't know exactly how this worked, but thinking of memory and mind the way he did in the 1890s was remarkable. When James was alive, people thought of each memory as a unit, a copy of reality, like something that could be pulled out of a folder in a filing cabinet. That the key to understanding memory was the seahorse—slowly swaying in rhythm with the sensory areas and the emotion and awareness centers of the brain—wouldn't be discovered for another hundred years. Just a few years before James's armchair observations, researchers had discovered how neurons are connected to each other with a slight gap in between them called a synapse: the so-called _neuron doctrine_. From that discovery to today's brain research, where we can virtually watch memories come to life in the brain, has been a long journey.
We can all benefit from making that journey and learning more about our memories. A small seahorse turned out to be the key to many of the brain's mysteries. When Julius Caesar Arantius named it the hippocampus, it probably was not solely due to its appearance. Seahorses, like silkworms, were special and somewhat mysterious during the Italian Renaissance. When an event is special and unique, it helps the hippocampus hold on to it as a memory. We know that now, but Arantius could not have known that about the tiny part of the brain he had discovered. He just wanted his discovery to be noticed—and remembered.
— 2 —
**DIVING FOR SEAHORSES IN FEBRUARY**
**_Or: Where do the memories go?_**
Memories have huge staying power, but like dreams, they thrive in the dark, surviving for decades in the deep waters of our minds like shipwrecks on the sea bed. Hauling them into the daylight can be risky.
**J.G. BALLARD _, "Look Back at Empire,"_**
**The Guardian _, March 4, 2006_**
BEYOND THE PIER at Gylte Diving Center, an hour's drive out of Oslo, Norway, there are more than forty different types of marine slugs (nudibranchs). They come in all colors, from dark purple to transparent white. Their bodies are covered with tentacles with small stars at the tip, or are decorated with pink fringes like a Disney character from the 1950s. They stretch orange fingertips toward the shiny ceiling of the water's surface or defiantly pull their luminescent, light-green feelers into their bodies. They slither around in clouds of glittery particles that swirl around the water here by the pier.
The water is only forty degrees Fahrenheit. Farther into the fjord, we've seen ice floes bobbing up and down at the water's edge. Soon, the slugs in the water will be joined by ten black-clad men chasing the seahorse's secret. The divers' flippers thump against the pier as they hobble like penguins toward the sea, then swirl up clouds of particles as the divers slowly sink to a depth of fifty feet. From our vantage point on the pier, we can see bubbles on the dark surface of the water, revealing where the divers are. The seahorses they are looking for are not in the water—we are, after all, in the Oslo Fjord. No, they are hidden beneath their tight diving hoods. The divers have plunged into the ice-cold February water to find out what goes on in the hippocampus. They're hunting for memory.
Together we are going to find out how memories behave when they enter our minds. Researching memory is, in a way, quite similar to diving. Our divers are about to break the surface and descend into the depths of memory itself. The only sign that there are memories below the surface is what rises and bursts, like the divers' bubbles breaking the surface of the water.
The experiment we are re-creating, famous in memory research, was first conducted in 1975 off the coast of Scotland. Memory researchers Duncan Godden and Alan Baddeley decided to test a popular idea, that you can remember something better when you return to the place where it happened. You know, like in crime novels, where the detective remembers an important detail when he returns to the scene of the crime. It's a simple theory: when we are in the same environment as we were when an event took place, the memory of it will come streaming back, whether we want it to or not.
Are memories easier to recall at the location where we first encountered them? How and where do they find a permanent place in our brain? To properly test this, Godden and Baddeley constructed an experiment in which people had to perform a task in two different environments, on land and underwater. Their assignment was to memorize lists of words either on the pier or twenty feet deep in the water, and later recall the lists either on the pier or in the water. One list was to be learned on the pier and recalled on the pier. After some time, a second list was to be learned underwater and recalled on the pier; a third list was learned underwater and recalled underwater; and a fourth list of words was learned on the pier and recalled underwater. The researchers anticipated that everything going on in the water—the cold and wet environment, breathing through masks, and so on—would make the divers remember less than they would on the pier. Theoretically, it should also be harder to learn something underwater as opposed to on land, given that the pressure and the mixture of gases the divers breathe would make it more difficult to focus.
On this cold February morning in 2016, when we send our divers into the Oslo Fjord, it's the first time anyone has repeated Baddeley and Godden's experiment in seawater—some have re-created it in a swimming pool, but we all know that's not the same. Will these ten men—thirty to fifty-one years of age—show the same results as in the legendary British experiment?
"Now I can tell you exactly where I have been underwater, after many thousands of dives. I could not do that before," says hobby diver Tine Kinn Kvamme, the experiment photographer. The lack of oxygen underwater, along with the stressful experience, means that people's brains function differently from how they usually do.
"When people first start to dive, few remember anything at all, nor can they report what happened underwater. First-time divers are asked to write their names backward underwater. Often, they will write things like 'backward,' or they will turn around only one letter in their name. If you ask them how many wheels a cow has, they'll answer four," she says.
Ordinarily, memories reside within a large brain network. When memories enter our brain, they attach themselves to similar memories: ones from the same environment, or that involve the same feeling, the same music, or the same significant moment in history. Memories seldom swim around without connections, like a lonesome fish. Instead, they are caught in a fishing net full of other memories. When you want to recall a memory, you have a greater chance at catching it if you scoop up the other memories around it. When you pull in the net, it's full of memories, and you can keep hauling it in until you find the memory you're after.
Would memory still work this way in a stressful situation, with subjects who had to deal with diving equipment and other distractions? Would context help the divers remember what they learned underwater when they're also asked to remember it underwater?
The experiment in 1975 showed the expected results: the word lists memorized underwater were also better remembered underwater, and the lists memorized on land were better remembered in a dry environment. We anticipate the same from our divers, but we don't want their expectations to influence the results, so we haven't told them what happened in the original experiment.
The atmosphere is tense at Gylte Diving Center. We are not re-creating this classic psychological experiment just for fun: results from psychological experiments are not always reliable. A great deal can happen by coincidence, and it's often only the results that confirm the hypothesis that are reported, while those researchers who find opposite results tuck them away in a drawer, ashamed and disappointed. When a team of researchers took on the task of re-creating one hundred experiments from different areas of psychology, only thirty-six were successful. The diving experiment was not among the hundred re-creations—but it's having its time today, an ice-cold and rainy February day in Drøbak.
Throughout history, philosophers and authors have asked themselves what memory is, how we learn and remember things, and what makes a memory reappear. At risk of offending an entire professional group: in many ways, we can call the philosophers of ancient times neuropsychologists, because they observed and tried to understand how the brain works without having access to today's research methods. The million-dollar question that everyone is trying to answer is where in our brains our memories actually end up, and how it is possible for all our experiences to consolidate into a pink mass of brain cells and blood vessels. In 350 BCE, in _De Memoria et Reminiscentia_ ( _On Memory and Reminiscence_ ), Aristotle compared the memory process to making an impression in a wax seal. But exactly how the experiences turned into memories, he couldn't say.
By studying the divers at Gylte, we may not be able to see their brains etching words into wax seals, but we can observe how memories connect and become dependent on each other. Context-dependent memory tells us something very basic about how memories are stored. How much you know in a broad sense determines what you understand of the new things you learn. Your understanding of your new experiences depends on your prior experiences. This network of knowledge creates context for the new learnings—they get caught in the fishing net, if you will. When you know what the French Revolution was all about, it's easier to understand the Russian Revolution, and when you have gained insight into Russian Communism, it shines a new light on the French republics, and so on. When our divers eventually resurface—ice-cold faces and eager eyes—and hand us their notebooks, filled with all they remember from a list of twenty-five short nonsense words, we will see with our own eyes how their brains have worked, linking words and seaweed and cold water together into the same network. But we're still standing on the pier, while the February cold eats its way into our woolen underwear. It's anything but magical.
By contrast, during the Renaissance, in the 1500s and 1600s, many viewed memory as something magical. At the time, magicians and alchemists not only tried to make gold, but first and foremost used rituals and symbols to gain power over the world through enlightenment. Secret organizations, like the Rosicrucian Order and the Freemasons, believed that an individual could progress through many stages of enlightenment to become almighty, almost like a god. The most magical art of all was remembering, which they believed was connected to imagination, to the divine creativity of humans.
When you think about it, it's not such a strange idea, because there really is something magical about our ability to store the past and retrieve it as lifelike images. Between our temples, most of us are equipped with our own private memory theater, which continually stages performances, always with slightly new interpretations—and now and then, with different actors. Today we know that everything we think and feel takes place in our brain cells, yet it is still almost impossible to grasp that our whole lives are to be found in our brains. So many emotions—fantastic, sad, beautiful, loving, and scary experiences—are hidden in our cerebral convolutions as electrical impulses, inaccessible to other people around us. Even people who have experienced the same thing have completely different memories of it. But what sort of physical trace does a memory actually leave in our brain, and if we can locate it, can it explain memory? Memories are both abstract (states or episodes we can return to in our minds), and concrete (strengthened connections between neurons). Memories are incredibly complex. They are more than the trivia required to win a quiz show, more than the individual facts you look for among thousands of less relevant items in long-term memory. Just think of something you have experienced, recall your memory of it, and feel the sensations it contains. Are you watching it on your inner film screen? Do you hear the sounds, the voices; do you see the smiles, the eyes of the one you're talking to? Are you on the beach on a summer's day while the waves break against the sand? And the smells! Unlike at the movie theater, here we can smell the cinnamon buns and the ocean breeze, the seaweed in the bay, and hot dogs on the barbecue on the neighboring beach. You can even feel things, like the water hitting your body as you dive into the sea. All these sensations flutter about our brains as we remember. It's not possible to describe a memory by pointing to a few connections in the brain. It has to be felt.
At any rate, the hunt for the memory trace, the physical imprint of memory, has been a major part of brain research ever since neurons were discovered—well, actually, ever since Aristotle talked about wax seals. Some called it the _engram_ , an inscription in the brain, and finding it became the holy grail of memory research. If we could find the engram, we would also understand the brain itself. With the help of our divers, we are trying to find the fishing net that holds our memories, the memory network. Every one of the squares in the net must be attached in some way; they are links that exist physically in the brain. Finding these links, and what they consist of, was a necessary step toward understanding how the brain handles memory. Before the 1960s, no one had succeeded in doing this.
A happy rabbit was perhaps all that was missing: Terje Lømo would find the very first memory trace, the smallest part of a memory, inside a rabbit brain. He is now professor emeritus in medicine at the University of Oslo and has worked mainly in physiology, the study of how the body works.
"I am most interested in how things work. Simply _describing_ the brain was not enough for me," he says.
In 1966, he was leaning over a rabbit. It had once lived in the countryside, happily eating clover, without a care in the world. In the hands of Lømo, though, it now faced a problem. There it lay, sedated and with a fairly big hole in its brain, while the researcher came closer with tiny electrodes.
"We sedated the rabbits and sucked out a little of their cortex, so that the hippocampus was exposed. Then we poured warm, clear paraffin in the hole; it gives a good view, keeps everything in its place, and makes it warm and moist enough for the brain to continue working through the experiment. We had a window into the hippocampus."
His main goal was to find out what happened when he sent small electrical impulses through the brain, not because he was particularly interested in the hippocampus, but because that part of the brain was easier to observe. As opposed to the very complex cortex, the layout of the hippocampus was much simpler and more understandable, and the routes through it were already well known.
At the time, Lømo worked with Per Andersen, who had discovered that neurons could suddenly send off a train of signals, which were first measured by small electrodes used in experiments originally not concerned with memory at all. But neither Andersen nor other researchers knew what these signals meant. Now Lømo had decided to examine them more closely, which is where the happy—but soon dead—rabbit came into the picture. Lømo used a small electrode to set off tiny electrical impulses to travel from one part of the brain into the rabbit's hippocampus, where he measured the signals with a small receiver.
What young Lømo found was astounding and had never before been described. When he sent these electrical impulses through the rabbit's hippocampus in small "trains" of repeated signals, the cells at the other end eventually needed less stimulation to become triggered.
Some form of learning must have taken place; it was as if the neuron remembered that it was supposed to send its impulse when it had received the message from the preceding neuron! As if, initially, the first neuron had to nag it to send its signal: "Come on, come on, come on, fire already!" After having been prompted enough times, it understood to fire after just a cautious "Fire now!" And this response persisted. Something had permanently changed in the brain.
What he'd discovered was simply the smallest part of a memory, a tiny little memory trace. This response is now called _long-term potentiation_ , meaning that a physical change occurs in some synapses in response to a recurring stimulus. At the same time as Lømo was making his discovery, neuroscientist Tim Bliss—a few thousand miles away from Oslo, at McGill University in Canada—had been looking for memory on a cellular level. What he lacked was the evidence that strengthened synapses were connected to memories. That is, until Lømo stumbled upon long-term potentiation! Bliss traveled to Oslo and the two did some experiments in 1968 and 1969, resulting in a scientific paper they published in 1973. Their paper presented a theory of how a memory is created on a micro level.
Almost nobody paid attention to the paper until twenty years later, because academia wasn't ready for it. There was simply no context; no other studies had trodden even close to this particular corner of research. Since then, though, Bliss and Lømo's paper has formed the basis for much of modern memory research. And now we know more: a memory consists of many of the connections they documented. One neuron can participate in many different memories. Memories are large networks of connections between neurons in the brain. When something becomes a memory, new links form—neurons either turn on or turn off, and either fire or don't fire a signal in the brain, and in that way form a pattern.
Our memories cannot all remain in the hippocampus, so they spread out across the cortex. It takes time before a memory matures and all the complex connections it requires to store all that makes a memory—smells, tastes, sounds, moods, and images—are established in the brain.
"Sleep is needed for a memory to consolidate. We believe that while we're asleep, we go through the events of the day in order for them to attach to the cortex. But when we are stressed, this doesn't always happen. The neurons don't fire in the same way. When I tried to re-create my experiment on other rabbits a couple of years later, it didn't work," Lømo recounts.
He'd been lucky the first time he experimented. His rabbit, despite its untimely end, had lived a happy life. The rabbits in the second experiment were stressed, so the neurons in their brains didn't work as they should have. In other words, you must treat your test animals nicely if you want to learn from them. The same goes for humans: when we are stressed, we don't retain memories as easily as when we are happy and relaxed.
At about the same time as Lømo's discovery, there were other breakthroughs in the hunt for the memory trace. In 1971, John O'Keefe at University College London found cells in the hippocampus that remember certain _locations_. For example, there are some cells in the hippocampus that are active only when we sit on a certain chair, and not on another chair—even in the same room. It is evidently up to some cells ( _place cells_ ) to remember where we have been at all times. But to remember a place in and of itself—is that a memory? The Norwegian neuropsychologists May-Britt Moser and Edvard Moser—together with John O'Keefe—were awarded the Nobel Prize in Physiology or Medicine in 2014 for their work on that very question. The two Norwegians received the prize because they decided to develop O'Keefe's research further and look beyond the hippocampus. Their work examined the entorhinal cortex, which connects the hippocampus and the rest of the brain. The Mosers experimented with rats, which, when they were free to explore their environment, showed cells firing in exactly that part of the brain.
With tiny metal electrodes surgically inserted into their brains, these rats wandered around their cages. A single neuron in the entorhinal cortex didn't react to just one place the rat had scurried to, like place cells, but to _several_ places. Amazing, that what they were expecting to be place cells didn't remember only one location but several locations in the same area! But when the Mosers marked the points in the cage where the cells had fired, they formed a perfect hexagon on their computer screen. The more the rats ran around in their cages and mazes, the more obvious it became; on the Mosers' computer, a clear honeycomb pattern emerged. One cell, one hexagonal grid pattern. It was a coordinate system of the environment.
"At first, we thought there was something wrong with our equipment," Edvard Moser says. "The pattern that emerged was too perfect to come out of something real."
Each of these neurons makes its own grid, each slightly offset from that of the neighboring cells, so that all points in the environment are covered. Some grids are fine-meshed, while others react to points far away from each other, even farther than it is physically possible for the researchers to measure indoors. Without these _grid cells_ , we are not able to understand or remember locations and where we are in relation to where we have been. We make these patterns wherever we go—wherever we stand, lie, or drive.
"We sent the rats into a ten-armed maze, and it turned out that they continued to make the grid pattern but also started a new one for each 'arm.' We believe that these patterns are patched together, so that the rats remember how to get through the maze," Edvard Moser says.
Since then, other researchers have found the same result in patients undergoing epilepsy surgery. It was as anticipated: in humans, as in rats, all locations are stored in a hexagonal pattern. We are all bees! We all organize the world around us as a hexagonal grid.
"We believe that this was developed very early in the evolution of mammals," Edvard Moser says. "And we believe that what we have discovered about grid cells is central for episodic memory. It is, after all, impossible to create memories without tying them to a place."
Other researchers agree that place and grid cells play a special role in episodic memory. Some go so far as to say that this system in the hippocampus and the entorhinal cortex has become specialized to assign each memory its unique memory trace, as part of a unique memory network. Perhaps, at first, the sense of place was the primary task for the hippocampus and the entorhinal cortex. But as evolution proceeded, our memory maps were given a new function: to take our individual experiences and tie them together in a grid. Hexagonal maps of the environment became hexagonal-patterned fishnets of memories.
Recently, researchers in California have been able to demonstrate, in the hippocampi of mice, how memory networks link themselves to context-dependent memory. Like Terje Lømo, they made a window into the hippocampus, to the tiny little piece of it called _cornu ammonis 1_ , Ammon's horn. Looking at the hippocampus in cross-section, it looks like a goat's horn, bent inward, into a spiral. Here, through the tiny window into the cradle of memory, the California researchers could see, under a slightly fancy microscope, how the neurons lit up when the mice were placed in different environments. They made three different cages, which would give rise to three different memories: a round cage, a triangular cage, and a square cage. The smell, texture, and other conditions also varied between the three cages. The crucial factor was how close in time the various experiences took place. Two groups of mice were compared. Half of the mice had a go at the triangular cage, and then directly afterward they were placed in the square cage. These mice got to experience two different cages in quick succession. The rest of the mice were placed in the round cage and then, seven days later, in the square cage. The second group of mice had two experiences—episodic memories—distinctly separated in time. When the researchers watched through the microscope while the mice were exploring the cages, they could see activity in the neurons in a defined area. Each of the three cages created a signature pattern of neuronal activity in the hippocampus, meaning distinct memories. The exciting part was that the experiences that took place close together in time led to activity in groups of neurons that overlapped. These two experiences hooked on to each other, not only in time but also in place, in the hippocampus of the mice. Meanwhile, when mice visited two cages a week apart, it was accompanied by activity in two separate groups of neurons in the hippocampus.
The researchers believe this happens because the activation of the one group of neurons causes other nearby neurons to become easier to activate. Everything links together in a network. The main point of Godden and Baddeley's context-dependent memory experiment has, in this way, been demonstrated in the brain—not in diving mice, but by diving into the cortex of the mice.
WHEN WE EXPERIENCE something—as we find ourselves in a specific situation at a specific location—and it becomes a memory in the brain, it spreads out across the cortex until we recall it. A memory is composed of thousands of connections between neurons; it is not one connection that makes a memory. A memory is more than Terje Lømo's long-term potentiation.
But what does a memory look like? Can we see a complex memory the way we can see a simple memory trace? To be able to do this, we must exit the rabbit and mouse brains and enter the human brain. And we must watch the brain while memories are recalled. Fortunately, we don't need to sedate humans and open their heads to get a glimpse of their memories. As we learned in chapter 1, Eleanor Maguire at University College London has used an MRI scanner and some reminiscing volunteers to observe the traces of their memories as they relive their past experiences.
An MRI machine uses a strong magnetic field to take pictures of the body. Different body tissues react differently to the magnetic field, which results in detailed images. The MRI machine can be programmed in a certain way to read the oxygen level in the blood flowing through the brain. Since neurons use oxygen to function, we can tell from the images where there's a lot of activity. We then know where in the brain nerve cells are most active while the test subjects remember things. This is called functional magnetic resonance imaging (fMRI)—images of the brain while it is working—as opposed to structural MRI, which shows us only what the brain looks like. The memories light up like tiny flashlights underwater, flashes that light up the sea in little spurts.
But is it really possible to see what memory a person is recalling? In Eleanor Maguire's laboratory, participants allowed themselves to be scanned by an MRI machine at the same time as they were asked to remember their own experiences. The professor actually managed to figure out what they remembered by studying the fMRI images. Maguire watched the activity in the hippocampus while the test subjects were thinking of episodes from their past, and she could see that each memory had a unique pattern of activity. She had a computer program that learned which of the test subjects' memories were tied to which patterns of activity. From that, the computer program could pick out which fMRI images hung together with which memories.
Is this simply a mind-reading machine?
"These are memories we had agreed with the volunteers, before the scanning took place, that they would recall, not random memories. In a way it's, in very general terms, a kind of _voluntary_ 'memory' reading," Eleanor Maguire says.
So far, she can see the track in the vinyl record, but she can't hear the music.
"The next step would be to be able to see what people remember without having decided on a fixed set of memories beforehand. But it's a long way until we get to that level," she assures us. We can safely leave mind reading to science fiction films and books.
Maguire isn't doing this because she thinks memories can be reduced to a checkerboard pattern in an MRI image. To her, memories are vastly complex—they are unique experiences that can only be fully known by the one who keeps them. They are also not static. She has observed that something happens to memory traces over time: two weeks after an initial memory is encoded, its memory trace is visible in the front of the hippocampus, but much older memories from ten years previous are processed further back in the hippocampus.
"Memories contain many pieces of the initial experience that are later brought back and put together again," she explains. "When the memories are still fresh, they are more easily accessible; we can easily picture the episode and how it happened. In the beginning, it is readily available within the hippocampus. As a memory ages, the pieces are stored in other parts of the brain and it takes more effort to reconstruct it and bring it back. The hippocampus puts all the pieces together in a coherent scene."
But what is she actually looking at? What gives the memories a unique "signature" in the fMRI images of the hippocampus? Eleanor Maguire believes that there are groups of neurons working together on one memory.
"The fact that we can see unique patterns for each memory must mean that information about the person's experience is present there; it has to be in some way related to the biological memory trace."
But because the resolution of an fMRI image is extremely coarse, we can only see large groups of nerve cells activated at the same time, as opposed to individual neurons.
"While it is important to study memory on a cellular level, we should also think of a memory rather like a big cloud of activity. A memory is more than the single synapses—it is much more complex than that," says Maguire.
To her, episodic memories are first and foremost about scenes. "All the little pieces that together make up a memory don't mean anything unless they are placed in a scene. The action _takes place_ somewhere."
But as an episode is tied to a place and forms a scene in your mind's eye, an important component of this may be a set of grids—the map within the hippocampus and entorhinal cortex. The memory is tied down by all the little synapses being strengthened through long-term potentiation. Synapse by synapse, the memories are clicked into place.
"We are hoping that our discovery can help solve the enigma of Alzheimer's disease. Long before there are other symptoms, people with Alzheimer's experience spatial navigation problems," Edvard Moser says. The newest episodic memories also suffer first when the disease sets in. They go before all the knowledge we have gathered throughout life does, and also long before mature memories from long ago dissolve, like clouds of sparkling particles that swirl out to sea, never to return.
BUT WHAT ABOUT our divers? You haven't forgotten, have you, that we sent ten men down into the ice-cold water of the Oslo Fjord at the beginning of this chapter?
The rain is dripping from the eaves of the diving center here on dry land, and we're rubbing our cold and wet hands together in a futile attempt to stay warm, our teeth chattering. The divers are, of course, voluntary participants; nobody is forcing them to do this. Still, with only a few remaining bubbles on the surface reminding us that they are down there, it's easy to be a bit worried. What if something were to happen? And what if they remember as poorly as, well, a jellyfish? We will return to the divers shortly, but since we brought it up: Do jellyfish remember?
"We don't know if jellyfish remember," biologist Dag O. Hessen says. "But jellyfish do have a kind of 'will,' since they swim in a certain direction, even if they don't have a brain, only nerve fibers. However, all animals, even the simplest ones, have a certain capability to learn."
How did human memory become as advanced as it is? Why do we remember the way we do and not the way jellyfish do? What might the alternatives have been?
"We have not been able to prove that animals have memories that work like human memories. We believe that other animals' memories associate to a situation and pop up when they see or feel something, as when for example a cat sees a cupboard door and remembers that it hurt its tail there once," Hessen explains.
So there's no proof that zebras can stare melancholically into the sunset and remember the great loves of their lives, or that a dog can suddenly bark mournfully because it's thinking of a sad episode from its youth. No gazelles cringe because they're thinking about an embarrassing moment two years ago, no leopards experience a flash of happiness when a memory hits them of how they killed their first prey. At least, not that we have been able to prove.
"We believe that only humans do this: look back in time regardless of context. All animals and plants have some form of memory, in the sense that they adapt to the environment. It's beneficial to learn to avoid dangers and remember how to secure food and partners. It's obviously an evolutionary advantage for all living organisms, even for short-lived ones, to be able to remember and not only live in the moment. What's special about humans is our ability both to see the past before us and to create visions of the future. To be able to envision the future is possibly a byproduct of memory," Hessen believes.
The biologist suggests that there's another reason for humans to have developed a large brain with advanced memory, something that has to do with our social groups.
"We know that social animals have larger brains and more memory than animals that aren't social animals."
An example: all bats are, in a sense, social animals, but vampire bats are particularly social. They live in groups, and they can't survive for more than three days without fresh blood. According to Hessen, researchers have found that bats—sympathetically enough—help each other by regurgitating blood for others, even bats outside their family, and it seems as if they remember favors that have been done for them earlier. There's a form of reciprocity between vampire bats that's very similar to humans, like friendship.
"Many believe that humans have good memory because people are social animals with many hierarchies and exchanges of favors. Sympathies and antipathies depend on remembering. And the longer one lives, the more one has to remember complicated social structures," says Hessen.
Animals that live longer remember more. An example is the elephant. It does actually remember—like an elephant.
This is just one of many anecdotes about elephant memory. In 1999, as the zookeepers in the elephant sanctuary at Hohenwald, Tennessee, introduced their elephant Jenny to a newcomer named Shirley, Jenny became agitated. Shirley also seemed more than usually preoccupied with Jenny. The two elephants behaved as if they knew each other. Upon investigation it turned out that, for a short while more than twenty years earlier, the two elephants had worked together in the touring Carson & Barnes Circus. According to Hessen, researchers that have followed elephants over long periods of time have found that elephant herds are highly dependent on good memory. The matriarch of the herd must be old enough to have the experience to lead her herd to safety if there is a fire or to find water during dry spells; younger matriarchs risk making fatal mistakes.
The elephants Shirley and Jenny acted as if they really had _human-like_ emotional memories of each other. But memories can also be far less complicated, without being less impressive. Several animals have a kind of instinct—or memory—for time and place. Puffins return to the west coast of Norway on exactly the same date year after year, regardless of weather. American and European eels swim all the way to the Sargasso Sea to spawn. Monarch butterflies have multiple generations each year, of which only one lives long enough to migrate south and back. It's impossible for the new generation of migrating monarchs to remember where their great-great-grandparents came from, but still they know to go south to particular wintering grounds. Is this memory or instinct? And can instinct be tied to a certain geographic location or a certain date?
"When the salmon returns to the spawning grounds it came from, it uses its sense of smell, and the sense of smell is closely related to memory in most animals. But there's a lot about animals' memory that's still a mystery to us, as for example this thing about the eel," Dag O. Hessen says.
Even in the human brain, the so-called olfactory bulb is situated close to the hippocampus, pointing to the fact that smell is the sense most closely tied to memory. This doesn't mean that the other senses aren't strong too. Marcel Proust came up with his seven-volume work when he tasted a madeleine cookie dipped in tea. For many, sounds and music are tied to strong memories; just think of how an advertising jingle can stick in your memory. How many thousands of tunes are we familiar with?
Songbirds are birds with good memory. Just like us, they have to learn tunes—they aren't born with them. A songbird placed in some other songbird's nest will learn the wrong tune; a blue tit that is placed in the nest of great tits will learn the great tit's tune. The songs of songbirds can have both dialects and other variants. The European pied flycatcher, for example, varies its tune according to its intended recipient: the "wife" or a "mistress." What makes a bird's memory especially impressive is its brain. Birds have several song centers in their brains, one of which is the higher vocal control center, which grows each spring and has almost completely receded again by the fall!
"We don't know why it happens, because the birds remember the tune they've learned even without the higher vocal control center," ornithologist Helene Lampe at the University of Oslo tells us. There is still a lot scientists don't know about this avian brain region. Female birds typically don't have particularly well-developed higher vocal control centers yet are still able to sing. It's believed they have it so they can identify and remember rivals, but in the case of the European pied flycatcher, it does the female no good; she watches the nest while the male is out looking for more "mistresses."
"This is a songbird mystery we still haven't solved. We don't know where the song is actually stored, but recent research points to the auditory center of the brain being used for some storage," Lampe says.
Many types of birds remember amazingly well: migratory birds remember where to go, parrots and crows can learn human language, and jays that cache food find their way back to their stashed nuts.
"Hoarding requires a good episodic memory—that is, having a vivid memory of the act of burying the nuts. Remembering this experience makes it possible to find them later," Lampe says. Herein lies one of the great controversies in memory research: How uniquely human actually is episodic memory, and can we find evidence that other animals and birds also have this form of memory? Scientists don't have a final answer.
We take our way of remembering for granted. The human, or mammalian, way of connecting experiences through long-term potentiation, creating large memory networks that are kept in place by the hippocampus, could be just one way of doing it. Nature has a wealth of alternatives to offer. Animals without hippocampi also have memory. Even one-celled animals, like slime molds (Mycetozoa), show signs of remembering. In one experiment, researchers exposed a slime mold to moisture and drought on a regular basis and watched it react. After a while, they stopped stimulating it this way, but it kept reacting at the same intervals as before, for quite some time. Slime molds have even found the quickest way through a simple maze! Amoebas leave slime where they've been, so that they don't reenter a dead end in the maze but rather explore new paths. They wander through the maze with their one-celled memory, never knowing that evolution has raced past them.
Slime molds, jellyfish, songbirds, eels, monarch butterflies, vampire bats, puffins, and elephants represent different mysteries when it comes to memory. Which ones have memory, and which just have instinct? They each show us that there are many ways nature can meet the need to keep information for later use. But human memory is perhaps the greatest and most complex. What other animals remember episodes from not only their own lives but also their ancestors' lives from many thousands of generations ago, and record their memories for others to read and remember?
THERE ARE ENOUGH mysteries within our own memories to keep us busy. Take, for example, Henry Molaison, who opened up so much research into memory: How could the man without hippocampi remember his life before the surgery? As we know, memories appear in the hippocampus when we retrieve them; they light up on the screen of Eleanor Maguire's MRI machine, where they create different patterns. How was it possible for Henry to remember anything at all without his hippocampus, when it is the hippocampus that reassembles memories? This is something memory researchers are still fighting about. The fight is as big as the battle about the role of the hippocampus in memory.
Henry's memories prior to the surgery had gone into storage the normal way, with the help of the hippocampus. His memories had consolidated as memory traces tied experiences together. Later, the synapses in his cortex were strengthened, until they could manage without the help of the hippocampus. This process may take many years. That's why Henry didn't remember anything from the last couple of years prior to the surgery. The memories from this period were simply too unstable and dependent on the hippocampus. For a long time, it was believed that this was the full explanation and that the hippocampus wasn't necessary at all when it came to recalling early memories. But then researchers, like Eleanor Maguire and others, started to notice that things happen in the hippocampus when we retrieve a memory.
They didn't question whether or not Henry's memories were real, but they did point out that a memory is not just a memory. A memory may have turned into a story that includes facts about what happened, not unlike an anecdote. On the other hand, a memory can also be something completely different: a re-creation of the experience, filled with sensory experiences, emotions, and details of how the episode unfolded in time and space. Henry's memories were probably more like the first kind, resembling book knowledge or simple tales, called semantic memory. He seldom gave particularly detailed descriptions of his childhood. Often, the stories began with "I used to... ," followed by facts about where he'd gone to school, where he'd vacationed, and who his family was. He possessed a rather dry encyclopedia about himself. Presumably, he could not recall lifelike, smelly, noisy, emotional memories. After having known Henry for years, researcher Suzanne Corkin was convinced that his memories lacked the vividness so characteristic of episodic memories. BACK AT GYLTE Diving Center, we've split the divers into two groups and numbered them from one to ten. The divers are completing their first memory test, the one we use for comparison, measuring their normal memory. The men are visibly sweating over the twenty-five words we gave them to remember. Not only because the test is hard; they have to look at their list of words for two minutes, then go for a little walk and return to the table to write down what they remember. But with the diving gear already halfway on, they are hot and perspiring more than they might like. The divers manage to remember between six and seventeen correct words, completely normal results.
That day by the fjord, the rain on our skin feels like pins and needles of nervousness as the first group goes down into the water. What if we don't find out anything at all? What if the men are diving in vain and don't get to prove anything about memory and context?
Of course, we can't go through life relying on our surroundings to help us remember everything. Godden and Baddeley also pointed out that this was an unreasonable idea. In _An Essay Concerning Human Understanding_ (originally published in 1689), the philosopher John Locke described a man learning to dance in a room with a large trunk. He could do the most elegant dance steps, but only as long as the trunk was there. If he was in a room without the trunk, he was hopeless on the dance floor. This sounds very strange, and fortunately the story probably isn't true. It highlights, though, the idea of context-dependent memory. The point Godden and Baddeley made was that our memory may rely on context _to a certain degree_. Can this be useful in some way? Should we cram for an exam in the location where we'll be taking it? Or remain in the same apartment until our dying day for fear of losing the memories that have been made there?
Fortunately, we do have access to our memories when we are not in the same environment as where we experienced an event. The divers at Gylte can recount the amazing experiences they've had in the water even when they are safely on shore.
Our memory networks—our fishnets of memories—benefit from context beyond just our physical surroundings. We create the strongest memory networks on our own, when we learn something truly meaningful and make an effort to understand it. Someone who is passionate about a particular subject, such as diving, will more easily learn new things about diving than about something she's never been interested in before. This is because she already has a large memory network devoted to diving where she can store her new knowledge, and because she is motivated. It's as if we can add another layer of netting just because the self is involved; memory is self-serving. Memories are linked to what concerns you, what you feel, what you _want_. Too bad, then, that so much of what we actually need to remember is so darned uninteresting!
Lately, others have tried to test context-dependent memory in other ways. Do we remember things we learn while skydiving? The researchers concluded that the stress level of skydivers was so high that it erased all effects of context. This may not be so strange—if we are so high on adrenaline that we barely notice where we are, there are no surroundings to support those memories. More practical were the researchers who wanted to examine if medical students remembered more when they were in the classroom where they had first been taught. The classroom, in this case, was either an ordinary classroom or an operating theater, where the students were dressed for surgery. Fortunately for the future patients of those medical students, it turned out in the experiment that the differences were so minimal that doctors can safely continue practicing medicine far from the context of learning.
In our experiment at Gylte, we split the divers into two groups. The divers in the first group would be tested on what they remembered on land after trying to memorize twenty-five words underwater. The others had to both learn and recall the words underwater.
The five divers in the first group come ashore, splashing as they go. They wriggle out of their masks and flippers, unhook leaden oxygen tanks and sit, legs spread apart, on the bench along the wall of the Diving Center.
Their results are miserable.
One of them remembered only words from the first test—the one for comparison—and got a zero on the underwater words. The best one remembered thirteen words from the list he saw underwater, but this too was worse than he'd done during the first test on land. The average result of the comparison test, inside the Diving Center, was 8.6 correct words. The divers remembered an average of 4.4 words when they emerged from the water.
"I sort of thought I had the words there while I was underwater, but then we got up on land, and it was as if my mind changed completely, and I lost it," one of the divers says.
The removing of flippers, tottering up from the edge of the pier along the walk to the Diving Center, lifting the tanks from their backs, and grabbing a piece of paper may of course have disturbed their trains of thought and pushed the words out of the way. Duncan Godden and Alan Baddeley had pondered this possibility and tested whether all the trouble of getting back onto dry land could have thrown off the result. They let one group of divers learn the words on land, then dive and come up again, and compared them with a group who'd learned the words on land and waited the same amount of time, but without moving. The group that dived in the middle remembered just as much as those who had remained still in the same place. So all the hassle of changing location could not have explained why the divers who learned in the water remembered less on land.
Deep beneath the surface, the divers in the second group have taken out their flashlights and waterproof notepads that make it possible for them to write underwater. Bubbles from their breathing pop on the water's surface; they are fifty or fifty-five feet down, and it's hard to handle the plastic-covered sheet to write the twenty-five new words. They've gathered in a circle in the dark, and short flashes from the flashlights tied to their arms shine through the water every time they move their hands and write. Like the words they learned on land, these are mainly one-syllable words: short and concrete and easy to write with gloves on.
This group had remembered an average of 9.2 words when they were tested in the Diving Center. But what happened when they tried to learn twenty-five words underwater and were supposed to remember them underwater? As the bubbles grow bigger and the divers slowly rise to the surface, those of us on the pier are long since soaked through and clinging to empty and wet paper coffee cups. Even the seagulls have stayed at home today.
The divers, on the other hand, are not in a hurry. They rest for a while a few feet under the surface before they get out of the water. Around us, clumps of old snow lie between tufts of rotten grass. Our excitement has been building this whole ice-cold morning, as has our longing for hot chocolate and dry socks; the divers, however, are satisfied with their dive. They proudly hand us their notes.
When we examine the results, it occurs to us that we have managed to re-create the experiment from the 1970s almost down to the smallest detail. The divers who were supposed to learn _and_ remember underwater have remembered on average 8.4 words in the deep, almost matching their achievement on land earlier that day. They pulled this off despite factors like increased pressure underwater, gas mixtures and masks and wet suits and the sound of breathing, clouds of bubbles swirling toward the surface, flashes from flashlights sweeping the bottom of the sea, blurry vision, uncomfortable wet gloves, and difficulties holding pens and waterproof notepads. In the famous experiment from the 1970s, it was clear that the context had an obvious effect—the divers had remembered the list of words much better in the water when they had also memorized it in the water. Actually, they remembered it equally as well as the list they memorized and recalled on land.
When the divers were in the water, they recognized where they had been before, and this memory triggered the memories of what they had learned, so that the words popped up almost by themselves, like images on a screen.
Caterina Cattaneo led the divers in our experiment. She has almost thirty years of underwater experience and has dived at a depth of two hundred feet. This was a simple dive for her. The water temperature was comfortable, she claims, as she swings herself up on the pier and wrestles herself out of her diving mask. The February rain sprinkles the fjord behind her.
"I've never seen seahorses here," she tells us. "I've seen two on Madeira. They were tiny and very cute. They bobbed up and down, their tails wound around a sea plant. But the current was strong, and suddenly I was far away from them. I only caught a glimpse of them."
— 3 —
**THE SKYDIVER'S FINAL THOUGHTS**
**_Or: What are personal memories?_**
All the flowers in our garden and in M. Swann's park, and the water-lilies on the Vivonne and the good folk of the village and their little dwellings and the parish church and the whole of Combray and of its surroundings, taking their proper shapes and growing solid, sprang into being, town and gardens alike, from my cup of tea.
**MARCEL PROUST _, In Search of Lost Time_**
FOR MANY YEARS, our sister was an active skydiver. Every weekend she would set out for the skydiving field at Jarlsberg or travel to the United States or Poland to jump in large formations with hundreds of other skydivers.
Watching Tonje skydive was often a terrible experience for us. During the minutes we observed her falling from the sky we imagined her funeral, complete with flowers and the music we'd choose to play as the coffin was carried out. Even though there are few accidents in skydiving, the few that happen are gruesome. You don't plummet toward the ground from fifteen thousand feet without it being dangerous. Every time she was about to land, we drew the deep sigh of relief that comes after holding your breath for too long. The cheeriness of the large, brightly colored parachute belies the grim reality of the accident it can cause if it doesn't unfold or if a sudden gust of wind grabs hold of the lightweight material. Tonje's parachute was reddish orange, like a sunset.
The plane drones so loudly on its way to jumping height that you have to shout to be heard. This Saturday, a day in July 2006, Tonje walks toward the open door of the little silver plane, a Soviet turbine machine, Antonov An-28. She positions herself on the edge. She believes all will go well; she can't possibly think anything else or she wouldn't throw herself out of a plane thousands of feet above the ground. Normally, it does end well; that's the thought you cling to.
Now we'll leave her standing there, watching the forested, billowing landscape from above, while thick clouds cast everything below her in a grayish light. The temperature hovers around sixty degrees Fahrenheit, and the summer has not yet fully set in. We'll let her stand there for a while longer, her slender body in her red skydiving suit, her dark brown eyes, her broad smile. Just a few minutes more.
What memories would you linger on if you had only a few moments left to live and were looking back on your life? What memories are like shiny pearls in an incredibly exclusive—exclusive, because you are the only one in the world with your memories—pearl necklace of important events? What flutters across the hippocampus as you say goodbye to life? How many monarch butterflies light on your hand?
Or what if you were allowed to pick only one, as in the Japanese film _After Life_ , where the deceased have to choose a single memory to relive, over and over, in heaven—the happiest moment of their lives. What would yours be?
Perhaps this is why people keep diaries. They don't want the magical moments to slip away.
When blogger Ida Jackson reads through what she has written, she remembers more of those days than before, she claims. She sees and smells and hears what happened. She discovers details she otherwise would not have remembered. She is, in a sense, a collector of memories, a memory hoarder.
"It feels as if, by doing this, I lose fewer memories. There is something existential about it. I think often about death, so I want to remember everything," Ida says. From 2007 to 2010 she wrote the award-winning blog _Revolusjonært roteloft_ under the pen name Virrvarr; it was Norway's third-most-visited blog. She saw it as an extension of her diary. She has kept a diary every single day since Christmas of 1999.
"Today, I got this notebook in the mail, and since my life is upside down right now, I might as well leave behind something in writing," is how twelve-year-old Ida Jackson began her first diary. Since then, she has written herself into the long tradition of diarists and autobiographers, philosophers, poets, and authors—from St. Augustine to Karl Ove Knausgård—who have transformed their lives into books, published or not. It seems as if written language is closely connected to our wish to remember. The first Babylonian writings from over four thousand years ago were memos, trade notes, and astronomical calculations etched into ceramic plates meant to be kept for posterity.
By the year 200 CE, emperor and philosopher Marcus Aurelius had written what is considered the earliest well-known diary, _Meditations_. But long before that, Japanese courtesans and other Asian travelers were in the habit of recording their experiences in writing.
So what do we remember of our lives when we write things down, or when we don't?
Psychology professor Dorthe Berntsen heads the Center on Autobiographical Memory Research in Aarhus, Denmark, and exclusively researches personal memories. "We remember best the period from our early teenage years into our twenties," she tells us.
It seems that not all memories are created equal. Some are given priority. Our memories peak during our formative years (teens and early twenties), a phenomenon called the _reminiscence bump_. During this period of our lives, many of our experiences are new and startling; there are so many firsts, and they stay with us for the rest of our lives. Middle-aged people who are asked to recall their fondest memories typically mention something from this period of their lives, Berntsen's research reveals. This area of psychological research is amazingly free from controversy.
But does it help if you keep a diary the way Ida Jackson does?
"Yes, it does help, but it might mean that we replace our memories with written stories," Berntsen says.
What else helps make memories last? It turns out that several factors determine whether an experience sticks with us as a memory.
One such thing is the emotional impact of an experience. Exciting events that provoke sharp emotional highs stay with us particularly well. Whizzing toward the earth from fifteen thousand feet in the air, for example. Or a first kiss, after anticipation has been building for weeks. Another important ingredient for a lasting memory is how much it deviates from what we expect—how distinct or remarkable it is.
Many memories are similar to a number of other experiences we have had. It's hard to tell them apart—thinking of them doesn't remind us of one specific incident. Like all the times we take the bus to work. We have a cumulative memory of these experiences under the heading "bus trip to work." Or all the times at the beach that have merged into "sunbathing at the beach": that feeling of a summer breeze grazing our face while we squint at the sun. This is not a single event; it has happened many times. Every time, we have soaked up the summer warmth and wished that the moment would last forever. Caterina Cattaneo added to her memories of diving when she dived for the seventy-third time: that feeling of sinking into the dark water, the bubbles rising toward the light surface, the maneuvers with the tank she had done seventy-two times before. All of this became part of the general memory of "diving," "diving in the Oslo Fjord," or "winter diving." But more exciting events remain as independent, unique memories. Like the time Caterina saw a rare marine slug for the first time, or the time she saw a seahorse in Madeira.
"The brain works with memory on two conflicting principles," psychologist Anders Fjell, from the University of Oslo, points out. "Part of the brain's work is to try to categorize and assimilate as many of our experiences as possible in order to save space, while the hippocampus fights to retain unique memories."
The hippocampus is finely tuned to notice and pick up events and experiences that stand out for being different. Their uniqueness is what creates a memory trace, a shiny pearl in the necklace.
As with all other information we encounter, the more we ruminate over and talk about a unique incident, the more ingrained it becomes in memory. All the little tales about our lives that we share around the lunch table, at parties, or on Facebook—small talk—make memories stick. The paradox is that those memories then become stories in our minds more than living experiences.
Dorthe Berntsen's research center is situated in Aarhus, Denmark. There, on top of the ARoS Aarhus Art Museum, you can enjoy a view unlike anything else in the world. On the roof, artist Olafur Eliasson has installed a circular tunnel of glass in every color of the rainbow. In every direction you look, you can see spires and low-lying stone domes that date back to the 1600s in various shades of red, orange, yellow, green, blue, indigo, and purple, depending on where on the roof you stand. Just as the city of Aarhus is rendered here in multiple beautiful shades, our memories are also seen through a filter: our emotions.
The fate of a memory is mostly determined by how much it means to us. Personal memories are important to us. They are tied to our hopes, our values, and our identities. Memories that contribute meaningfully to our personal autobiography prevail in our minds.
Personality and identity can also be maintained without memories. Even Henry Molaison, the man without a memory, obviously had a sense of a _self_. He knew who he was, even though he didn't remember the full story of how he had become that person. Who we are is partially determined by factors like temperament and habits, and how we face the world and all its challenges. But our core memories in our own personal autobiography define us. Even if we don't write six volumes about ourselves, as Karl Ove Knausgård has done, all of us walk around with an autobiography stored in our memory. It isn't just a random stream of events we have experienced; our memories are structured and organized in accordance with our own life story. We are all authors.
"A _life script_ is what we call it in memory research," Dorthe Berntsen says. "It's a script for how life should unfold; it structures our experiences."
If you ask children what they want to be when they grow up, they might answer police officer, firefighter, or doctor, or maybe author, psychologist, or skydiver. In other words, they know that adult life includes a job, perhaps even marriage and children. Before we even start school, we understand that life has direction. Our life script contains expectations of how life normally looks, with milestones such as starting school, getting a driver's license, graduating, starting a career, getting married, becoming a parent, and retiring. Gradually, as life progresses and we adjust our expectations, our life script also helps us access our memories by providing chapters we can browse in our book of life: "School," "Marriage," "Work," "Skydiving." When we activate part of the life script, we activate all the related concepts in the network it's part of, just like marine slugs, air bubbles, flippers, and seaweed triggered undersea memories for the divers in our diving experiment. When something reminds us of our student days, we mentally travel back to the student cafeteria, making it possible for us to remember many experiences from that time, especially emotionally loaded memories—ones that stood out, that we thought about often and discussed.
"We can't walk around remembering everything we've done in life all the time," Dorthe Berntsen emphasizes. The life script gives us an overview of life. It portions out our memories. Should we search in the wrong chapter, we won't find the memories we are looking for. Parts of our life history are therefore not always available to us right in the moment. When we enter a new chapter of life, it takes more effort to retrieve memories from an earlier chapter.
Stepping outside our life script comes at a cost, something astronaut Buzz Aldrin knows well. He was the second human in history to set foot on the Moon, an event that turned his life upside down. His personal memories are, to say the least, remarkable. There are not many who can look up at the Moon and reminisce! In one of his memoirs, he describes his lunar memories in vivid detail:
"In every direction I could see detailed characteristics of the gray ash-colored lunar scenery, pocked with thousands of little craters and with every variety and shape of rock. I saw the horizon curving a mile and a half away. With no atmosphere, there was no haze on the moon. It was crystal clear."
As Buzz Aldrin is about to set foot on the Moon, he takes his time to absorb some of the impressions the beautiful view offers: "I slowly allowed my eyes to drink in the unusual majesty of the moon. In its starkness and monochromatic hues, it was indeed beautiful. But it was a different sort of beauty than I had ever before seen. _Magnificent_ , I thought, then said, 'Magnificent desolation.'" This description became the title of one of his books about the Moon landing, _Magnificent Desolation: The Long Journey Home from the Moon_ , from 2009.
When Aldrin began training as an astronaut, he had his sights set on the Moon, and everything he did became part of a new life script that included landing on the Moon. The life script contained earlier chapters from his time serving in the air force and studying to become an engineer, the natural introductory chapters to his personal saga. But representing NASA—and perhaps becoming a large part of the United States' Cold War identity—was not part of the original script. Aldrin dealt with the strain of being in the spotlight by consuming alcohol. In description as detailed as his memory of the Moon landing, he relates his memories of his first glasses of whiskey and the feeling of calm they brought him. Sinking into alcoholism was far less heroic than traveling to the Moon, but fighting his way out of it was equally brave. And for that, there was no script.
"How did it feel to be on the Moon?"
Buzz Aldrin has been asked that question thousands of times. It's the world's best opening line, one would think. To Aldrin it has become as familiar as a broken record, and he won't answer the question any longer.
"I have wanted NASA to fly a poet, a singer, or a journalist into space—someone who could capture the emotions of the experience and share them with the world," he writes. Still, it would be incredibly interesting to find out how his memories from the Moon have affected him through the years. Are they memories he consciously retrieves and enjoys? Does he reexperience the excitement he felt right before the _Eagle_ touched down on the surface of the Moon? Do memories from the Moon appear spontaneously in his daily life? Does he walk on the Moon in his dreams?
Psychology professor Dorthe Berntsen examines, among other things, spontaneous memories in her research. These are memories that appear on their own, without our consciously searching for them. But how do we capture a person's personal memories in the moment? Berntsen is interested in the average memories of ordinary people who haven't performed extraordinary feats, in outer space or elsewhere. To research spontaneous memories, she gives her subjects a timer and a notepad to carry around with them as they're going about their normal day-to-day activities. When an alarm sounds, she asks them to write down whatever memory comes to mind. She found that what people often remember is something their environment reminded them of. Spontaneous memories are not unlike a cat's memory when it sees the cupboard door that once closed on its tail—and jumps. For people, though, the associations are much more complex. The environment is full of potential cues that may trigger obscure memories. The things we see, and also smell, taste, talk about, and hear—particularly music—are paths into memory.
"Remarkably often, music is mentioned as a trigger for a personal memory," Berntsen tells us.
When her test subjects share the memories they had during the course of the day and when they had them, they point to music on the radio as a typical cue to a particular memory.
Play the music you loved listening to when you were young, and see if you are not suddenly back in the place where you first heard it. The feeling and the mood can come on so strongly that you suddenly remember smells and colors, clothes and details from your home, things you thought you had forgotten.
"Soft music began to flow from the ceiling speakers: a sweet orchestral cover version of the Beatles' 'Norwegian Wood.' The melody never failed to send a shudder through me, but this time it hit me harder than ever," is how Haruki Murakami's _Norwegian Wood_ begins _._
The book is a nostalgic love story woven through with symbolic meaning from the Beatles song by the same name, and the opening of the book describes the strong memories music can evoke in us. Whole landscapes and stories can appear, unbidden, in our awareness.
It is well documented that music, which speaks so directly to our feelings, is a powerful memory cue. But what about smell? The olfactory bulb, which allows us to perceive odors, is located very close to the hippocampus. We may forget it sometimes, but humans are animals, and animals depend on their sense of smell to avoid danger. Why, then, isn't smell the best key to our personal memories? But smell _is_ an important cue. Berntsen's research shows that our sense of smell is particularly important early in life. Perhaps this has something to do with childhood memories being less tied to our later interpretations and stories about ourselves, allowing more room in our memories for smell, which is more immediate and sensuous. Or perhaps it is because the odors we smelled in childhood aren't ones we encounter every day. When we get a whiff of childhood, it's a potent trigger for a distinct memory trace, because it hasn't been watered down daily during the years that have passed since we last smelled it. It is a time capsule which takes only a moment to send us back in time. Think about this: Can you remember the smells of your childhood home?
In Marcel Proust's _In Search of Lost Time_ , he opens up a world of memories when he soaks a madeleine cookie in weak tea. Taste and smell are similar gates to the land of childhood.
"Apparently, Marcel Proust's trip into memory did not start with him eating a madeleine—a disappointingly tasteless cookie; tasty, but not distinct. Proust was eating toast, but along the way, he replaced toast with a madeleine cookie. A piece of art is more than just memories; it gives the memories a form," says Linn Ullmann, who in her novel _Unquiet_ explores her childhood memories and her relationship with her father, the world-renowned director Ingmar Bergman.
The path into her memories followed the winding road of free association, not the logical archival approach one might have chosen when writing an authorized biography, yet her method is the one that best mirrors the way memory works. A life history can just as easily unfold while chasing a white rabbit as by following the historian's strict logic. Ullmann's research period was thus not spent scouring the comprehensive archive of her father's letters and documents, but by following her emotions and immersing herself in art and music and dance, putting herself in the right mood for the book she was about to write.
"Writing about memories is hard work; it's more than just transcribing recollections. I used to think I couldn't remember anything in particular from my childhood, but when I began writing I could conjure up complete episodes," she tells us. The memories Ullmann describes in her book are malleable. They are not static archives that hold perfect representations of things she has experienced. Because memories take many forms, we can approach them in different ways.
"Like the choreographer Merce Cunningham, I am thinking about what happens as our eyes follow the motion of a body from center stage to the outer edge. When I write, a small motion can suddenly become important, and something larger can become insignificant," she says.
In her book she describes how she celebrated Christmas the only time she ever spent it with her father. She is newly divorced, he is a recent widower. They walk through the snow from his small apartment to the Hedvig Eleonora Church in Stockholm. The snow whirls in front of their faces and around the church spire. She describes how, for a long time, she thought that he needed her because he didn't want to spend Christmas alone. With time, her understanding of that night changed. He always celebrated Christmas alone—in fact, he preferred it that way. It was she who needed him. The memory turns itself around and becomes another memory.
"I can't remember if the snow really fell that way. At the end of James Joyce's 'The Dead,' he describes the kind of snowy weather I am talking about. I don't know if it's actually his snowy weather I wrote into my story. However, it doesn't matter; things I have read and things I have experienced have blended together; I am not writing a biographically true story," she tells us.
Why do so many authors draw on their own memories? Maybe there is something authors can teach us about memory?
"Memory is a basic survival tool. We use it to tell stories about who we are; we _are_ our own stories. Our love stories help us build our romantic relationships. On birthdays and anniversaries, people make speeches about things we have done. We tell stories about ourselves and about each other, on a personal level, on a national level, and an international level, as cultural stories. But our memories are actually fragmented, special, and creative! Memory is a force that both creates and preserves, because it writes new stories at the same time as it maintains our lives in little time capsules. For me, as an author, it is an exciting and unreliable tool. I often remember incorrectly," she says.
What Ullmann does is not unlike what all of us do, all of the time: we make things up, structure and transform, and suddenly our memories include things we haven't really experienced—just read, seen, or heard. Like James Joyce's description of snow that wove itself into the tale of the walk to Hedvig Eleonora Church. Memories _are_ unreliable.
"I wanted to see what would happen if I allowed us to emerge in a book as though we didn't belong anywhere else. For me it was like this: I remembered nothing, but then I came across a photograph of Georgia O'Keeffe that reminded me of my father. I began to remember. I wrote: 'I remember,' and felt unnerved by how much I had forgotten. I have some letters, some photographs, some scattered scraps of paper, but I can't say why I kept precisely those scraps rather than others, I have six recorded conversations with my father, but by the time we did the interviews he was so old that he had forgotten most of his own and our shared history. I remember what happened, I _think_ I remember what happened, but some things I have probably made up, I recall stories that were told over and over again and stories that were told only once, sometimes I listened, other times I listened with only half an ear, I lay out all the pieces next to each other, lay them on top of each other, let them bump up against each other, trying to find a direction," Linn Ullmann writes in _Unquiet_ , almost as a report on how she has used memory as a method.
The debate about what autobiographical fiction really is, compared to autobiography, has been going on for a long time—long before Karl Ove Knausgård wrote _My Struggle_. But the raw material in both cases consists of memories. In autobiographical fiction, memory triumphs over hard sources and personal experience has greater value than objective fact. Memory, with all its creative misinterpretation, gets top priority.
"I discovered that memory isn't a locked trunk full of true recollections, but a creative sponge—it absorbs everything around it and renews itself," says Ullmann.
Ullmann's book is an exploration of the conundrum of constructive memory. What is actually true of what she remembers? While her father was alive, he talked to her about Bach's cello suites and described the saraband, one of the movements, as being like a painful dance between two people. Ullmann's book was inspired by their conversations about Bach. The book has six parts, just like the six parts of Bach's fifth cello suite.
In her book, Ullmann writes: " _To remember_ is to look around, again and again, equally astonished every time." She probably wasn't aware of how right she was from a scientific point of view. Our personal memories are always reinventing themselves; new details are added all the time. She says that turning her memories into a novel involved both artistry and hard work. "Nothing is more boring than listening to someone who has just woken up tell you about a dream. It only means something to the one telling it. A dream can be an interesting experience, but it's not art. It is the structure that makes it into something more," she says. Memories, too, need conscious elaboration to become literature. What she thought of as a fragment of a memory might have become several pages as she reconstructed it factually and artistically. The title of _Unquiet_ may very well allude to the fundamental nature of memory. Memories are not static, not authoritative, not solid as mountains. They are diffuse, they move around, they collide; they are like seahorses dancing restlessly amid the seagrass. Memory is constructive; it picks up fragments of an experience and builds a framework, a story about what happened. Once, that experience was fresh in our minds. But our senses, our attention, our ability to interpret, and our memory did not manage to absorb everything down to the smallest detail. Still, when that memory is retrieved, it seems as if it is intact. The memory itself becomes a new moment in consciousness, although as from a parallel reality. But beyond our perception, both hard work and artistic effort lie behind each memory.
The recorded conversations between Ullmann and Ingmar Bergman offer an illusion of truth. They represent exactly what was said, etched into a digital memory. But are they actually more truthful than the thoughts, feelings, and experiences that also form part of the memories she describes in the book? Are your Instagram and Facebook accounts telling the truth about your life, or is the treasure trove of unreliable memories you carry within your temporal lobe?
The early psychologist we met in chapter 1, William James, was something of a celebrity in late nineteenth-century America. He thought memory was the relationship between what we see and hear (we'll call that A), and what we store and can retrieve (we'll call that B). The way he explained memory was almost as a formula, with strict logic. But he missed the part of the formula that calculates how memories are constantly re-created using the machinery of our mental time machine. William's younger brother, the well-known author Henry James, so looked up to his intellectual big brother that he endeavored to write his biography after his death. The result was instead two volumes of Henry James's own memoirs, a look back that dealt with himself as much as his brother. What he discovered in the process was the true nature of memory:
"To knock at the door of the past was in a word to see it open to me quite wide—to see the world within begin to 'compose' with a grace of its own round the primary figure, see it people itself vividly and insistently," he writes, not unlike the way Linn Ullmann describes her relationship to her memories in _Unquiet_.
While William James described memory in a strictly mechanical way, his younger brother Henry managed to describe it far better in his literature. And yet he believed a lowly author's perception of memory was nothing compared to the psychologist's strictly scientific analysis. That the memory was _composed with a grace of its own_ is, however, a far more apt description of memory in the way we understand it now. The insistent vividness Henry James describes is a result of the reconstruction our brain engages in when we remember something. It is a creative process that happens without conscious effort. Today's memory researchers agree much more with Henry than William James. And Henry James was not the only author to describe how the mind behaves using the meanderings of their own memory. When Marcel Proust began to write his four-thousand-page novel in 1908, he based his writing on the very nature of constructive memory. The novel grew out of Proust's spontaneous memories, his sudden recollections of times past. His life's greatest work came into being not as a traditional story normally unfolds, but as something that swelled little by little as his memories appeared. To write based on memories is to take the process of remembering and transform it into words. The border between creative writing and brain processes is vague. Writers are the most visible representatives of memory and inspire both researchers and ordinary readers to reflect upon its nature.
We will never relive our experiences as they played out in reality, but our memories can, in theory, stay with us until we die, albeit distorted, beautified, reconstructed, elaborated. One of the leading memory theories now is that the hippocampus assembles the elements that make up a memory like a director of a play. When we reach for a memory, the hippocampus finds all the elements and arranges them for us, filling in any missing details from what else we know of the world. As we remember something personal, we are simultaneously adding it to our life story and elaborating on it as an episodic memory.
During psychology's humble beginnings, it was difficult to conduct memory research. Memories are subjective, and examining them was seen as unscientific. Still, the first psychology researchers tried to make the study of mind and behavior a science, like physics. Just as in physics, that study involved measurement. Memory was reduced to something that could be quantified—a set number of words, for instance, that entered the brain and once forgotten were subtracted from the total. The memories these researchers studied were as sterile and impersonal as possible; they didn't want personal memories to get mixed in and dirty the evidence, so to speak.
The unpredictability of personal memories meant they stood in the way of science, which was rational and controlled. Only for the past twenty to thirty years have personal memories been really considered a field of interest to memory researchers, and for the past ten, the field has flourished.
According to Dorthe Berntsen, we can thank the introduction of modern brain imaging techniques, such as fMRI, for this increased research interest.
"'How can we be sure someone has a memory of something if we can't verify it?' That's what we thought about personal memories before. But now we can measure those memories and see whether what happens in the brain reflects what the test subjects have only been able to describe to us before," she says.
With fMRI we can _see_ the memories acting in the brain. Even though the experiences remain hidden in the awareness of those who remember, the patterns that light up in the brain images that accompany the memories are measurable. And the patterns that appear are fairly consistent. When people allow a personal memory to play out across their inner movie screen, we see simultaneous brain activity across areas both in the front and back of the brain, and in the hippocampus, in a coordinated pattern.
"Memory research is perfect for functional MRI studies. It can be carried out without any special equipment—beyond the MRI scanner—and the research participants perform a mental activity they are highly familiar with, without any outer influence," Dorthe Berntsen explains. "All we have to do is ask the test subject to retrieve a memory, perhaps with the help of a key word."
The test subject ends up doing most of the work, as opposed to other types of psychological experiments that require chessboards and divers, questionnaires and interviews, film clips and gorillas. Remembering is such a normal part of life that we don't have to wait particularly long for our test subjects to start remembering. Researchers have actually discovered that the network that's activated when the test subject is asked to think of a personal memory is remarkably similar to the network of brain regions that is activated when one asks people not to think of anything at all! We call this the _default mode network_ , as opposed to _task-dependent networks_ engaged when test subjects are asked to use their brains actively to solve a math problem or count backward. In the default mode, memories pop up easily. Who can really think of _nothing_ when asked not to think of anything in particular?
Though fMRI makes memories visible and measurable, it doesn't mean that brain scanning is the only way to make memory "scientific." It is high time now to insert a small warning about brain imaging: just because something lights up in an MRI doesn't mean that it's real.
When used incorrectly, fMRI has even shown signs of empathy in a dead salmon. The salmon was placed in an MRI machine by four American psychologists, who then "instructed" the salmon to look at several situations from a different perspective than its own. The results were surprisingly good. An "empathy center" lit up as an unmistakable red dot in the brain of the dead fish—but this was because of the way the results were read, not something actually happening in the salmon's brain. The researchers conducted the study to make others aware of some important principles regarding proper use of fMRI, and ways the statistics and mathematics behind fMRI can be misapplied. They received the humorous Ig Nobel Prize for having demonstrated that even a fish ready to be served for dinner can show signs of compassion, if you look for it hard enough.
Used correctly, brain imaging is a good tool for showing how memories are organized in the brain. Although we don't need MRI to tell us that memories _exist_ , the mapping of brain functions to brain regions and networks is helpful in the quest to solve the riddle of memory disorders caused by Alzheimer's, epilepsy, and other diseases.
Research on personal memories is also carried out _without_ MRI machines. Seeing the signs of a memory in a magnetic resonance image is not the same as understanding its content. It's like looking at a vinyl record as opposed to hearing the music recorded on it: understanding how the track makes the sound does not give us the sound itself.
The closest researchers can get is to ask people to describe their memories. The ways people experience memories vary, and your experiences are unique to you. You alone have the blueprint of your own experience. Solomon Shereshevsky's memories were colorful in a completely different way than yours and mine, since he had synesthesia. Those of us whose senses aren't entangled cannot imagine the way he experienced the world. We can only take his word that he was telling the truth when he described his recollections to researcher Alexander Luria.
How events recorded in a memory took place may be the simplest part to figure out. Descriptions of what happened, however, are often riddled with flaws and missing details—something we'll return to in the next chapter. But what is most difficult to capture is the texture of memories: what sensory experiences they contain, what feelings flow through them, how intensely they come to life. We often use questionnaires for this, in which people rank their own memory experiences on a scale.
Why do we make this our business? "Research on personal memories helps us understand, among other things, depression and post-traumatic stress disorder," says Dorthe Berntsen.
This is one of the most compelling reasons to research people's personal memories. One of the discoveries that's been made is that individuals suffering from depression have less distinct personal memories. Learning more about why can help depressed patients better hold on to their memories, so that they can find joy in experiences from the past. A study done by Susumu Tonegawa and his research group showed how happy memories can actually relieve depression. In an experiment involving mice, they first determined which neurons were activated while a mouse had a positive experience—in this case, a pleasant encounter with a mouse of the opposite sex. Then they stressed the poor mouse for ten days by immobilizing it for two hours each day, until it was fairly depressed. That's when they delivered the surprising antidote: they reactivated the mouse's positive memories by "turning on" the network of neurons connected to the original positive experience. After a few days of this "therapy," the mouse was fine again; it became more active and showed a new interest in its surroundings. By comparison, mice that were offered new pleasant moments with a partner of the opposite sex did not get any less depressed. Reliving a memory was more effective than experiencing something nice in reality. Maybe this proves that a happy memory is our own built-in antidepressant?
We think of our emotions as irrational and volatile. They don't follow logic, and they can disappear before we have time to put a name to them. They flow through us organically, coloring our lives and our memories. They're the joyous amazement that simmers when you see two seahorses swaying in the seagrass in Madeira. They aren't columns and graphs and white lab coats. How can we force emotions inside the scientific framework that makes research possible? For years, researchers in laboratories have tried to isolate the effect emotions have on memory. It's like using a chemistry set with flasks and test tubes, where the goal is to distill the purest form of emotional memories. Imagine the following student assignment in a natural science lesson:
**Creating Sad Memories**
_Equipment:_ Film clips of natural disasters, children sick with Ebola, funerals, and tears. Some willing volunteers. A questionnaire about a personal memory.
_Procedure:_ Place each volunteer in front of a computer monitor and play a film clip. Follow the changes in the person's face, from a neutral, perhaps a bit curious, facial expression to more and more sagging at the corners of the mouth, then a concerned frown and increasingly moist eyes.
Then give them the memory questionnaire.
_Results:_ The past suddenly has a grim feel to it. Repeat until the teacher is satisfied with the number of sad memories.
But what happens if we don't have any personal memories? We don't mean like Henry Molaison, who couldn't remember anything that happened after his surgery. What if we _know_ what took place, only the episodes won't let themselves be recalled, can't be reenacted, aren't coming alive? For Susie McKinnon, the memory theater is on strike, or maybe never actually opened. She lives in Olympia, Washington, and has been diagnosed with _severely deficient autobiographical memory_ , the first person in the world to be identified with this disorder. This means she can't recall a single episodic memory from her own life. She knows she is married to Eric Green but isn't able to recall details from their long marriage, or to relive those experiences in her mind. She can't even recall how they met in a bar in the 1970 s—only her husband can describe that memory in detail. She knows they have taken many fantastic trips, but she can only point to the souvenirs on display in their home if anyone asks about the Cayman Islands, Jamaica, or Aruba. She knows who the people are around her, though, and has successfully worked in health care and as a pension expert for the state. Her entire life, she has been a well-functioning employee, wife, and friend. There is nothing wrong with her semantic memory.
The difference between semantic and episodic memory was first described by Canadian researcher Endel Tulving. Semantic memory is, as we've said, what you know about yourself and the world—these memories are the facts about our lives which we feel we know are true. Episodic memory is what we experience when we travel back in time and _find ourselves right where something happened._ We conjure smells and sounds and feelings, and whole scenes are reenacted in our minds. It's our inner time machine that lets us feel and hear and taste and see things that are no longer here.
Susie McKinnon is missing all of this. However, living a quite ordinary life with no obvious problems, it was easy for her to believe that everyone felt the way she did. In an interview with the _Huffington Post_ , she describes the first time she was given a psychological questionnaire; she was confused when they asked her about childhood memories. She believed nobody could remember their childhood and thought everybody was doing what she was doing: making up episodes from the past to spice up conversations. She didn't realize there could be something special about her memory until she read about Endel Tulving.
For years, researchers have documented people who lack episodic memory, but these individuals were usually victims of injuries or traumas that made their memories dysfunctional. But Tulving anticipated that someone like Susie would come along one day; he assumed that it would be possible for many people without episodic memory to exist in the world, undiscovered, simply because they can live full lives, have distinct personalities, and keep jobs and families, all without having episodic memory. Psychology professor Brian Levine, who studied Susie and others with her predicament, found that it's more common than previously believed. Via an online questionnaire about memory, he has—so far—received more than two thousand responses from ordinary Canadians.
"Many of them report severely deficient autobiographical memory, so I'm beginning to think that this is not a rare occurrence at all."
"Is it normal not to remember anything from childhood?" the writer and musician Arne Schrøder Kvalvik asked us when he realized we were writing a book about memory. "And I mean nothing at all!"
Arne was nominated for the Norwegian Brage literary award for his first book, a nonfiction work called _Min fetter Ola og meg_ (Me and my cousin Ola), and is part of the award-winning band 120 Days. He is a respected musician and writer, and a devoted father. But something is different about him. Like Susie, he remembers nothing from his years growing up.
"Gradually, I guess I realized that I was different, because people were mentioning what we had done as kids. But I remembered nothing," he tells us.
He knows very well who his relatives are, where he went to school, what he did in his spare time. He just doesn't have any memories of those things. He can tell you where in the school his classroom was, but that's about it. He has nothing beyond the location. He is unable to recall how it smelled, what he said to his teacher—neither happy nor sad memories appear. He knows he played with his band in front of the whole school, but he can't recall the experience of standing there, young and nervous, with classmates and teachers watching him onstage.
"I worried that I was repressing memories, that I had experienced something traumatic. But that's not it either! My memory is simply weaker and weaker the further back I go. Things that happened ten years ago I can remember, but only a few episodes—even though I was traveling around the world as a musician. I have performed in concerts throughout Japan and the USA."
His life doesn't lack unique moments that should have etched themselves into his memory. But it doesn't bother Arne that he remembers so little. And if we are measuring people by their success, he has it all: he is a happy dad of two with a brilliant career. But behind him, the memories are waning, disappearing, evaporating into thin air. When his parents told him that he had been in Portugal in his teens, no pictures emerged from his memory of the family they shared a house with, of the sunlight, the sea, the bacalao, or old, dilapidated stone houses. He remembered only one thing: a white pair of pants.
"I don't remember my first kiss, for example—and not because I was drunk. But there is one thing I remember from when I went to school: the terror attack on September 11, 2001, when I was seventeen," he says. "But I only remember where I was when I watched it on television, nothing else."
He doesn't remember how he met his love, or what they talked about during those first trembling moments of romance, but he knows he loves her. And, after all, that's enough. "It's not a problem for me that I have so few memories. It doesn't bother me."
We don't know why it's like that for Arne. We don't know if he falls into the same category as Susie McKinnon, who has her diagnosis—if we can call it a diagnosis. Perhaps it is only a reflection of the great variety in people's memories. Some experience memories very visually, others don't. The opposite of severely deficient autobiographical memory is what Levine and his colleagues call _highly superior autobiographical memory_. People with this memory capacity often remember the exact day something happened, even many years later, and their strong feelings connected to past experiences don't wane easily.
Ida Jackson, the blogger we met earlier, is the complete opposite of Arne. To her, the ability to remember _is_ important. She wants to remember everything, and most of her memories appear as evocative images—sometimes too colorful.
"Sometimes my memories are so strong and unpleasant that I feel physically sick, and to work through these feelings, I talk to a psychologist and write in my diary and on my blog. Writing about a memory sort of removes its power; it simply turns down the volume of the memory. In that way, I change the memory from something I see and hear before my inner eye to a story," she says.
One of the memories she has written about is her experience of being bullied in school. Her blog post was picked up by a magazine in Oslo, which posted Ida's story on its website long after her blog post had first appeared online. Six years after she'd first written it, Ida watched her post go viral on social media.
"On the internet, it's not newsworthiness that determines whether a post is shared—it is the emotional strength of the writing. This blog post was very painful for me to write. I shared all the shame I felt with my readers. The problem is that my memory was highly biased by a story about being a sympathetic victim, but that was not really the case. I smelled bad and picked my nose and ate it in front of my classmates. But that did not fit into my story, so I didn't include it. I didn't deserve the horrific bullying I received, but in truth, I was revolting! It was up to the adults to stop the bullying, of course. Beware, that when we write stories based on our memories, we often grab the most stereotypical tales available. When I saw how my blog post swept across social media, I had to correct myself and write a truer story."
"We are strongly affected by the story lines in Hollywood films, we know that. We look back at our childhoods and try to find foreshadowing of who we will become: the sign, the key, the trigger that makes things what they are," clinical psychologist Peder Kjøs says. He participated as a group therapist for youth on a Norwegian TV documentary in the spring of 2016 and writes a psychology column in an Oslo newspaper.
In his therapy practice, Kjøs helps people restructure their lives by writing their life scripts. Our memories become stories about ourselves. Some stories are easier to hang on to, because they fit our self-image better than others. In many ways, the psychologist is a coauthor of life scripts, or at any rate a cautious editor. And we are all authors of our own life stories.
"We have a tendency to look for a certain dramatic structure in our lives. Since we can't scroll forward in our lives, we look backward to write the story about ourselves. And when we rewind, we direct, cut, and photoshop. We can change the script as we go along, find reasons for things being as they are. Sometimes, clients want there to be a turning point in their childhood, so they don't have to blame their parents even if they were neglected. On the other hand, if we have had it reasonably good but life is not going as expected, we may well blame our parents. Of course they may have done something wrong or fallen short; no parents are perfect. This doesn't mean that people haven't had bad experiences during childhood, but we often lend great significance to modest events."
His clients' problems arise when they edit their stories too harshly. It's one thing for our memories to be reconstructive and elastic, and another if we bend them around absolute untruths.
"A narrative that doesn't agree with facts doesn't work. It is important, however, in a treatment situation for clients to arrive at narratives themselves. I don't know what's true, and I can't present them with a solution."
Working with people whose life stories are made up of predominantly bad memories demands something special of the therapist. It is important to give the clients a feeling of power and responsibility without saying all those bad things that happened were their fault. Without power and responsibility, we can't change anything—we become a minor character in our own narrative.
Most difficult is changing a life that has only gone from one dark moment to another. How can we imagine anything good can happen if all we know from the past is pain? How can we see the light at the end of the tunnel? In _Soria Moria_ , a painting by the popular nineteenth-century Norwegian artist Theodor Kittelsen, a hero from folk tales gazes toward the glow of the sunrise, which resembles a golden castle on the horizon: it's a mirage, a goal for Askeladden's wanderings. Askeladden's courage and daring are probably what allow him to see a castle at all, just beyond the dark rolling hills. To a depressed person, even the hills would be out of focus.
THIS BRINGS US back to the lush forest landscape over which our sister has finally jumped out of the plane, parachute fastened to her back. Her heart beats quickly and the adrenaline pumps so vehemently through her body that it's hard for her to perceive what's happening. She releases her parachute after ten seconds of free fall. Contrary to what we might believe, the most dangerous part of the jump is still ahead of her—the landing. The much-anticipated feeling of flying is all-consuming. She is overwhelmed by it and by the routines she must keep in mind throughout the jump. She completely forgets to pay attention to the ground rushing toward her. At first, it seems like an abstract map, a quilt of forests and fields. The trees speed closer and closer, and every second counts. The field she was supposed to land on glides past below, and she is on her way toward the forest and what might be her return to the ground. Finally, she reacts and steers the parachute. But it is just a little too late!
The top of a tall spruce tree is where Tonje ends up. Though unharmed, she dangles there for two and a half hours before the search team finds her. And yet, this experience does not deter her from trying again soon afterward. It is not until she is sent up with the plane to make her second jump of the day—her second jump alone, ever, actually—that she has an experience we expect on our deathbeds: her life passes before her eyes. It turns out that the images are disappointing! Instead of high point after high point, pearl after pearl of unforgettable moments, she sees only meaningless, mundane images from childhood, mostly standing on the lawn at home as a seven-year-old, or walking, backpack on her back, along the asphalt driveway up to our house.
"They were very boring experiences, and I don't know why they were the images that popped into mind," Tonje says now.
The second jump cured her of the anxiety she felt from the first jump. Since then, she has jumped thousands of times and never experienced anything like it again.
We assume that as we die, the most important moments of our lives will appear before us. That's why we collect them, isn't it? Suddenly, as we're about to write our life story's finishing line, our most important memories are supposed to present themselves to our inner eye. We will see clearly what life was all about. The actual meaning of what we've experienced will be revealed to us. The end of the story will explain the beginning. Or will it?
Caterina Cattaneo, who led our diving experiment in the Oslo Fjord, was unconscious under water—medically defined as drowned—for thirty minutes once. After a particularly difficult dive, Caterina woke up in a hospital in Oslo. She had drowned. She was only twenty-one years old, and she had taken risks in the water. The last thing she thought as she was embraced by the darkness: _That guy at the party last night, why didn't I sleep with him?_ None of her important memories surfaced; no crucial revelations. Her life script was neither rewritten nor revised. There was just a trivial thought, and then black.
The last thing Adrian Pracon thought at the cliff's edge, imagining he would die, was more concrete. He envisioned the coffin containing his body being lowered into the ground. His parents crying, shattered by grief. The image came to him from nowhere, without his willing it to come, and he was surprised at how clearly he saw it, as a murderer aimed a gun at him.
Adrian Pracon was twenty-one years old and a youth politician. For the first time, he was participating in the Norwegian Workers' Youth League summer camp on Utøya, an island in a lake about half an hour's drive from Oslo. Some six hundred committed young people from around the country had gathered for a few intense July days of political work and evenings with singing and political discussions. Even the country's prime minister and foreign minister, as well as previous prime minister and former World Health Organization director-general Gro Harlem Brundtland, visited the camp that summer in 2011. Politics, power, and youthful dedication came together on that small island, coloring the nights with hope and plans for the future.
Anders Behring Breivik had been preparing for a long time. The bomb at the government building, which killed eight, and the attack on the youth camp, where he killed sixty-nine, were thoroughly planned in solitude. As Adrian envisioned his own funeral, the killer stood on the shoreline at the southern tip of the island, aiming his gun at him. There he stood for a couple of seconds. Then he lowered the rifle and walked on. Adrian remained hiding in plain sight, lying down on the point, which jutted out like a gray finger over the water. The landscape was completely open and unprotected, rocks dotted with low, naked bushes. Adrian lay there with a jacket over him, pretending he was dead. Perhaps doing so saved his life when the terrorist returned to the point to make sure everyone was dead. Failing to realize Adrian was still alive, he may not have bothered to aim properly. Adrian was hit by the last shot fired on Utøya. The bullet entered his shoulder and exploded into more than seventy pieces of shrapnel, lodging in the muscle tissue as little reminders of the day his life changed forever.
"The first years after it happened were totally out of control. The memories returned completely involuntarily, often when I was stressed. The more I needed to clear my head, the worse it got. Three years of my life are completely lost," he says today.
He survived the shot in the shoulder, but life after the massacre was not the same. Adrian had been on the threshold of something new and exciting; it had felt as if he were soaring into the future. He had landed the job as regional leader in the Telemark Workers' Youth League; he had a boyfriend, a dog, and a place to live. But after the nightmare on Utøya, his life became a constant repetition of what he had gone through. Over and over again, he suffered through some of the most horrifying moments of his life. He analyzed them from all perspectives, thought of what he might have done differently, how little it would have taken for the bullet to enter his head, his heart, or his spinal cord, rather than his shoulder. Sometimes he would imagine picking up a rock and killing Breivik before he could do more harm. Sometimes he would focus on his guilt, because it had been up to him, as regional leader, to recruit participants for the summer camp. One of the youths he recruited never returned. He was only fifteen years old.
In the period after July 22, Adrian began to drink heavily. Uninterrupted sleep was a luxury he could no longer enjoy. The man who used to be boyishly messy became extremely fussy about cleanliness; his behavior bordered on mania.
"My boyfriend at the time told me I would take a sleeping pill and then clean the whole house. I remembered nothing and woke up to a clean house."
During Breivik's prosecution Adrian began to write a book about his experience. He drove back and forth from his hometown of Skien to Oslo to follow the legal hearings and work on the book. It was a very hectic and emotional time. One afternoon, after a couple of beers with friends, everything went black. Adrian came out of it as the police were handcuffing him. He had to go to court himself, and he was sentenced to community service for his violence against two men that night.
"It scared me. I can't drink like that anymore. If someone suggests a beer, I have to take a walk first, find out how I feel. I have to know I'm having a good day."
The terrorist is serving a life sentence, and so are Adrian's memories. He takes them out for fresh air and walks them in the exercise yard before he forces them back into the dark; they are strictly supervised through most of Adrian's waking hours. Allowing them out for an interview will result in a bad day afterward. Now that he knows this will happen, he can plan accordingly.
"For a period of time, I drank a lot, probably because I didn't want to remember anything at all. I didn't want to remember all those evenings when I was not feeling well. I just wanted to get away."
July 22, 2011, was a national trauma. The new realities of the world reached the safe country of Norway. The Norwegian relationship with safety and danger was changed forever. The terror also gave Norway a new memory milestone. All Norwegians have a memory tied to July 22, 2011. American researchers have called this phenomenon, whereby strong emotions tied to a shock glue an experience to our memory, a "flashbulb memory" because the experiences seem frozen in time, like a photo in which the flash has gone off and thrown a glaring light over everything in an otherwise dark room.
In many psychology textbooks, the explosion of the space shuttle _Challenger_ is used as an example of an event that could have caused a flashbulb memory, as are the terror attacks of September 11, 2001. Before Breivik, Norway didn't have any obvious, tragic examples. But there were positive ones. Where were you when Oddvar Brå broke his ski pole? The time a Norwegian skier came close to losing a gold medal because his ski pole broke is a memory common to many Norwegians, one they can laugh over and share stories about (although most of the memories involve sitting on the sofa in front of the TV or standing along the ski trail during the World Ski Championships in 1982).
"Where were you on July 22?" is a question that ties our personal life stories to that of Norway. For those directly affected, it's another story; memories of what happened will follow them the rest of their lives. At the Norwegian Centre for Violence and Traumatic Stress Studies (NKVTS), the survivors and their families have been studied. When something this serious happens, it's necessary to bring in investigators and terror experts so society can learn from the events. But for the researchers at the NKVTS, the important thing is to learn about trauma, to better help survivors the next time something happens. People go through trauma all the time. They are victims of rape, assault, car accidents, and wars around the world. Many carry traumas that get far less attention than those resulting from July 22, although they are no less serious for those affected. How can they be helped to escape their intrusive memories?
Ines Blix is one of the researchers at NKVTS studying this national tragedy. She has followed those who worked in the government building where the bomb went off, using both interviews and questionnaires to see how their lives have been affected by the terror act.
"There are two traditions within trauma research about how we remember traumas and what trauma memories do to us. This has been called the memory wars. Some believe that we remember traumatic events quite differently from other events, and that traumas can lead to fragmented memories, extreme repression, and dissociative personality disorders. Other researchers, like myself, believe that traumatic events, like other emotional events, are often remembered very well. Memory behaves to a great extent as it always behaves, but it turns up the volume to an extreme degree; an ordinary memory system on volume ten."
Blix's research shows that among the most common problems people report after traumatic events are intrusive, detailed memories that appear over and over again for a long time after the event.
We have known about intrusive, involuntary trauma memories for a long time. After World War I, these were a symptom of what was called "shell shock," and in Virginia Woolf's classic _Mrs Dalloway_ , they were what made a young soldier jump through a window to his death. At that time, post-traumatic stress disorder (PTSD) was an unknown illness, and people wondered why soldiers became unfit for battle without being visibly injured. They retreated from society, didn't sleep, didn't eat, were unable to take care of themselves, and often lapsed into apathetic staring or behaved in a panicky and irrational manner. The gruesomeness they were exposed to during the war was extreme. For the first time, millions were mowed down by machine guns in muddy trenches, in a brutal war that divided Europe. Since then, knowledge of trauma psychology has increased. It wasn't laziness or head injuries that made the soldiers ill. What was it, then?
A strong tradition within the research suggests, as we've pointed out, that trauma memories are different from ordinary memories. When people develop split personalities or other dissociative disorders, these are survival mechanisms that help them master their lives through the crises.
But how can that be, when we know that shocking images and strong emotions associated with upsetting events can slash memory open and burrow in far more strongly than anything we experience in everyday life? Trauma ties itself to memory in every way possible. Traumatic events are powerfully emotional, unique from everything else we have experienced, and upset much of what we assume about ourselves and the world. It's not only that trauma is hard to forget, it's that it pops up unannounced, like a jack-in-the-box. Victims of trauma are often unable to lock that box, and their upsetting memories appear over and over again in all their cruelty.
On a questionnaire given to 207 government employees who were at work on July 22, half responded that they were still troubled a year later by recurring memories from the terror attack. For a quarter of those examined, the effects were so serious that they could likely be diagnosed with PTSD. Even employees who were not at work that day were affected. They knew that they could have been at work and suffered from recurring thoughts about colleagues who had been hurt.
PTSD develops gradually over time after a traumatic event. When the memories don't subside, a person's attempts to avoid them only strengthen them and make them uncontrollable. Someone suffering from trauma avoids everything that reminds them of it so as not to relive it again and again. This disrupts everyday life and makes it harder for them to return to work and studies. It is also extremely difficult to keep from thinking about the trauma. It's like saying "Don't think of an elephant!" What happens? The elephant stomps around, knocks things over, and takes up an enormous amount of room the more you pretend not to see it.
Spontaneous and pleasant memories pop up out of nowhere too. As Dorthe Berntsen found in her research, we can be reminded of them by whatever we're experiencing at the time. Music we hear on the radio transports us back to when we were fifteen. We don't give this much thought. It becomes obvious to us only when the volume on spontaneous memories goes through the roof, as it does with traumatic memories. Obviously, these memories take up space, as does any memory. Sometimes, the memories consolidate and turn into PTSD. Other times, even the trauma memories subside and become stories that can be told without strong feelings—no longer the elephant in the room.
"The big question is why some people develop PTSD and others don't," Ines Blix says and points to several explanations that together can perhaps show part of the picture. It may be due to differences in how people handle an event in their working memory: to what degree they are able to filter undesired information out, how flexible they are in steering memory. Small variations in such basic brain functions, not noticeable normally, can make a difference in extreme situations, which trauma and life thereafter are. There can also be differences in how people organize their memories, which can result in traumatic memories taking up more space in some than in others.
Blix calls it centering. "In our study, we found that those who placed the events of July 22 in a more central place in their autobiography, as a major turning point in their lives, were more likely to develop PTSD. Centering was a predictor for who would have PTSD symptoms three years after July 22. We believe centering makes the traumatic memories more easily accessible. They become a point of reference."
It's as if you are actually riding the elephant. Not thinking of the elephant is difficult when it is constantly following you around. Then, one day, you become the elephant. You are identifying with the trauma, and it has become a part of you. It has become a central point of your life's story.
The hippocampus plays an important role here too. Several studies have found that people with PTSD have smaller hippocampi than average. The question everyone has asked in response is obvious: "Are psychological traumas harmful to the brain?" The stress reaction, when we are extremely scared, can trigger the body to produce sky-high levels of the hormone cortisol, which in large amounts can be harmful to the brain, especially the hippocampus, which is about as vulnerable as its namesake seahorse. But a unique study of twins, conducted by Mark Gilbertson and colleagues, gives a possible alternative explanation. Among the twins who were studied, one in each pair had been exposed to a psychological trauma. That's how they could compare the hippocampus—normally very similar in identical twins—in one person that hadn't experienced trauma and one that had.
What was surprising was that Gilbertson and colleagues found the hippocampi were fairly similar in the twins, both with and without trauma. "This may mean that the size of the hippocampus before the trauma can be a risk factor," Blix says.
It is still a mystery why _smaller_ hippocampi can produce such powerful memories that they can almost put a human out of action. Shouldn't it be the other way around, that a _larger_ hippocampus can more easily replay the bad memories?
We can't do anything about the size of our hippocampus. We can't strive to shape our memory in a way that makes us better equipped to survive catastrophe. But when the trauma is a fact, is there anything we can do? Blix believes that, more than anything, knowledge of normal brain reactions can help people handle traumatic memories better and faster.
"It is beneficial for people to know that it is common to react with intrusive memories and that for most people, the memories will weaken as time passes." The elephant will stomp less frequently around the room, which is our awareness. Eventually, we can take control and lead it back into its enclosure. It is the fear of it always being on the loose that hurts us.
Trauma treatment is first and foremost about turning down the volume on memories and breaking the vicious cycle of avoidance. PTSD puts us on high alert for spotting possible new dangers; we are easily startled and sleep poorly. Some studies even point to a worse general memory in the wake of PTSD. It may not be an odd thing to suggest, if the traumatic memories are taking up space. The fear of the memories can almost amount to a phobia. A phobia sets us up with a pattern of reactions that steer our actions. Phobias can be extremely tough to shake simply because avoiding something feared offers such relief. The relief acts as a reward. If we can choose between feeling relieved—by, for example, hanging out in our apartment, feeling safe—and going out and being reminded of something bad that happened and feeling extreme fear, it's easier to choose relief. The result is that we stay home more and more. So do the memories. We learn that the memories are to be feared, and we should avoid them. The more we avoid them, the stronger they get. The same happens if we're afraid of wasps, injections, sharks, dogs. If we avoid them, we will undoubtedly continue to be afraid. The alternative is to face our fears. How is this best done when it hurts so much?
"Trauma-focused cognitive behavioral therapy and eye movement desensitization and reprogramming (EMDR) are the preferred treatments for PTSD," says Blix. The idea is not to throw ourselves at the memories we fear like a kamikaze pilot, but to approach them cautiously and gain more and more control. We get used to the memories and deplete their powers.
Therapists often use relaxation techniques such as EMDR, in which they move their hands back and forth in front of their patient's face. It might sound weird, but it gives the patient something external to focus on while they talk through their memories, dividing their attention between their traumatic feelings and the therapist's strange hand movements.
In an ideal world, there would be a vaccine for PTSD, so that if we encountered something horrific, we could go to the doctor, get vaccinated, and immediately feel safe—not unlike getting a tetanus shot. Emily Holmes's research team at Oxford has tried this exact thing. They believe that playing _Tetris_ in the hours following a traumatic event can considerably reduce the occurrence of intrusive memories. The way they came to this conclusion was by showing the volunteers in an experiment a very traumatic film. Some of the participants got to play _Tetris_ afterward, while others were left to their own devices. Then all the researchers had to do was wait for the traumatic memories to appear—voluntarily, that is. In these experiments, _Tetris_ had an obvious protective effect. The idea is that the game competes for space with the strong visual memories associated with the trauma. The visual impressions immediately following a traumatic event remain vivid as they begin consolidating into memories. Playing _Tetris_ prevents the images from the trauma from having proper access to our memory. In comparison, they found that those who played a word game—such as a quiz—had more flashbacks than those doing nothing. The linguistic distraction probably kept the participants from storing their own interpretations and assessments of what they had seen, but it still left them with a set of immediate, intense visual impressions.
Will this therapy work in the real world? When your world has been turned upside down, and you're thrown into a completely genuine panic state—not just a reaction to a film in a lab—will it seem reasonable to pick up the smartphone and play _Tetris_?
What may feel more natural to most of us is to try to understand, find a context, some order. The experience of a traumatic event is not like a film. Our attention decides what makes it into our memory and what is left out. But our attention is also affected by terrible fear. We cannot take everything in. In the experience of trauma, our personal worldview—what we normally use to interpret and understand new experiences—is put to an enormous test. Something that breaks with all expectations of a peaceful life, such as a bomb in a government building, takes an extra long time to understand. We don't have time to understand it at the moment the bomb explodes—the understanding will come later, perhaps never. When researchers at NKVTS and the University of Oslo examined the stories of the youth that survived the Utøya massacre, they found that those who developed PTSD symptoms remembered more external details about the event and had fewer internal thoughts and interpretations. This suggests that those who continually assess and interpret their situation are better prepared to handle their memories, while those who are attending to the details of their surroundings are more troubled by their memories afterward.
Adrian Pracon worked through all the details from the horrific day on Utøya when he wrote his book, _Hjertet mot steinen_ (Heart against stone). Writing helped him to put the gruesome details behind him. Now he doesn't feel the need to remember as much. His detailed memories are contained within the black box—his book—and don't fight to get out as aggressively as before. But making the memories fade wasn't as simple as writing a book; that was just one step on the path toward his new life. Like everyone who has been through trauma, he longs for the normalcy of everyday life. The PTSD always has him on high alert. In new places, like a café, he will still look for possible escape routes and hiding places, and the screams of children playing can make him nervous. Seeing pictures of the murderer inevitably triggers a reaction. Of course, it is almost impossible not to see pictures of him. Especially in the time following the massacre, Breivik was all over the newspapers and blogs and incessantly talked about on TV and radio.
"I saw him, once. It was at the convenience store. He stood in a corner and turned toward me. I had to calm myself down; I knew of course that he couldn't be there."
A picture or a comment, a poor night's sleep, or something else had triggered the memory of Breivik so strongly that he was visible to Adrian. Several survivors state that they are thrown into the situation and _are on Ut_ ø _ya_ when they hear the loud voices of children. They can see the grass below and the trees around them and feel the panic reaction take over, even if they are safe, in the middle of the city.
Returning to where it happened may be the most frightening thing Adrian could do; the memories are extra strong on Utøya. That's part of what we showed with the diving experiment: how a memory is connected to, and appears in, a particular place. What, then, do we want to accomplish by bringing Adrian to the place where he was shot? Won't seeing it again overwhelm him with bad memories?
"It's beautiful, but for me, it's like there is a dark cloud over the island," he says as the boat, MS _Torbj_ ø _rn_ , steers toward the pier. The chugging sound of the old boat's engine fills the April afternoon with summer memories. The water rushing along the side of the boat may tempt us to go swimming, but it emits a raw chill. On July 22, close to five years ago, it was raining and cold here. The Tyrifjorden—one of the deepest lakes in Norway—wasn't suitable for swimming, even in the middle of the summer. When Adrian stood on the shore that day and felt the water fill his shoes, he suddenly woke up and realized that something very dangerous was happening. Even a few minutes earlier, when he watched a young girl get shot, all he could think was _It must be an exercise, role-playing._ It wasn't real.
"It still controls much of my experience of what happened, that I thought it wasn't real."
We walk around the island, which is now dotted with spring flowers, on a kind of guided tour of terrorism. Had we been simple tourists, we wouldn't have known it was anything other than a beautiful idyll. Blue and white anemones, typical Norwegian spring flowers, poke up everywhere between rocks and under slender trees. And even though we feel like it, we are no more voyeurs than those who go to Auschwitz to comprehend more of the Holocaust. It is sad and strange to be here.
New buildings are being erected here to replace the café where many of the bodies of those killed were found; they will become a learning center for democracy and freedom of speech for young people. We are being shown around one of the buildings by a manager on Utøya, Jørgen Watne Frydnes. Inside the newly erected building, which includes a café, an auditorium, and large windows that frame the nature outside, there is a library of political literature. The shelves are fifteen feet high. We remain standing for a long time in front of the bookshelf. Here, the politicians of the past will speak to the politicians of the future from the pages of books.
Right by the new construction, somewhat hidden in the forest, there is a memorial to the sixty-nine who were killed here, a delicate metal circle suspended from the trees. The names of the victims and their ages are stamped into the metal, children who should be here and would have been five years older today.
Adrian stops at the circle and reads the names. We put flowers on the ground under it. Then we walk down toward the place where Adrian was shot. A swan floats in a small bay, illuminated by the sun that emerged after the spring snow that was falling when we first arrived. The fragile flowers have captured white snowflakes that already have begun to melt.
"I don't think there was any real change in me until I accepted that life as I knew it would never return. That's when I quit fighting and could begin building my new life, the one after the event."
The memories can still overpower him, but he has gained more and more control over them. Trips to Utøya (this is not his first) serve as yet another way to gain the upper hand.
"I know from experience that periods of stress release the memories. This can ruin an exam, a job interview, an assignment deadline. This winter, I was stupid enough to wait until the last day to finish a take-home exam. Then the trauma memories took control in the middle of all the stress, and I couldn't deliver on time."
Adrian has already planned not to do anything after our trip to Utøya. Taking the memories out for a whole day in the fresh air is demanding enough. "Much about me changed after what happened. I was messy before, now I am orderly. I wanted to work in the civil service, now I want to research terrorism. I didn't used to read the foreign news in the paper, now that's all I read. Before, I couldn't envision myself living in Oslo."
Adrian moved to Oslo in 2012 and eventually started peace and conflict studies. He wants to conduct academic research on terror. He is hoping that what he has lived through will help inform his research.
We're gazing beyond the point, where he lay during most of the terror. It is covered in gray rocks and some dried-up, half-dead trees that even in the summer hardly have any leaves.
"I can see the ghosts of everybody who came and went here, and I can see him. It is like a film, where you see transparent people come and go."
"Have you ever wished that you could forget everything that happened before July 23, 2011—erase it from memory forever?"
"I have daydreamed about it. When I was very sick, I thought about it a lot. But I have so many good memories too. I don't want to lose them."
— 4 —
**IN THE CUCKOO'S NEST**
**_Or: When false memories sneak in_**
"I can't believe _that_!" said Alice.
"Can't you?" the Queen said in a pitying tone. "Try again:
draw a long breath, and shut your eyes."
Alice laughed. "There's no use trying," she said. "One
_can't_ believe impossible things."
"I daresay you haven't had much practice," said the
Queen. "When I was your age, I always did it for half-an-hour
a day. Why, sometimes I've believed as many as six
impossible things before breakfast."
**LEWIS CARROLL _, Through the Looking-Glass_**
HOW MUCH IS it possible to believe, without a belief being true?
This "memory" was donated anonymously to the False Memory Archive:
"I remember so clearly taking a medal that belonged to my father and burying it in the garden. I then looked for it for ages, digging up little pieces of earth but never found it. When I think of it now it must be a false memory. Why would my father have medals? Why would I bury them? But the memory feels like truth—shiny colours and crisp edges."
This may not be the most serious of misrememberings. Something like this may or may not have happened—most likely not, yet it feels as real as any memory. But as innocent as this false memory may be, it illustrates how vulnerable our personal memories are and makes us question whether we can trust our own past. Artist A.R. Hopwood became interested in Elizabeth Loftus's research at the University of California, Irvine. Loftus is the world's leading expert on false memories. Hopwood decided to make an art project, the False Memory Archive, surrounding people's common distortions of the truth. People who falsely believe they have experienced an airplane's emergency landing or a car crash appear side by side with someone who is absolutely sure he remembers Live Aid in 1985, even though he was born after it happened. In the course of Hopwood's tour, his audience contributed to the combination of art and documentation by adding their own false memories, making the collection grow.
One would think that since people believe their memories are true, they would not recognize that they remember things that never happened. Nevertheless, the project has accumulated a significant number of false memories. Many of the memories date back to early childhood. Memories of having flown around the nursery are easy to explain as the result of a certain lack of understanding of reality in small children. The reality of such a memory is, of course, soon discarded when we are old enough to realize how things really must have happened. But false memories can also occur in people with a fully developed memory and a sound worldview. Psychology professor Svein Magnussen, who has devoted much of his career to false memories, was himself the victim of a false memory. For a long time, he thought he had committed a crime in his youth.
"We had traveled from Oslo to Copenhagen in the little car we had purchased for high school graduation. The car broke down. I remember clearly that we pushed it off the pier, and it ended up in the water. I even remember a wooden pier—although, when I think about it, I am sure that there are no such piers in Copenhagen," Magnussen, now professor emeritus at the University of Oslo, tells us.
For thirty years, he believed the story of the car was a somewhat off-color episode from his life; it is, after all, illegal to get rid of cars that way. Then he met his high school buddy again at a party. His friend was the one who had bought the car in the first place, and, it turns out, eventually sold it to a junkyard in Copenhagen. It had never been pushed into the sea!
"Somewhere along the way I had made up a clear memory of us pushing it off the pier. We may have discussed it; it may have come up as a possibility. And then I created an image of the situation, which wound up in my mind as a true memory," Magnussen says.
His story demonstrates an unpleasant fact: not everything we think we experienced is real. Not even remotely.
We create false memories in many ways. We may "steal" other people's memories. For example, we know that war veterans in group therapy gradually adopt each other's stories. For some, becoming engrossed in another person's exciting story over dinner can lead to that story finding a place in their own memory. Childhood memories can be even murkier—it is often unclear if a personal experience is something that really happened or just a good story that a peer group has told over and over—or perhaps something you have seen in a photo. False memories can be formed when we see something on TV, take part in group therapy, or talk to our siblings about something that happened in childhood. So can we trust our memories?
"Why some people are inclined to create false memories, and others not—what characterizes a person who creates false memories—we don't know. You would think that people who remember their lives clearly, in vivid detail, would be incapable of making up false memories, but that is not the case. Even they may carry around false memories," says Magnussen.
The unbelievable stories in the False Memory Archive ruin most of memory's credibility. Our memory is reconstructive and elastic. It is not a PDF we open and reread on a computer, or a camera filled with high-definition images. Memory is more like live theater, where there are constantly new productions of the same pieces. In some performances, the heroine wears a red dress, in another a blue one. Now and then, actors are replaced and the plot revised—even quite substantially. Sometimes the play is about something we have actually experienced, other times about something we have just imagined. In the memory theater, there are many strange reenactments.
Each and every one of our memories is a mix of fact and fiction. In most memories, the central story is based on true events, but it's still reconstructed every time we recall it. In these reconstructions, we fill in the gaps with probable facts. We subconsciously pick up details from a sort of memory prop room. This is the brain's way of being space efficient—we don't need to store everything we experience as exact film rolls. We can store items as persons, things, sensory experiences, actions—each stored on its own but tied together in a memory network maintained by the hippocampus. This frees up space in our brains and liberates our thoughts. We are not slaves to our memories, even though we actively use them all the time. But this elasticity comes at a cost: things can easily become confused. Like when a witness believed he had seen two people rent a truck the same day in 1995 that Timothy McVeigh bombed Oklahoma City, killing 168 people. This kicked off a manhunt for another accomplice—on top of McVeigh's known accomplice at the time, Terry Nichols—who did not exist. The witness, who worked at the body shop where the truck was rented, had definitely seen two men. However, he saw them the day after the terrorist had been there, and one of the two men unfortunately looked a little like McVeigh. The witness had confused the two events. He exchanged McVeigh's face for that of one of the innocent customers he saw the day after. This witness has a memory no worse than most people's. For any clerk, what customers come in at what time is not worth remembering—normally.
Mix-ups like this aren't noticeable in our everyday memories. Yet if we were to examine each of our memories down to the smallest detail and compare them to, for example, film footage, most would fall short. Visualize your office or classroom or convenience store. You probably won't remember every single detail—what books are on the bookshelf, how the cord of the cell phone charger coils across the desk, where the coffee mug sits, or how the light from the window reflects on the wall. Still, the memory can feel trustworthy enough. You have enough memories of the coffee mug and the cell phone charger to be able to pick them up in the prop room and put them in place. If you have spoken in front of a group of people, you won't remember every single face in the room. Still, if you try to conjure them from memory, the room will be just as full as the first time you were there. But though the atmosphere may be the same, the individual people are picked from a pool of extras in your memory.
In fact, according to a study conducted by Loftus and her colleagues, people with very good autobiographical memories remember more incorrect details from a picture presentation than people with average memories. It seems as if those with good memories use their memory theater to the fullest. They have a large memory repertory, but with that comes a tendency to reconstruct a little too much.
But there are more factors at play when it comes to constructing false memories. The more time passes, the more probable it is that fantasies—like the car that was pushed off the pier thirty years ago—can sneak into our memories. The time aspect is significant; we seldom recall incorrectly what happened yesterday, but what happened last year is more unclear. Even though the most entertaining examples involve dramatic events, mundane happenings have an easier time becoming false memories compared to remarkable fantasies.
Solomon Shereshevsky, the man who couldn't forget, claimed to remember what it was like being a baby. He described in detail how the light fell across the cradle, his mother—or nanny—far above him. But since he had such a vivid imagination, this is probably a false memory. It is difficult to believe that Solomon would be exempt from the rule that everything we experience early in childhood disappears into the abyss called childhood amnesia.
Solomon's imagination often played tricks on him. He had a terrible experience as a child when he and his family were moving to a new home. When they departed in the moving truck, he imagined that he was left behind, a vision so vivid that it felt real. What researchers have found, using modern MRI scanners, is that when we imagine something, the activity in our brains is similar to what it would be when we experience the same thing in real life. Imaginings, memories, and false memories actually behave quite similarly in our brains. It is only how our brain sorts things under the labels of "true" or "not true" that determines what's what. A real memory _is_ a form of imagining—an imagined reconstruction. False memories make use of memory's natural laws, however irrational they seem. A false memory moves, in some way, from imagination to memory and is suddenly seen as something real. It steals a label that says "true," and just like a common cuckoo—a bird that lays eggs in other birds' nests—it hatches in the reed warbler nest, pushes the baby warbler out, and begins to grow into a big, fat cuckoo bird.
Since our imperfect memories can make us believe in something that never happened, can memory be manipulated from outside? Is it possible to deliberately create false memories in others?
Actually, researchers have managed to plant false memories in the brains of mice. Do you remember what we said earlier, about place cells in the hippocampus that help us remember certain locations? Researchers placed an electrode in the hippocampus of a mouse, where the place cells are, so they could register the nerve signal when the mouse arrived at a certain spot in its cage. Then they waited for the mouse to fall asleep. When both mice and humans sleep, place cells are activated—it's as if sleepers return to the places they've been to that day, to keep them in memory for later. And so this particular place cell in this particular mouse reactivated on its own while the mouse slept, because that's what place cells do. This is where the researchers could do some manipulating. They also planted an electrode in the reward center of the mouse's brain. When the researchers applied a tiny touch of electricity in this area, the mouse was bathed in a feeling of wellness, similar to what it would have felt if it ate sugar, had sex, or did something else that felt good. The reward center sends out neurotransmitters that, in addition to making a mouse or person feel good, also help strengthen new connections between neurons, creating a memory trace. The researchers stimulated the mouse's reward center at exactly the same time as this particular place cell was active. This strengthened the connection between the exact location this place cell represented, which the mouse had stored in memory from before, and the feeling of wellness it experienced. Links like this are usually made while the mouse is awake by giving it sugar or some other treat just when it is at the chosen place. In this experiment, however, the link was created artificially, without the mouse ever feeling good at the specified place in reality. But after having been supplied a memory of wellness at that place in its sleep, the mouse returned more often to that place in the cage. It had been given a false memory.
In a less pleasant experiment, mice were implanted with false memories of receiving electrical shocks at certain locations in their cage using optogenetics. Optogenetics uses light to control cells by implanting a gene that codes an on-and-off switch steered by a laser. Such light-driven switches exist naturally in some organisms (e.g., one-celled algae), but with the help of gene technology, they can be inserted into a cell in a mouse's brain and can be used to turn the neuron on and off, so that it fires in exactly the way you decide. When the laser is turned on, the neuron is also turned on and fires a nerve signal. Using this technology, researchers first isolated the small neuronal network that was activated within the hippocampus of mice as they explored their cage. Then they implanted the light-controlled switch. Next they put the mice in a different cage, and delivered a small electric shock to their feet while simultaneously activating the memory of the first cage. In this way, the mice learned that the memory of the first cage, where there had been no electric shocks, was related to feeling pain in their feet. Back in the original cage, they acted as if they were expecting to get shocked. The researchers could trigger the mouse's fear response and get it to stiffen up in anticipation of an electrical shock, even if they had never been shocked in that particular environment. A false memory of receiving pain had been created.
What is the benefit of manipulating memories like this? Isn't it rather heartless to play with the feelings of small rodents? In a dystopian nightmare scenario, we can imagine that evil super-villains use technology to tamper with people's minds, whether they are enemies of the state or living in a dictatorship. However, this research is not being conducted to gain world domination over rats and mice, but to demonstrate the basic mechanisms behind memory in the brain, on a cellular level. Perhaps in the future we will be able to physically do something to weaken extremely painful memories, or to improve memory in people with memory loss.
Fortunately, nobody has tried to tamper with the human brain to change our memories the way they have with mice and rats. To plant memories in humans, we must turn to psychology. It's been proven beyond doubt that we can manipulate people's memories by pushing the reconstructive nature of memory to its limit.
Elizabeth Loftus and her colleagues have conducted many creative experiments in which they convince their guinea pigs, mostly students, that the most ridiculous things are true. Thanks to Loftus, who is now over seventy, false memory has become a major area of research in psychology. She, her researchers, and her successors have conducted numerous studies in the area. She stumbled into it in the 1970 s, after she heard of something resembling an experiment that was conducted on American TV, for entertainment. The network showed a staged crime, and viewers were to call in and vote on who had done it. The staging was very realistic: over the course of thirteen seconds, a man robs a woman, knocks her down, and runs away. As in real robberies, the lighting was bad, everything happened quickly, and there was a lot of movement and many distractions, like screaming and shouting. Crimes like this are complicated, compounded by the fact that witnesses are taken by surprise.
Two minutes later, viewers were presented with a traditional police lineup, containing the robber alongside five innocent volunteers, and were encouraged to call the network to identify the perpetrator. More than two thousand people called in to say who they thought was the guilty person, but the result was astoundingly discouraging. Roughly equal numbers chose each of the people in the lineup, with only 14 percent pointing to the right person. If we take into account that one of the possible answers was that none of the six in the lineup was guilty, the result was the same as if the "witnesses" had guessed blindly. How could so many remember so poorly, even though they had watched the incident with their own eyes? The TV show made psychologist Elizabeth Loftus curious about how false memories are created, inspiring a completely new area of research.
One of the experiments she conducted was intended to make test subjects believe they loved eating asparagus. Before and after the experiment, they monitored subjects' eating habits, and found that after they had planted a false memory about being particularly fond of asparagus as children, the subjects began to buy more asparagus, happily pay more for asparagus, and order it more often at restaurants. The opposite happened when researchers convinced the test subjects that they had once eaten a bad egg. Even those who at first denied that they had been food-poisoned by an egg were, after their meeting with the psychologists, more skeptical of all types of egg dishes and bought fewer eggs. Loftus also tested how different ways of phrasing questions can influence memory. One group of test subjects watched a film where two cars collided. Afterward, they estimated how fast the cars had been driven. Those who were asked "How fast were the cars being driven when they crashed?" thought that the cars were going a lot faster than those who were asked "How fast were the cars being driven when they hit each other?" The wording of the question also influenced how they saw the collision in their memory. Those who were asked about "the crash" saw shards of glass, which weren't there at all.
Loftus also made people believe that as children, they had once been lost at a shopping mall. Her techniques were so convincing that they changed central childhood memories. "I came up with the idea for that experiment while I was driving some friends to the airport, and we drove past a mall. That's how it often works—I get an idea for an experiment just like that," she tells us.
Today, Loftus is ranked as one of the hundred most influential psychologists of the twentieth century, on the same list as Freud, Pavlov, Skinner, and Alexander Luria, who researched Solomon Shereshevsky.
Stories can be very convincing. Memories and stories are strongly connected, as they are in the life story we author throughout life. Perhaps it's the appeal of telling a coherent story that makes witnesses believe in their own guesses after observing a crime? In the experiment shown on TV in 1974, 14 percent recognized the real robber in the confrontation. Hypothetically, this could be due to their exceptional attention and memory, but it could just as well be the result of guessing. When you witness a crime and what you remember can determine if a person is arrested and tried, it may—subconsciously—be tempting to complete the story by offering an answer. When you have given an answer, your assessment continues as a memory, which is almost impossible to separate from the original, volatile memory of the robber. His face was, after all, visible on the TV screen for only three and a half seconds.
In 1844, master storyteller Edgar Allan Poe managed to trick Americans into believing that the first transatlantic crossing in a hot-air balloon had taken place. In bold type in a special edition of the _New York Sun_ , he painted an impressive picture of the alleged accomplishment. "ASTOUNDING NEWS! BY EXPRESS VIA NORFOLK: THE ATLANTIC CROSSED IN THREE DAYS! SIGNAL TRIUMPH OF MR. MONCK MASON'S FLYING MACHINE!!! Arrival at Sullivan's Island, near Charlestown, S.C., of Mr. Mason, Mr. Robert Holland, Mr. Henson, Mr. Harrison Ainsworth, and four others, in the STEERING BALLOON 'VICTORIA,' AFTER A PASSAGE OF SEVENTY-FIVE HOURS FROM LAND TO LAND. FULL PARTICULARS OF THE VOYAGE!!!"
Poe included details that could have been true. He used—or perhaps misused—names of people the general public already knew and drew a convincing map of the craft and the route. For Poe, playing with fact and fiction was joyful—because what's really true, anyway, when you look at the big picture? His way of mixing the two is not unlike the way our memory handles recollections and truth. If memory were a writer, she'd have a lot in common with Poe. But it is one thing to trick all of the American eastern seaboard into believing that _someone else_ had crossed the ocean in a hot-air balloon. It is something else to trick people into believing that they themselves had been in the basket.
That's exactly what one of Elizabeth Loftus's former students, Maryanne Garry, wanted her test subjects to believe. Garry and her team showed volunteers several photos from their childhood and asked them to talk about them. One of the photos, however, was photoshopped so that the subjects could see themselves, as children, soaring through the air in a hot-air balloon. Fifty percent of the participants claimed they could remember the hot-air balloon and proceeded to describe their flight in detail, even though they had never been on such a ride. They had made themselves a genuine false memory on the spot.
How do researchers convince their test subjects that something that isn't true has really happened? They prepare themselves well and tend to collude with "the victim's"—that is, the test subject's—family and friends to learn as much as possible about the person they are going to lie to. Presenting a story that includes significant, true details increases the likelihood of its being believed. This was Edgar Allan Poe's technique for deceiving newspaper readers. But simply presenting a false story is not enough. A combination of authority, veracity, and interview techniques is also needed. The researcher conducting the interview is a credible person, perhaps someone with an office filled with psychology books and certificates on the wall. A lab coat helps too. The interviewer should also give the impression that they know details about the event—of course, without divulging them all. It is, after all, the participant's memory that is about to be tested. The researcher offers up _some_ details, planting a seed and later watering it with follow-up prodding along the lines of "Try to remember; most people need some time before the memory appears," "It's totally normal that you don't remember very well when you haven't thought about it for so long," "Try to picture it," and—when new details make themselves known—"What happened next?" The whole thing is wrapped up in a blanket of kindness, security, and helpfulness from the interviewer. The interviewer is trained in good interview techniques: close to ten hours of training before conducting the interview is not unusual. How to best present images and other types of material to the test subject is drilled, down to the smallest detail. No details should stand out in an odd way or create suspicion.
Now that we're equipped with the recipe for false memories, the question occurs to us: _Who can we trick?_ People like us can plant false memories, can't we? A psychologist and an author can quickly become first-class manipulators, right? The only thing is, it feels very wrong! We can't just haul in the first person we see on the street, or one of our friends! It feels dishonest, and not only that, we would risk both the license to practice psychology and a friendship. All signs point to one person, the subject who most shares our interest in showing the consequences of the constructive, whimsical nature of memory, and the one who has everything to gain by taking part in a fantastical hot-air balloon trip: our book's Norwegian editor, Erik.
We can't wait to send him skyward.
But before we begin, we have to ask Elizabeth Loftus some questions. How did she manage to trick so many people in her research? Does she like practical jokes?
"No, not at all! This is only for science. The research on false memories has huge practical consequences; that is why we do this," she patiently points out over the telephone from Los Angeles, nine time zones away.
We simply have to try this ourselves; we want to see it with our own eyes. It will be our gift to Erik: a happy and completely false memory of soaring over Oslo in a brightly colored hot-air balloon when he was five years old.
We pounce on the task, filled with beginners' courage and spurred on by our knowledge of Loftus's successes. Asparagus! Crashes! Eggs! Erik's wife provides us with vital information about his childhood and a bunch of photos. Then it's time to photoshop. A professional designer patches a photo of a hot-air balloon from the 1970s together with one of Erik, five years old, and smooths it out until it looks like a regular photo. His little face pokes up over the edge of the balloon basket, which is still planted on the ground, about to take off. The dumbfounded look on his face suits the situation. Maybe he is a little nervous about flying in the big balloon? It looks completely convincing. Then we book a meeting with our editor "to discuss the book and conduct an experiment about childhood memories."
In his office, we present him with the pictures, the real childhood photos and the one false one. It is the second to last one in a pile of five. Photos from a birthday, boat trip, school, Erik as Superman—the last a good choice; someone who likes to fly will surely be excited about a hot-air balloon trip.
While we interview him about the three first pictures, which he tells us a lot about, our hearts start beating faster. We are about to lie to someone, for real! But what happens when we lay down the photoshopped image surprises us too.
Our editor looks startled and exclaims, "Is this a manipulated picture? I can't remember doing this! No, this is strange. Where did this photo come from? I don't think it looks like me. What is this?"
We have to calm him down, make him think that he simply forgot the incident, and plant little ideas about what might have happened when the picture was taken and why he doesn't remember it—at all! For people like us who aren't used to lying, the urge to break down and confess is overwhelming, especially when our editor picks up the picture and gazes at it in open disbelief. But we stick to our guns. Maryanne Garry, we remember, managed to extract false hot-air balloon memories from half of her unsuspecting participants. It's still possible to make this balloon rise.
"We approached several sources to get these. There are some photos you know from before and some you haven't seen for a while," says Ylva, the psychologist, calmly.
She runs the show now, because her authority as a specialist is one of the few advantages we've got. She tries to wrap Erik in a blanket of calming expert talk—smiling, not too pushy.
"Just take your time. It is completely normal that you don't remember it. We can't remember everything from our childhoods."
It's all about getting him to accept that the balloon ride may have happened, even if he can't remember it. Most of us have had experiences we can't remember afterward.
"Perhaps it was such a strange experience that you didn't have anywhere to place it in your memory?"
It feels fundamentally wrong to feed him one memory myth after the other. Of _course_ he would have remembered a hot-air balloon ride. _A special, outstanding incident is more likely to be preserved by the hippocampus._
Erik's face is still distorted by skepticism. He is desperately scrambling for the truth—is this a fake or a real photo? At the same time, we search his face for some tiny sign that he is slipping.
"Haven't you ever talked about this event at home?"
Erik shakes his head, but he seems calmer now. We have made it past his shock, luckily. He is prepared to negotiate.
"When you were a boy, you were fascinated with the idea of flying. We were talking about the picture of you in the Superman outfit a moment ago. Maybe it helps if you imagine yourself flying? Maybe that will trigger some memories?"
"I think I can picture myself standing in a basket like that, that might have been attached to a hot-air balloon; that I can feel." Erik tries to help. He is, even in this unsettling scenario, a pleasant and courteous man.
"If you can imagine it, it must mean that you've had the experience; all imaginations come from somewhere. Just try to think about going for a ride in a hot-air balloon, and it will come back to you," Ylva the specialist assures him—completely the opposite of what we know about memory.
Because, no, imagining something definitely does not mean that it's true. If so, novelists everywhere would be living their daily lives with some pretty remarkable truths. Imagining something just means that it can, with some distortion, _seem_ true. At that point, we're halfway toward a false memory. Erik is an author himself and has a vivid imagination—but does he want to come with us up in the air? In our minds, he is already far beyond the treetops, over the fields. He can look out across the Oslo Fjord and see his sisters below, patiently waiting for their turn. His father is with him in the basket, his arm around the boy's tense little body, which, in a mix of adrenaline and joy, finally gets to fly.
We tell Erik to keep our conversation a secret, another trick we have learned from the researchers. Isolate the test subject, let him brood further on the fantasy of what might have happened, and perhaps, just perhaps, the cuckoo egg will hatch and let the bedraggled baby monster emerge so it can grow into a big and strong hot-air balloon ride in his imagination. Without aunts or uncles or old friends offering the correction "No, you've never been in a hot-air balloon," the fantasy, the dream of soaring, might lift the memory off the ground.
We leave the meeting with mixed feelings. As soon as we're out of earshot, we let loose with laughter. "Do you think he bought it? Good Lord, I hardly managed to keep a straight face!"
There was no hot-air balloon ride during this first meeting, but we haven't given up. This was only the beginning. We didn't expect it all to happen at once. This process takes time, up to three cautiously conducted interviews, combined with the subject's brooding alone over the idea and how likely it was to have happened. The false memory will slowly sink into the network of memories and get caught in the fishnet.
When we arrive the second time to talk to Erik about the false memory, we bring some questionnaires, to make it seem more scientific, and plan to hypnotize him, which should relax him and make him more willing to get into that balloon basket.
But when we take out the file with the pictures, he suddenly says: "I've thought about this since the last time we saw each other. You're trying to trick me, aren't you? This is a fake photo, isn't it?"
For a nanosecond, we get a stabbing feeling in our stomachs and reevaluate whether we could keep pressing, just a _little_ bit further. But no, all we can do is put our cards on the table. Perhaps it was due to the fact that our meeting happened on April Fool's Day, perhaps it was just the guilty looks on our faces, but this balloon would never fly. Maybe we stretched the tethers too much during our first meeting, maybe the ropes began to tear as a small, fragile flame breathed the first puffs of air into the red and yellow fabric.
Now, as we sit in our editor's office, our balloon has deflated and lies, flat and airless, across the floor. All of us are laughing at our unsuccessful attempt at memory manipulation, which, in hindsight, we realize was bound to fail. Creating a false memory is hard work, and our efforts were not thorough enough.
The problem with using our editor as a subject is that we, his authors, don't hold the authority in our relationship with him, even though we tried pulling the psychologist card. At best, we're equals. And Erik should also, as a good editor—which he is—know what's in our book and remember that we are writing a chapter on false memory. Even worse is that he, in his position of power, is supposed to be critical of most of what we show him—even pictures. In other words, we'd made our job particularly difficult for ourselves. And it's not just that it's harder to trick an editor than a student, for whom a professor is an authority. It has also been sixteen years since the original balloon experiment was conducted, and in that time people have learned about photoshopping. Today, everybody is aware that photos can be convincingly manipulated.
We aren't alone in our failure to plant a false memory. The researchers Chris Brewin and Bernice Andrews are skeptical that it's as easy as Elizabeth Loftus claims. They carefully examined a large number of experiments on false memory that were conducted all around the world. They found that many of the experiments may not have been measuring false memories at all. Some asked participants to answer how _likely_ it was that a memory was genuine on a scale from one to five. The people who experienced a memory manipulation rated the memory more likely to have happened than those who didn't have their memories manipulated. But this is not the same as saying that the participants had actually constructed a new memory. A _genuine_ false memory—if we can call it that—requires careful preparation. In more complex experiments where memories are manipulated through multiple interview sessions, false memories seem to appear, while simpler experiments, where the subject's only task is to imagine how things _could have been_ , don't show any conclusive effects. Based on this, Brewin and Andrews believe that we have to rethink what false memories really are, and how often they really happen. Yet others consider Brewin and Andrews's work controversial and believe it's an attempt to downplay the very real effects false memories can have on people's lives. It's a thorny subject.
It's fascinating that it is so difficult to trick someone into a false memory when people have created their own memories of unbelievable things with zero outside influence. Just look at the False Memory Archive and Svein Magnussen's tall tale about the car. When they sprout up in the wild, without excessive pruning or outside intervention, false memories grow better—likely because they entwine themselves into our life story. In natural surroundings, they are more convincing.
Maybe we should have tried to trick our children instead. They believe everything we say—or do they?
"There is no difference between adults and children when it comes to false memories. There have been examples of children who absolutely refuse to agree to things that aren't true in police hearings, which demands great mental strength. So children won't allow themselves to be led to false memories any more easily. The percentage of children who experience false memories, compared to adults, is not larger," Svein Magnussen tells us.
Why, then, has it been so important for researchers to make people believe in false memories? Why is it so important for Loftus to trick people into liking asparagus?
The point is not the asparagus or the eggs. Loftus's research has saved lives and changed the whole justice system's relationship to eyewitness testimony. When she began her colorful experiments in the 1970s, everybody was convinced that what independent witnesses said they saw was the truth—well, it had to be the truth! Why shouldn't it be? And when people confessed to a crime, after weeks of interrogation, it was because they were guilty, weren't they? Back then, the criminal justice system relied on the idea that memory functioned as a precise documentary: expose the film, and you'll have a murderer. But as we've said already, memory is not like that; it is reconstructive.
"Our memories are not made for the criminal justice system," Anders Fjell of the University of Oslo says. "They aren't set up to help us to remember details like the color of a bank robber's clothes. When we are scared for our lives, there are other things on our minds. Memory is an important tool that helps us avoid danger, and in that way, it functions well."
Loftus has examined what happens when test subjects tell a detailed story about something they have observed and are then presented with a written report of the same event in which some details have been changed, such as a jacket's being brown, not green. Many don't react to the planted mistake and begin to believe it to be true. This means that central evidence in a criminal case can change when, for example, a detective listening to a witness's observations makes a sloppy transcription for the witness to approve. Without the witness's noticing it, a typographical error can become a false memory, which in turn can lead to the wrong person being convicted.
"The problem is that false memories are really similar to 'true' memories; even the emotional strength is the same. Most of the time, it doesn't matter whether I had a pizza or a burger last night, but in a criminal court case, such details may be detrimental. We will always have to rely on eyewitness testimony in criminal court cases; we will never be able to rule out the importance of someone's memory to solve cases. All we can do is improve our knowledge of how memory works, in order to minimize the risks," Loftus says.
When the Innocence Project (a nonprofit dedicated to exonerating wrongfully convicted people) examined three hundred cases where DNA evidence has later acquitted the convicted person, it turned out that in three-fourths of the cases, a witness had pointed out the wrong person and gotten that person convicted. In each case, the witness had been absolutely sure that he or she saw the innocent person run away from the scene of the crime or lean over the victim with a gun—or similar observations with great judicial consequences. These well-meaning witnesses had nothing to gain by pointing to the wrong offender. It's just that memories are fallible.
Svein Magnussen has been an assisting expert witness in several criminal cases and has prepared a curriculum for Norwegian judges and lawyers. He has written the standard work on eyewitness psychology in Norway. He knows of at least two murder cases in Norway where there were no corpses or even missing persons, likely caused by someone's false memories of having witnessed a murder, and claims of group sexual assault as part of satanic cult rituals, which have later been proven impossible.
How is it possible to erase the difference between imagination and memory? How can false become true?
"We just don't know," Magnussen says. "I believe that most of us carry around false memories. We think we remember things we have not experienced. But they are often insignificant things. We don't notice them because they're not that important. Even Freud described false memories, but of course they had no significance on the therapist's couch. In the courtroom, though, they have great consequences."
Since publishing his book about eyewitness psychology and false memories, Magnussen has had several inquiries from people in therapy who have been helped to "remember" abuse.
"False memories can result in real traumas. In these people, the false memories are ruining their entire personal history and their relationship to people around them."
Memories of serious traumas seldom appear out of the blue after having been forgotten for many years, despite what you've heard about repressed memories. Most people exposed to serious abuse don't walk around blissfully ignorant until they suddenly remember the horror. A study of 175 men and women who had demonstrably been exposed to abuse as children showed that those who had been abused always knew what had happened. They didn't suddenly recall it in therapy. When asked if they had ever not remembered what they had gone through, they said no.
"To suddenly discover something like that as an adult is close to impossible," Magnussen says.
On the other hand, it may happen under the influence of a therapist who assumes authority and leads their client through the door between the world of imagination and the world of memories.
This doesn't mean that if someone you know all of a sudden tells a story of abuse from their childhood, you can dismiss it as "false memories." Repression can take other forms. It may be that they didn't want to admit to themselves or others what happened but always knew deep inside. Or they have rewritten their life script so dramatically that the abuse wound up in a chapter that they don't reread very often, in order to maintain a necessary relationship with the abuser, whom they may depend on.
Adrian Pracon has a striking false memory from his traumatic experience on Utøya. The last thing he saw before he was shot was a girl being shot and dying by his side. For a long time, he thought that it was one of his best friends he saw dying. It wasn't until he was writing his book that his version of events was overturned. A girl did die by his side, but not the one he thought. His friend was shot on another part of the island.
"I was completely certain it was her, but the girl who actually was killed beside me didn't even look like her. Not even the color of her hair. The only thing they had in common was gender. When I realized my mistake, I had to reexamine all my memories from that day, from every single minute of it. What if I couldn't trust anything I had seen?" Adrian says today.
During the course of the trial, it turned out that most of Adrian's memories actually could be trusted, when compared to the other evidence. It was only this one crucial thing he remembered incorrectly.
How could he have mistaken something so important?
"He must have thought of her for a millisecond, and suddenly she was the one being shot. Perhaps he was afraid that it was his friend who was killed. That's all it takes. The thought becomes real and transforms into a memory as strong as a genuine memory," trauma researcher Ines Blix tells us.
It's one thing for the victim of a crime to remember what happened incorrectly. It's something else entirely for a perpetrator. Is it really possible to believe and admit that we've done something we haven't done?
"Nothing surprises me anymore," Loftus says now, after years of conducting experiments on false memories and monitoring the whole field of research.
"In one of our latest studies, we tried to make people admit to crimes they didn't commit, after depriving them of sleep. It turns out that people's memories are more malleable when they lack sleep," she says.
Even without sleep deprivation, it's incredible what people are willing to admit to. Canadian researchers Julia Shaw and Stephen Porter demonstrated this in a sensational experiment in which they managed to convince 70 percent of their volunteers that they had, when young, committed crimes like burglary and armed assault, without any basis in reality. How is this possible? You wouldn't agree on the spot to having done something that serious in your youth, would you? The participants in the study were convinced. They described the incidents in detail, and what they told was just as evocative as a real memory. The result surprised the researchers too. They had originally planned to conduct the experiment with seventy participants but stopped after sixty, since they already had enough false memories for their results to be statistically significant.
How did this happen? As in similar studies, Shaw and Porter started with a selection of both genuine and false stories from the participants' youth. They worked together with the participants' parents, who gave detailed descriptions of real events and their children's adolescence: where they lived at the time of the alleged criminal act and the names of their best friends. They snuck this information into the first description of the false event to give the story a certain hint of truth as well something for the participants to latch on to.
What Loftus and the other researchers have proven is crucial to the application of law in our society. Both what we remember as witnesses and what we admit to as suspects is no longer seen as inherently true and credible. Without Loftus, more innocent people would have been convicted. Judicial systems have changed fundamentally in this respect, and more and more often psychologists are brought into the courtroom to explain to the jury what a false memory is. The American Supreme Court has recognized what false memories are and knows that the general population from which jury members are chosen still doesn't know how contorted and accidentally changed memories can be.
"When I started working with false memory in the seventies, it was because I wanted to work with something that has practical consequences for people. It has of course been personally rewarding to contribute to a safer legal system in the US," Elizabeth Loftus says.
In the United States, a confession-focused interrogation culture prevails. Police officers have sometimes used rough and unpleasant methods to solicit confessions from people who couldn't possibly have done what they were accused of. For example, a woman was raped in Central Park, New York, in April 1989 and a total of five young men confessed to taking part, even describing in detail what had happened. DNA evidence later revealed, however, that none of them could have been the guilty one.
The Norwegian Centre for Human Rights is located a stone's throw from the new National Museum, overlooking the Oslo Fjord. At the Centre, there are no memory researchers. Nobody here spends days repeating meaningless words in order to count how many were remembered, in or out of the water. Those who work here are lawyers and political scientists—and one police officer. The latter now greets us in a small seminar room on the second floor. How did a homicide detective end up here?
Everything started with the Birgitte Tengs case. Detective Asbjørn Rachlew has delivered hundreds of lectures about his work, and every time he has had to talk about Birgitte Tengs's murder and the ensuing miscarriage of justice involving her cousin. It is one of Norway's most cited criminal cases, but it is also part of Rachlew's personal memories, his life script. That case changed the direction of his entire life story.
On a late May evening in 1995, the life of a cheerful seventeen-year-old girl from a small city in southwestern Norway, till then known for its beautiful heather moors and sandy beaches, was brutally cut short. A few years later, the interrogation methods used during the investigation of her homicide made history. Tengs was the image of Norwegian innocence. A photo of her dressed in folk costume with blond, wavy hair cascading over her shoulders was shown in newscasts. The police were faced with a murder by an unknown offender in a small, safe island community. When Tengs's cousin ended up in the police spotlight, they recklessly pushed for a quick resolution. There was just one problem: the cousin denied committing the murder. The interrogators were determined to break him.
In gangster films and crime TV shows, we have all witnessed the good cop/bad cop routine. The methods used when Asbjørn Rachlew started out as a detective were very similar. A tough tone, the "we know you did it; it's just a matter of time until we have the evidence" tirade. They conducted long interviews without breaks, and the accused was seated on a lower chair than the detective, so he had to look up at him. The chair was old and rickety, set up to make him realize that this was a place where people remained sitting for a long time, so there was no use fighting it. The suspect had contact with only one detective, to create a kind of dependency, and the detective had the sole power to stop the interrogation, or get water, food, coffee, tissues. The detective was supposed to, little by little, become a person to confide in. He could also tactically use body contact to create trust—put his hand on the suspect's shoulder, his arm.
"We learned the interrogation techniques from other, more experienced detectives. These were not standardized methods; each detective had their own signature moves. We copied American interrogation methods and were inspired by whatever could give us some guidance regarding the questioning—films and TV series," Rachlew tells us.
What happened when the police located a suspect—Tengs's own cousin? The detectives isolated him. Two of them took turns having sole contact with him, and they forced him through long interrogation sessions. They told him that he most likely had repressed the memory of the murder because it was just too horrible to think about. They had methods to help him bring back the memories. He was supposed to imagine how it hypothetically could have happened, had he been the murderer.
Does it sound familiar, like the hot-air balloon experiment we conducted on our editor? It is not a coincidence. The methods used by memory researchers trying to create false memories in test subjects come directly from the police interrogation room.
His isolation and desperate situation wore on Tengs's cousin. He was promised rewards if he cooperated. He eventually began to look at his time with the detectives as welcome social contact. He was caught in a bubble, and the detectives made it shrink. After a while, his reality was just the one he shared with them, in the interrogation room. He cooperated. He implemented the thought experiments, imagined the gruesome acts. He began to doubt his own understanding of reality. Could he really have repressed it? What he thought he remembered of that evening, the trip home from the city, was it just constructed afterward to cover up this unthinkable evil? The tasks the detectives gave him became more and more concrete. He had to write stories about the murder. He penned several versions, imagining the evening it happened and possible scenarios for how it went down. He had grown up in the same town as Tengs. He knew the area well and could clearly see the heath, the heather, the path where her body was found. He felt the adrenaline in the tense situation—we can all imagine the feeling. When he wrote a well-executed story, he was rewarded with goodies and social contact with the detectives. The tissue box was pushed across the table toward him, the chair was moved closer to his, a hand was gently placed on his shoulder; someone understood. His written story gradually became more and more similar to the story the police had managed to reconstruct from other evidence. Tengs's cousin was convinced of and confessed to the crime—but DNA found at the crime scene belonged to others.
There are three different types of false confessions. There are the voluntary ones, when people confess to something they haven't done because they want the attention or because they think they deserve blame in a broader sense (perhaps they're guilty in the eyes of God—who knows). Then there are the forced false confessions. People may make these after torture or long periods of being pressured. Many suspects think it's easier to confess to escape immediate stress or pain, hoping that the judicial system will clear them later on. They are often wrong. Their earlier confession will accompany them and appear as proof of guilt. The third type is when they themselves believe they've done it and freely make their own confession, based on a false memory. Which type of false confession the cousin made, no one is completely sure. It is possible that, right then and there in the bubble, he briefly owned the evil story about himself as a rapist and murderer. Even without an episodic memory of the event, it's possible that he believed he did it. In any case, his confession was immediately rewarded—of course, not in the form of release, but in the form of resumed contact with the outside world. It didn't take long for him to withdraw his confession and assert his innocence.
Tengs's cousin was convicted in criminal court and later acquitted in the court of appeal. But in a civil suit initiated by Birgitte Tengs's family, he was sentenced to restitution. In civil cases, guilt is determined based on a balance of probabilities, whereas in criminal cases, guilt has to be proven beyond a reasonable doubt. The cousin sued the Norwegian government in the European Court of Human Rights for wrongful prosecution and won. And Tengs's true murderer is still on the loose.
In the aftermath of the case, the Norwegian police were raked over the coals by the Icelandic eyewitness psychology expert Gisli Gudjonsson, who dissected the interrogation methods that had been used and showed how the cousin could have been manipulated into producing false memories. He also referenced research literature on eyewitness psychology, including the work of Elizabeth Loftus.
As the ripples from the Birgitte Tengs case spread far beyond the small island community where she was found murdered, Rachlew was working as a homicide detective with the Oslo police. When it was revealed that the cousin's confession had been solicited under pressure, the media also started to investigate. What methods had the police actually used? What had gone wrong?
"Of course, we shrugged collectively when the media interviewed Gisli Gudjonsson and British interrogation experts. They spoke of totally different methods than those we were used to. But it made me curious. Suddenly I understood that there was a whole discipline I didn't know about. Why hadn't I heard of this before?" Rachlew says today.
His job at that time involved conducting interrogations of murderers and gang criminals with the intent to manipulate them into a confession. When approaching the point of a possible confession, the detective would showily put out a box of tissues to appeal to the suspect's feelings, and lean in with a sympathetic touch on the arm.
"Physical touch to push the suspect over the edge and finally help him ease his conscience was something we used more and more systematically," he tells us.
It was outright manipulation; he knows that too well today. He even developed his own signature maneuver, which, together with his charisma, made him a high-achieving detective early in his career.
"I am not proud of this. What I am most ashamed of is how I screamed at a suspect that I'd be back and he wouldn't know when."
Sitting by Rachlew's side this afternoon is his daughter. She is writing a letter with the deliberate lettering of a five-year-old. It's hard to imagine this calm man, who is patiently and quietly helping his daughter spell a difficult word, shouting at suspects in murder cases.
The pressure surrounding the Tengs case forced Rachlew to make a choice that would change the Norwegian police and judicial system forever. He took time off work to study British interrogation methods in the Investigative and Forensic Psychology program at the University of Liverpool. Today in the United Kingdom, the police use an interview technique called "investigative interview." Contrary to the confession-driven interview form of the old days, where the goal was to get a confession at whatever cost, the purpose of this interview form is to ease out as much information as possible from witnesses' and suspects' memory, whether or not they are thought to be guilty. You are supposed to secure important evidence from both suspects and witnesses.
"Our methods were totally unscrupulous!" Rachlew understood, shocked, in the course of his education in England.
In the work for his PhD, he investigated a case that had affected him deeply: a rape that had taken place on the outskirts of Oslo. The woman who was raped was also the only witness. How could they secure evidence?
The woman gave a description of the rapist: "Male, approximately forty-five years old, approximately six feet tall, a slightly stocky built, a bit of a paunch. Short, dark-brown hair, graying, thinning in front. Very bad teeth, possibly some missing. Medium-dark complexion, possibly southern European, perhaps Turkish. Spoke broken Norwegian and said that he had lived in Norway for ten years."
A facial composite was sketched and distributed to national media. Tips came in to the police. The drawing looked like a Bosnian-Norwegian family man who denied any involvement in the rape. The woman saw a picture of him in a photo lineup. He did look like the drawing; it must have been him. But she wasn't completely certain yet, so a live lineup of people was arranged. The suspect was presented along with six other men, all police officers or interpreters, all with similar features. All of them knew they were safe from prosecution except the Bosnian, who was so nervous he couldn't follow the instructions of keeping his arms by his side and standing to show his side profile. He clearly resembled his picture from the photo lineup. The photo looked like the composite sketch. The composite sketch looked like the woman's memory of the rapist. And the memory...? It's like a memory telephone game. The memory of the rapist gradually became the memory of the suspect. It doesn't mean the woman's memory was poor, or that the traumatic experience had weakened her judgment in any way. This is just the way memory works. It is a living organism, always absorbing images, and when new elements are added, they are sewn into the original memory as seamlessly as only our imagination can do. Furthermore, all of us have different abilities to remember faces. There is actually a special part of the brain set aside for just that; that's how important it is to us. Some of us need to see people several times before we are able to recognize them again the next time. It's likely that a rape victim will remember the face of a rapist clearly. But even if the memory of a traumatic incident is stored well in the brain, that memory isn't spared the art of reconstruction when we try to remember it again. We know that from Adrian Pracon's story.
The Bosnian family man was first convicted in district court. This happened despite the fact that there was DNA evidence, from someone who wasn't him, on a pair of men's briefs found at the scene. The witness testimony was given the most weight in the trial, and she was certain that he was the offender. But in appeal court, he was acquitted.
What made the case so heartbreaking was how it was finally solved. The DNA from the real rapist later appeared in the DNA registry as part of the evidence from a serious new case: he had killed his wife.
"A woman lost her life, and a child lost both parents when he became a murderer, and we could have prevented that," Asbjørn Rachlew says.
After Rachlew's return to Norway after his studies, the reforms he instituted were hard on all involved. For some of his colleagues, the transition to the new British methods was difficult. Many of them didn't speak to him for several years and avoided him in the corridors. But today he has resumed contact with many, and most now understand why the old rules had to go.
Rachlew's time in Liverpool spurred the beginning of a new era in Norwegian policing. Based on the British model, Rachlew created guidelines for a Norwegian adaptation of the investigative interview. Today this method is used by all Norwegian criminal detectives, and their training includes, among other things, basic instruction in how short-term and long-term memory work, and how false memories come about.
"The consequence of not knowing how memories work is that detectives don't treat testimonies from witnesses with the same strict discipline as they do with hard physical evidence," he explains.
Picture a murder scene on your typical TV crime series. The crime scene is teeming with technicians in white or blue overalls and face masks. They cautiously move around, picking up evidence with tweezers and putting it in marked bags to be sent for advanced analysis. Now Rachlew shows us a picture of a beautiful forest path, covered with a fresh, velvety carpet of new snow. In the forefront, the path is cordoned off with police tape.
"The evidence lies under the new snow. You can't just randomly stomp around. Every step you take leaves a track that changes the truth. It's the same with witness evidence," he says.
Most of our common-sense beliefs about witnesses, confessions, and detective work come from books and TV. And most of how memory is represented in the crime genre is flawed.
"Crime literature has definitely contributed to creating a false idea of how memory works. For example, the truth in witnesses' statements is seldom questioned," Jørn Lier Horst says. He was once a top Norwegian police investigator and is now a best-selling crime writer. His books have been translated into a number of languages, including English and Japanese.
In April of 2016, he was given a Polish award for realistic presentation of police work in his books.
Eyewitness psychology plays an important role in the plot of his crime novel _Ordeal_ , in which—without revealing too much—a false memory is gradually uncovered. Those familiar with the literature about eyewitness psychology can find clues throughout the book pointing toward a false memory. Even the investigative interview method has its place in Horst's books; he has taken a course taught by Rachlew.
"The interrogation methods used in crime films and books are totally wrong. Behaving boorishly in front of witnesses, interrupting them in the middle of a sentence or threatening them; this is not the way the police want to work to get at the truth. Often, in these stories, they make a big mistake which we would never make in real life. We never interview two witnesses at the same time. You can see that on television: a married couple is summoned for an interview, and the detective talks to them together. That would never happen. They're supposed to give one statement each, independently, of course," Horst says.
He thinks many crime witnesses are surprised by how little they remember when they compare it to what they've seen in crime stories.
"Witnesses are unreliable, and they often remember things incorrectly. As a new policeman, I once worked on a much-publicized murder case where four witnesses described seeing the suspect riding a moped. The problem was that the descriptions were all totally different. A couple of the witnesses even remembered the license plate on the moped. It turned out that the color-blind witness had the best description of the man who was later convicted," Horst says.
How would the eyewitness psychologist's _CSI_ look? Well, for example, they wouldn't make the mistakes the Stockholm police did when the Swedish foreign minister Anna Lindh was stabbed to death in a department store in 2003. The witnesses were immediately ushered into a back room, where they sat together, waiting for the police to question them. Five of those witnesses said the suspect had been wearing a military jacket. This description was sent out to the media and all airports and border crossings. When the police later watched the surveillance footage, it turned out there was no military jacket to be seen anywhere. What happened was that one of the witnesses had tampered with her own memory—of course not deliberately—and had "seen" a military jacket, probably because she associated it with violence. She had then talked about it with other witnesses in that back room, and her mistake had spread.
Now when witnesses are called in, the police work _with_ the fundamental laws of memory, instead of against them. They try to avoid helping mistakes sneak into a witness's testimony. First, they establish a good relationship with the witness. Memory works very poorly under pressure.
"Just think about how difficult it is to find your wallet when you're dashing around your apartment, stressed because you can't find it!" Rachlew points out.
Rachlew emphasizes that detectives' openness and integrity are prerequisites for a good relationship with witnesses and make them less anxious. When witnesses know how the interview will proceed, they relax more. They have to be able to trust the detective to be prepared to open up. Then they do the most important job by themselves: describe what happened. Most of the events should, if possible, be retold in the witness's own words, relating their own experiences, without outside involvement.
No leading questions, no manipulative use of tissue boxes. There are prescheduled pauses, there is a predictable framework. When the witness can't think of anything else, the detective can use memory-promoting techniques. The most important of them is based on what we know from, among other research, the experiment with the divers: being in the same environment as when you first experienced something awakens more memories. Witnesses are asked to picture themselves at the scene and in the situation. More details may then come forward.
"We check what the news and the weather was on the day in question. Perhaps something happened that can help the witness remember the day—such as a skier winning a gold medal or unusual weather."
The follow-up questions need to be phrased carefully so that no new information is eased into the memory of the witness. Everything is recorded on film, so that others are able to scrutinize it later. The method is standardized and totally transparent.
The reason that Asbjørn Rachlew, though he once behaved as a manipulative bully, sits here today in an office at the Norwegian Centre for Human Rights is that he chose not to defend his actions. Instead, he regarded the criticism that was directed at the police (and by extension, himself ) with curiosity. He may have perfected the methods he used, but they didn't stand up under scrutiny, so they had to be replaced by something more scientific. Loftus's research from the 1970s may not have reached the Norwegian police until the 1990s, but today Norway is on the forefront of human-rights-friendly investigation methods, mostly thanks to Asbjørn Rachlew and Svein Magnussen.
Reforming interrogation techniques helps us preserve human rights and prevents us from convicting innocent people. But it also ensures that murderers aren't acquitted because important witness information has been lost.
For several years, Rachlew and his good friend and colleague Ole Jakob Øglænd did a lecture tour where, alongside the innocent suspect Stein Inge Johannessen, they described what went wrong in a murder investigation and how their mistakes could have been prevented. The ex-junkie Johannessen, who was the main suspect, was heavily pressured in accordance with the old methods and kept in custody for nine months. A faulty eyewitness testimony was one of the reasons the police strongly maintained their suspicion. But a few days before the case was to appear in court, the actual murderer turned himself in. The lecture tour allowed the three to teach people how the investigation should have been conducted. Johannessen has since passed away, but Rachlew still lectures in schools, and to journalists and investigators, about human rights and interrogation methods, including the investigative interview. He was also an expert advisor during the questioning of Anders Behring Breivik.
Recently, Rachlew traveled to Geneva to give perhaps the most important lecture of his professional career. He spoke at the UN about his methods, how they were implemented, and why they are important. Everything he said was simultaneously interpreted so that those who didn't know English could follow his lecture in their own language through headphones. And so his message about memory functions, human rights, and witness psychology—and the truth—spread across the globe.
Although, the truth. How can we trust our memories to provide the truth? Memory is, as we have said many times now, reconstructive, and there are mistakes and flaws in all our recollections. The difference between a real memory and a false memory is not that the false memory contains mistakes, because all memories are fallible, but rather how wrong they are. Picture yourself putting on a Beatles record and hearing "Yesterday" sung by the Rolling Stones—or the Beatles singing "Satisfaction" instead. A false memory means that the wrong track has snuck onto your record.
"We can never know with hundred percent certainty that a memory is true or false, unless there is objective evidence to support it. We just have to live with this uncertainty, making sure that work is done to facilitate memory as much as possible, avoiding mistakes that we know may mislead memory. Court trials will always rely on eyewitness memory. The goal is to make sure that memory comes as close to the truth as possible," Elizabeth Loftus says.
— 5 —
**THE BIG TAXI EXPERIMENT AND A RATHER EXTRAORDINARY GAME OF CHESS**
**_Or: How good can your memory get?_**
"You appear to be astonished," he said, smiling
at my expression of surprise. "Now that I do know it
I shall do my best to forget it."
"To forget it!"
"You see," he explained, "I consider that a man's brain
originally is like a little empty attic, and you have to stock
it with such furniture as you choose."
**ARTHUR CONAN DOYLE _, A Study in Scarlet_**
AS YOU APPROACH London by air, you see the city sprawled out far below. The Thames shimmers like a ribbon thrown on the floor by an impatient child. Two thousand years of history shines back at you—from 50 CE until today, the city has grown without any coherent plan. It is a chaotic wilderness of streets and landmarks from every century, churches and steeples, prisons and palaces, hospitals and museums all scrambled together; five-hundred-year-old pubs with crooked floors and modern buildings with facades of glass and steel sit side by side. Originally, London consisted of several separate villages that gradually grew into each other, and so the city has no single center but rather many different ones. The streets take strange turns, suddenly stopping or transforming into alleys. It's no coincidence that so many action movies set in London feature car chases ending on foot, with the hero jumping fences and turning tight corners. The heart of Britain is a tight nest of streets with no structure, an untidy assortment of architectonic candy—a city planner's nightmare. How is it even possible to learn the streets of London by heart?
Eleanor Maguire, whom we met in earlier chapters, became famous for her research on London taxi drivers. She showed that there are visible differences between their brains and the brains of those who never acquired the Knowledge, the test all London black cab drivers must pass before they're allowed behind the wheel. The Knowledge requires them to learn the names and locations of 25,000 streets, 320 specific routes, and countless landmarks, all without the help of a map or GPS. The revelation that this visibly changes the brains of taxi drivers may have led the general public to view them in a different light. Who knew that, behind the wheel, they harbored such a stunning neuroscientific secret?
"To our surprise, we found an increase in the posterior part of the hippocampus in the taxi drivers," Maguire says.
London's convoluted maze of streets and alleys from throughout history works brilliantly as an environment for extreme training of spatial memory. While Maguire sat in her office, wondering whom she could research, thousands of the most highly trained memories in the city passed by her window in their shiny black cabs. Suddenly, the idea hit her. Had it not been for London's messy structure and the rigid test the cab drivers must endure, Maguire would not have become known as a leading memory researcher, not only among her peers worldwide, but also among an entire fleet of drivers.
How did cab drivers become the key to some of memory's most tightly guarded mysteries? British taxi drivers spend years training before they take the test and graduate. Many work full-time in other professions so they can live in London, spending all their free time learning routes. You can see them driving around the city marked with an L for Learner and bearing a map clipped to the handlebars of their mopeds, attentively studying each street they travel.
"There were four hundred routes when I took the Knowledge seventeen years ago," a taxi driver named Judy tells us with obvious pride in her voice, accompanied by a certain amount of contempt for those who get away so easily with the test today. She spent two years and ten months studying for the Knowledge, and passing it was a big struggle.
"I am one of few female drivers, so it was important for me to pass on those grounds alone," she says. She refused to give up, even though the instructors did everything possible to stress out the taxi novices during the tests. If you're going to make it as a taxi driver in one of the world's largest cities, you've got to be able to handle some stress.
As a cab driver, Judy has to know how to navigate all the roundabouts and traffic lights in the city, but she also has to be able to drop off customers with the correct address to their left-hand side, so they don't have to cross the street. At the same time, she keeps up with the names of pubs as they change owners, the new hot spots that constantly pop up, and traffic announcements about closed streets or traffic jams. If a London cab makes a detour, it may be because the driver knows that the obvious, quickest way is not so quick on that particular day.
We have now given Judy a difficult task, we think. We're in Bloomsbury and want to go to Short Street, a street only two blocks long located on the South Bank, two and a half miles away. A short, insignificant road is of course more difficult to remember than a major thoroughfare. At first she thinks we're asking for Shorter Street by the Tower of London. But then she gets it.
"Wait a minute. Yes, I know," she says and describes a theater, a pub, and a store located along the street leading up to Short Street. "I can clearly picture the street."
We nod and smile and think that she may be wrong as she drives us through the city toward the stubby little street. We're going in the right direction, at least.
"We're supposed to learn so-called points of interest, and that's how I navigate. If I want to know where to go, I visualize the street. I see it in front of me," she says. She searches her memory for relevant points of interest close to her destination, and when she finds them, it's like a map of the area unfolds in front of her.
And then we're there—after sailing past the little theater, the pub, and the store, just as she described.
"People think the internet is replacing memory, but that's what they said back when they invented books, once upon a time," Eleanor Maguire says. "We are always going to use our memory. Even if we have GPS, we'll need memory to find our way—for instance, inside large buildings, like a hospital. Anyway, taxi drivers make quicker and better decisions than GPS."
She bemoans her own poor spatial memory. She sometimes has to call for help just a few blocks away from conference centers—and a lack of experience isn't to blame, as she travels almost as much as a head of state might in a year.
Her research team has examined the taxi drivers' brains several times. What grabbed everyone's attention the first time was the first visible proof that our brains may change when we are studying. Maguire's research won her an Ig Nobel Prize "for presenting evidence that the brains of London taxi drivers are more highly developed than those of their fellow citizens." Maguire traveled to Harvard to receive the prize, a small trophy supposedly containing a nanoscopic gold nugget. She held it on her lap during the flight back, only to later drop it on her office floor. The gold nugget was probably devoured by the vacuum cleaner. But the London cab drivers are proud to have proof of their superior brains. Perhaps it has had a slight effect on their professional pride, which was, by all accounts, already quite noticeable.
Maguire's research, however, raised more questions than it actually answered. She showed that the cab drivers, with their intense spatial memory training, had a larger posterior (back part) of their hippocampus. But is this really proof of plasticity, evidence that the brain can actually change? Couldn't it be the case that those with large posterior hippocampi might be the ones cut out to become taxi drivers in the first place? To get a final answer, Maguire and her team conducted a much more involved study. This time, they followed taxi drivers from their first day of training until the day they passed the Knowledge. They measured their brains and memory before training started and after it concluded. This time, they were able to clearly show that the training was what caused the hippocampus to change. Before their training started, the aspiring taxi drivers had exactly the same sized hippocampi as most people. Their hippocampi were not visibly larger until after years of zealous effort on their mopeds. This should be proof enough that the brain is trainable. But there was something else: the change only happened in those who passed the test. Evidently, the amount of training someone does affects the result. It could be interpreted as more proof of the training effect. But the reasons for not passing the Knowledge are varied. Some people give up because they can't handle the years of low income and spending all their spare time on training. Some have family obligations that prevent them from training often enough. Another possibility, which is hard to measure, is that those who pass the Knowledge have brains with a greater potential for change than those who don't pass. What determines this—genes, special growth substances in the brain, diet, or something else—we still don't know.
"But what we do know now is that memory adapts to what we need it for, even when we grow older," Maguire says.
Maguire's words offer hope not only to those of us struggling to keep our brains nimble as we age, but also to those whose brains have taken a hit, whether from injury, epilepsy, or even the early stages of dementia.
There is one small problem in specifically training a single part of the brain. Inside the skull's boundaries, there isn't an unlimited possibility for growth, so memory training won't give anybody a gigantic brain. It actually seems as if memory training comes at a cost to other areas, at least in the case of the London drivers.
"The anterior part of the hippocampus—so the front part—was actually a little bit reduced along with the increase in the back," Maguire tells us. The training led to the drivers' performing worse in another area of visual memory. Maguire could measure a statistically significant difference compared to a control group using a simple memory test in which drivers had to redraw a complex figure from memory. "It's as if their brains had to prioritize spatial memory, and this compromised other aspects of memory to some degree," she says.
So how is it possible that the brain can actually change due to experience?
So far, what lies behind the training effects in the brain remains a mystery. When we lift weights, we know for certain that there are changes in the muscle cells because our muscles grow. With the brain, it's not that simple. When Maguire says that she can see a difference in the taxi drivers' brains, she can't, of course, see it from the outside, in the way you can see bulging muscles on someone who has taken up weight lifting. The changes she has seen in the taxi drivers are actually tiny when compared to the whole brain, and can only be detected by comparing groups of trained and untrained people. Nevertheless, there is an actual increase in gray matter. What does this increase consist of? Every single memory we create changes the connections between thousands of neurons, as Terje Lømo demonstrated using rabbit brains. Can these changes in and of themselves lead to a bulging hippocampus?
Long-term potentiation triggers physical changes in brain cells. Cells grow and change so they can deliver a stronger signal. The cell receiving the signal grows more receptors so that it can react more strongly when it receives a message. For a long time, we believed this was all that happened. Up until recently, everyone agreed that our brains were fully developed by our twenties. Our neurons were in place at birth, all of them. _All one hundred and some billion neurons!_ From birth until the day we die, they slowly disappear, one after another. Cerebral loss is all we have to look forward to, apparently. But, like the songbirds whose brains can grow in adulthood, adult human brains have been shown to develop new neurons too.
In some animals, scientists have discovered several places in the brain where stem cells "give birth" to new neurons. In the human brain, this has been shown to happen in only two places: the hippocampus and the olfactory bulb (where our brain processes scent stimuli). But we're most interested in these new neurons in the hippocampus. Why would our brains develop new neurons there, if not to grow more room for memory? Memories are stored in several places in the cortex, but it's the hippocampus that has the most important job when it comes to coordinating our various experiences and assembling them into complete memories.
The newborn neurons in the hippocampus have a lot of growing to do before they can become full-grown memory carriers. They must find their place in networks of other neurons, networks that are already connected to other networks in a meaningful way. Otherwise, they end up isolated and lonely, like an astronaut untethered from the spaceship, drifting alone in space. It's been difficult showing how new neurons make that journey. In humans, it is impossible (so far) to follow a neuron as it gradually forms connections to other neurons—its great transition into an active memory trace.
Even in rats' brains this is complicated, but it is easier to demonstrate there than in a human brain. Researchers have managed to measure the activity in newborn neurons while rats attempt to navigate a maze. When new neurons are four weeks old, they begin to synchronize with the neurons that were there before them. This must mean that they are connected to the memory network. Perhaps the new neurons have a special role, acting as a unique signature of a given memory so that it stands out from other, similar memories.
London's taxi drivers have so much professional pride and love their jobs so much that they rarely quit before they have to be carried out of their cabs. But when their adventures in taxi driving are over, they can look forward to a pleasant retirement—and their hippocampus becoming normal again. Gone are the special skills they have spent an entire professional life practicing and maintaining.
"We didn't find enough retired taxi drivers to be able to make real conclusions—they never, ever quit!" Maguire sighs. "But the results do point to a return to a normal state of the brain."
Like rats in an unbelievably challenging maze, London's taxi drivers scurry through their city's labyrinthine street-scape. And exactly like rats, their grid cells and place cells are activated when they locate places in their memory. But so far, nobody has embedded little electrodes deep inside their brains to watch this happen while they drive around, not even May-Britt and Edvard Moser.
"It's not unthinkable that there are grid cells that cover great distances, as in London, but we don't have any methods to study them," Edvard Moser says.
Extreme learning leads to extreme remembering. The brain can even change visibly. But taxi drivers are not the only ones who have to commit something huge to memory. Professional chess players spend their days focusing on chess strategies. Does that mean that chess players also have freakishly good memories?
Simen Agdestein, chess grand master and former instructor of the current world champion, Magnus Carlsen, has spent most of his life playing chess on an international level. In his office, at the Norwegian College of Elite Sport (NTG), he shows us how to prepare for a game of chess. With the help of a statistical program, he can see what typical moves to expect from other players and figure out ways to feint them. It's a matter of memorizing, pregame, what an opponent's weaknesses are.
"In the olden days, we used to study yearbooks filled with descriptions of past chess games," he says, pulling some examples from his shelf. The volumes he flips through with the same nonchalant motion as a magician shuffling a deck of cards aren't exactly summer beach reading. They're just endless lists of dry chess moves. "A57—1.d4 Nf6 2.c4 c5 3.d5 b5."
"I don't remember any of this now, but I used to pore over these books," he says. Now he trains future chess talents.
The Magnus Carlsen room, where the young chess players have their daily sessions, looks like some sort of shrine to the world champion. The walls are covered with his photos, ranging from when he was a little kid up to the championship position he holds as a young man today. We have laid out seven chess boards behind a curtain, partway into a game—somewhere between the twenty-first and twenty-fourth move. Four of them are positioned like well-known games from past tournaments. Magnus Carlsen versus Viswanathan Anand is there—the famous game that made Carlsen the world champion, when he beat the reigning world champion. Three of the board setups are complete nonsense. We have made up the nonsense games by starting from a point in known games, and then switching the position of all the pieces by lottery draws, so they end up completely scrambled. On one of the boards, the two kings are positioned right beside each other, an impossibility in chess. On another, a pawn has inexplicably snuck past the opponent's bishop to stand right behind the enemy line.
The four champions we have challenged get to see the boards for five seconds at a time and then have to reproduce what they saw. Will they remember all the boards equally well? Or will it be more difficult to remember the nonsense setups compared to the logical, realistic, historical games that might already be familiar to the players? We're talking five seconds here. That's the time it takes to unlock your door at home or pour yourself a glass of water!
The boards we've prepared have plenty of pieces, more than twenty on each. How will they manage to remember more than a few pieces? Our experiment, first attempted in the 1940s with Dutch grand masters, was designed to show that chess players have developed an almost intuitive memory of the game. Through endless chess games, they have learned positions, known openings, and typical moves. They can identify nonsense setups immediately, and past games are supposed to remain ingrained in memory. Their chess expertise helps them to absorb and understand what they're looking at more quickly than the average person, and it's easier for them to reproduce what they have seen, even if only for five seconds.
Our first participant is Aryan Tari, one of Norway's greatest chess talents. The shy teenager recently became the world's fourth-youngest grand master and, after our experiment, the Junior World Champion. He fumbles a little bit on the first board, a real historical one, where he can place only six pieces correctly, but then it picks up. His best score is sixteen correct placements in the Anand–Carlsen game. This is a game he has analyzed carefully, as have all Norwegian chess talents, and he knows every move. But when it comes to the nonsense games, Aryan manages at best seven pieces.
In the experiment from the 1940s, the best players correctly placed up to twenty-four pieces. When the experiment was repeated in England in 1973, one grand master remembered, on average, the locations of sixteen pieces in the real games.
Olga Dolzhikova and Simen Agdestein attempt the same task. When Olga places her pieces on the board, her maximum score is also sixteen, but in several instances, she has positioned a black rook where a black queen should be, or a pawn where a knight should be. In her memory there are black and white pieces. She often remembers exactly where each color of piece goes, just not always exactly which piece it is.
"I first look at the middle rows on the board; all the action takes place here," she explains. That's also where she has placed most of her correct pieces. Toward the edges of the board, her memory is more blurry and imprecise.
When chess instructor Simen has his turn, he zooms in on the board in front of him, focused. His gaze darts across the chess board for the five seconds he has available. Very quickly, he grabs the pieces with both hands with the smooth motion of someone painting a large canvas, and swings them across the board. When he steps back and checks his result, only a few pieces are placed incorrectly. He gets twenty of them right. The next board is not as good. He remembers only six correct pieces. This is one of the illogical boards.
"This is nonsense," he says. He frowns and scratches his head with a pawn, looking displeased with himself.
The next time he throws the pieces out randomly. His self-assuredness is completely gone. After this round, though, his successes continue with the real boards. Of course he remembers the game between Carlsen and Anand. He was the expert commentator when it was played and was interviewed about it in the media in his role as Carlsen's former trainer. For a long time, he swings the queen between e1 and d1 and finally lets her land on the wrong one, e1. This is his only mistake on that board. He has twenty-two correct placements out of twenty-three.
"I was thinking that she would be on d1, but then it seemed illogical too. But, of course, there might have been a situation over here earlier," he says, waving his hand over the right side of the board, "which made her go there."
Olga has the highest scores on the nonsense boards, with ten as her best result.
"I remembered it because it was so illogical. Every single illogical position burned itself into my memory. I think it is a memory advantage to be a chess player, even when it comes to the nonsense boards. In my head, everything is chess positions, impossible or possible, and I remember things based on that. I did my PhD thesis in pedagogy, and I found that those who played chess had better short-term memory than others, and I think it is because we are thinking about relationships all the time. We see things in relation to one another," she points out.
For the average person who doesn't play chess, all the boards look more or less the same, but to the professional chess player, the nonsense boards stand out right away. For Simen, the illogical boards were total chaos. When he encountered the first nonsense board, he tried to take a mental snapshot of the board, but that didn't work at all. His next strategy was to try to remember only a few pieces so he could at least get a few right.
For both Olga and Simen, there was a major difference between the nonsense boards and the real chess games in terms of how they appeared in their memory.
"With the proper games, it was like I blacked out for a couple of seconds, remembering nothing. But then an image of the whole board appeared in my mind, like out of a fog. With the nonsense board, there was nothing, no image. All I could do was try to remember as much as possible," Olga says, and Simen nods in agreement.
"But if you tested us again now, on the proper boards, we would do it perfectly!" Simen says. "They are swirling around in my head now. I'll be thinking about them for the rest of the day."
The only one left to go is Jon Ludvig Hammer, one of the world's best active players and Norway's second best. When we test him, the game turns, and we are faced with defeat—the experimenters are suddenly the ones who are tested.
BUT FIRST, LET'S find out a bit more about how much it's possible to remember, and how those with great memories learn the things they need to remember. There are, of course, professions unattainable to those with bad memory.
Actor Marie Blokhus played the main role in _Hamlet_ on one of Norway's major stages, Det Norske Teatret (The Norwegian Theater), in a gender-reversed version of Shakespeare's most famous tragedy. The play is heavy with monologue. There is a lot of text to be memorized, long passages that are recited by the main character.
Blokhus remembers the role as being like an ice-blue spiral. Yes, that's how she explains it. She has synesthesia, like Solomon Shereshevsky. Sounds give rise to colors and shapes in her mind. When a trolley filled with props for a play bounces past us, Blokhus says that it makes a brown sound, shaped like a curled-up snake. Sudden sounds are yellow or green; nails on a blackboard make a "funny, pointy, and yellow sound."
Music tends to become complicated geometric shapes, but theater plays and poems also evoke complex shapes and colors. _Hamlet_ , as a whole, is an ice-blue spiral to her. That's how she remembers her role.
"Perhaps the blue comes from the sea and the sky and solitude in nature, I don't know. But most of the play relates to that feeling, and then other colors and images superimpose themselves on certain scenes. Blue is the base color. Everything emerges from that. But remembering the role isn't as difficult as remembering to _forget_ the role," she says.
Every evening, she stands onstage trying to think that she has never before experienced what's happening. It's supposed to be as new to her as it is to the audience. She doesn't want to deliver a monologue like a robot.
"I have to be completely open to what happens on the stage; otherwise it won't seem real. I expose myself and my overwhelming feeling of loneliness, veiled by the character of Hamlet. The words are part of me. I often pace back and forth when I'm rehearsing, to make the words enter my body. And when I'm onstage, I have to trust that they're there, somewhere, in my body," she says.
Through her actor's training, she has learned several techniques for analyzing texts and characters, but she doesn't use any purely mnemonic techniques. She puts her character on a psychologist's couch, reveals his childhood memories, and examines metaphors and context within the script. But there are many methods for understanding a character and the complex subtexts of a play. One of the many methods for rehearsing is a twelve-step model created by Ivana Chubbuck. It's popular among Hollywood actors, and Blokhus uses it too. The gist of the method is finding motivation in the piece as a whole, but also in each separate event. It's a memory-friendly method, because it works on the principles of memory: we try to understand events in our lives by tying them to our own goals and wishes. The idea is to flesh out the character by creating a backstory for them and making up inner monologues that would naturally have run through their head. Actors do this to get better acquainted with their character and, by doing so, enable themselves to express their character's feelings more genuinely. Neuropsychologists would classify this as a form of deep encoding, whereby memories are consolidated into a robust memory network. But, ultimately, colors and shapes are what hold it all together for Blokhus. Her synesthesia is a surprisingly useful tool for her as an actor.
"I remember the role because I go to an emotional place, and via my emotions, confront an existential problem where something in my own life is at stake. The colors and the shapes express the emotion to me and help me remember," Blokhus says.
For an outsider, it may seem incredible that a person can remember that much, a script that takes hours to perform. But is there anything even more difficult? What if you had to perform an hours-long script set to complicated music?
Johannes Weisser is an opera singer, and his job is to memorize three-hour operas, sometimes in languages other than his mother tongue. An opera singer who can't remember their lines will soon be out of work.
"I have no specific technique apart from approaching it from an artistic and musical perspective. I have to understand what I am singing; I have to know what each word means. I have to learn where all the pauses are in the music. But of course, the music and the director's instructions help me. As a rule, interpreting the music is more taxing than memorization. When that part is done, I have so many hooks to hang the words on that I know them by heart," he explains to us. He doesn't hide the fact that he sometimes has to cram in order to memorize the material. As he practices, he stands farther and farther from the music stand. "When I can no longer see the notes, I know it by heart."
He can sing _Don Giovanni_ or _Così fan tutte_ any time. He's nailed these two Mozart operas to the point that he only needs to flip through the music to find his role again. That's hours of music.
"The most difficult thing to learn is unchallenging music that offers no resistance, or music that doesn't interest me that much. Difficult things are easier: things I don't understand, or things that are challenging. The difficulties I encounter are the hooks that help me remember. For example, I'm working on the opera _Onegin_ at the moment. I discovered pretty quickly that the piece poses totally new challenges for me, and that made me happy. Whenever I struggle with a part, I have to take the time to get it right, and that gives me something to remember it by."
There is more to this than simply cramming. Like Marie Blokhus, he approaches the work as a whole, tries to understand what the opera is about and how the music is assembled. Everything must mean something to him.
Weisser's and Blokhus's experiences fit with our knowledge of how memory works. Both the opera singer and the actor use their own memory to their advantage. When they understand whatever they sing or say, they can remember it better, because they've created a memory network. Connecting a role to one's own emotional life will strengthen the memory further. But what if you have to remember something outside of the way memory works best—that is, without a context? What if there's a lot at stake, and you have to remember many details without any history or emotions to tie them to?
"My understanding is that in the world of pub quizzes, people seldom or never use memory techniques. 'A gentleman quizzer never crams,' or so they say. Expert quizzers take pride in remembering things naturally. But people who are into quizzes read the paper with a notebook by their side and write things down. Every time I'm curious about something I read, I check with Wikipedia to remember it for later," says Ingrid Sande Larsen, three-time Norwegian champion in team quizzes who has also been president of Norway's quiz association.
The problem with cramming for a quiz is that you're supposed to know a little bit of everything. Where would you even begin?
"It's hard to remember things you're not interested in. Generally speaking, the quiz teams are made of people who are more curious than most, who are interested in all kinds of things," she says.
"I've discovered that many of the things I know best are from when I was ten and up through high school. I can hear a tune and know exactly where I was after school when I heard it the first time, who I had a crush on, and how things smelled and tasted. I know the hits from the 1980s and 1990s whether I want to or not," she adds.
In other words, she benefits from the reminiscence bump and her own personal autobiography.
She also remembers well things that have been asked in earlier quizzes.
"Right before the European Championships in Derby, England, in 2010, I had checked on Wikipedia to see who invented rugby. As it happened, I got the question and I nailed it: William Webb Ellis. I can still envision the room when I answered it: where I was sitting, and details such as the fake marble columns and the copper ceiling lamps."
As with the divers, the place where Larsen learned something became part of the context and helped her remember it in the future.
It seems that many people who rely on their memories don't use mnemonic techniques, nor do they cram. They're just passionate about what they're doing. Are memory techniques useful at all?
"Of course, if you have a good memory, you have no need for memory techniques," Oddbjørn By tells us.
By makes a living as a memory trainer. He has written several best-selling books on the subject and teaches courses for people who want to improve their memory. He is a Norwegian champion in the sport of memory and was, at his best, ranked twenty-second in the world. He participated in the World Memory Championships for ten years. Competitors in the championships take tests they can't possibly cram for in advance, such as memorizing endless lists of numbers they have to repeat in the right order, or remembering the order of a deck of cards they saw for only a few seconds.
"I envy cross-country skiers, who can work out with others in nature, while I sit alone indoors memorizing numbers off a sheet of paper," By says. "We have to memorize completely useless things, and it's difficult to find the motivation. That deck of cards, for instance; I am really tired of cards."
The best way to remember an entire deck of cards in the right order is to associate each of the fifty-two cards with a person or a particular object. Then when two cards appear side by side, they become part of a story. There are billions of possible combinations in a deck of cards, and the story that connects them can quickly become unlikely and bizarre. Every time By pulls the eight of spades out of the deck, his story includes the character he's linked to that card—Saddam Hussein. The seven of spades is a slave. If they appear side by side, it's a question of linking them together in a meaningful way, preferably as some kind of a story.
"You never know what story may emerge. Not long ago, for instance, Saddam Hussein had a baby!" By tells us.
His technique doesn't just work for memory championships. A more practical application is helping people with memory loss improve their memory. By calls it "artificial memory." He doesn't think he has an exceptionally good memory; he is just good at using memory techniques.
"People with memory problems tend to blame everything they don't remember on things holding them back, like disease or old age. They forget that it's common to forget," he argues. Forgetting—although we have healthy and quick brains—is seen as proof of a flawed memory.
That's why many people won't use memory techniques; they want to prove to themselves that they can remember without them, that they're healthy and normal.
Some of By's techniques are surprisingly mundane, such as writing things down, taking photos, or leaving his umbrella in his jacket; there is, after all, no point using all your energy to memorize things. But there are other techniques made for memorizing things without using external aids—phones, calendars, notebooks. These are the techniques that memory artists use to wow audiences in championships and make memorization appear almost magical. The best known among these was developed two thousand years ago by Roman orators and is called the "method of loci," or the memory palace technique. It involves placing items along a path within your mind.
Before we learn more about the method of loci, let's head back to London for a bit. We've now given cab driver Judy yet another task, but this one's so easy she could do it in her sleep. From Short Street, we're driving to Shakespeare's Globe, the re-creation of Shakespeare's famous theater that has been built by the Thames, and soon she's opening the cab door for us on the left-hand side. But though Judy pilots a machine driven by memory, she has no idea that she has delivered us, in her black taxi, to the biggest memory machine of the Renaissance: a theater.
We're now standing in the rebuilt theater with a group of tourists from Holland, Australia, the United States, and Denmark, the home of Hamlet. The theater was completed in 1997, four years after the death of Chicago philanthropist Sam Wanamaker, the man who financed the rebuild.
There's an open atrium in the center of the circular wooden theater, and in the 1500s when tickets were a penny each, the London rain spattered the cheeks of those standing in front of the stage. For two pennies, people could sit, safe and dry, up in the galleries. The roof is covered in moss, the sprinkler system clearly visible. The guide tells us that the roof, a fire hazard, was built with an exemption from the London fire regulations. There's a good reason why they're worried about fire. The original theater burned to the ground in 1613.
How did the Globe get its name? And why did someone bother painting the signs of the zodiac (Cancer, Pisces, Taurus, and so forth) on the ceiling above the stage, where only the actors could see them? The Heavens, they called it—a counterpart to what was taking place beneath on the stage, where even the devil could make an appearance.
Onstage this cold day, a group of children recite Shakespeare in high-pitched voices. It's a school class practicing the master's pieces. A visible white mist accompanies their words, evaporating in the gray air, before the children, laughing, disappear again.
They know little about how people saw the world in the Renaissance.
Picture yourself standing on the stage of Shakespeare's Globe Theatre—the original Globe—playing Hamlet. For a quick second, you glance up at the ceiling. Now you can remember where you are in the script, because above you there is a mnemonic aid—an astrological map painted yellow on a blue background.
Some do claim Shakespeare's theater was simply built as one big memory machine. The method of loci was developed long ago by the great orators, such as Cicero, to help them remember what they wanted to say from the podium. They attached specific images to the ideas they needed to remember and then placed the images along a familiar path they visualized in their mind—the road to the Senate, for instance. While they spoke, they could mentally walk the road and easily pick up the next point in their speech. The Renaissance thinker Giulio Camillo introduced what he called the "memory theater" based on this technique; his memory palace was a theater stage. The idea was refined by the Renaissance alchemist Robert Fludd, who considered the theater to have magical connections with our memories. He extended the idea to the zodiac, which he used as a memory aid; the way he saw it, humans were connected to the stars in the universe. Mastering the art of memory meant becoming a real magician with power over the stars. The modern Renaissance man stood in the center of the universe, under the stars, and via the magic of memory, he could move the world.
"Give me my Romeo: and, when he shall die," Juliet sighs from the stage of the Globe and glances at the star-sprinkled ceiling above:
"Take him and cut him out in little stars,
And he will make the face of heaven so fine,
That all the world will be in love with night,
And pay no worship to the garish sun."
The globe and the stars; the Globe and the ceiling above the stage. That was the world that would help the actors remember the piece they were performing and, at the same time, connect them to the universe and all the magical powers it contained.
Today, people don't consider the method of loci to be magical, but it's still a very useful mnemonic technique. It relies on two important factors. One is picking a familiar setting for your memory palace, and the second is choosing significant images to represent the things you want to remember. Using a well-known place saves space in your memory and provides a natural order to what is to be remembered. Imagine, for example, that your path takes you from your home to your school (even adults remember well their way to school, though many years have passed since they last walked it). You choose some typical stops along the way: a bus stop, the yellow house down the street, an intersection, a corner store, and so on. Then you pick keywords to signify what you have to remember at each stop—but the keyword must be reworked into an evocative picture, creating a unique memory trace. A good example of something one might memorize this way is the periodic table. Imagine hydrogen (a big part of water) at the first stop: the bus stop has flooded! People cling to the bus stop sign, they sit inside their umbrellas, using them as boats (not the least bit probable, but at least distinct!). Don't fall for the temptation to use the little puddle that was there before, thinking it will help you think of hydrogen. Things that might be related to what we need to remember but were already there, part of the environment, just fade into the background and disappear. The next stop is the yellow house down the street. There you find helium, in the form of an enormous bouquet of helium balloons attached to the house, almost lifting it from the ground. The next stop is the intersection, and there you will find lithium in the form of a giant container of lithium batteries in the middle of the intersection, so big the cars have to detour around it. The memory palace technique can be used to memorize ordinary things too, like shopping lists, the keywords of your history syllabus, or chore lists.
"I have about one hundred different memory palaces because if I am supposed to remember different things, I have to vary the route so I don't mix things up. My favorite palace is my brother's barn. I know it well, and it has many nooks and crannies," Oddbjørn By says.
As a student, he used his memory to pull a stunt that aggravated his fellow students. Without enrolling in a class, he registered for the final exam and memorized the coursework in only two days. His secret was the method of loci.
"A good friend of mine was studying extinct religions, and I borrowed his well-structured notes. I placed the material in mind palaces and was able to remember it for an oral exam," he recalls. He got a B in the subject, and that's what irritated the others. Why would anyone struggle for months at a time learning a subject if it was that simple? But today, after twelve years have passed, By doesn't remember much about the Mesopotamian gods. But a history course, on the other hand, which he diligently studied for an entire year, has stuck with him, though his grade was not too impressive.
"I don't recommend that people study for a course in this superficial manner, but the memory palace technique can be combined with other, deeper study techniques," he says. "If you happen to have some extra time, and nothing to fill it with, why not use it to learn something new?"
Creating a memory palace may sound difficult at the outset, but it can be used in many different, even stressful situations: for the exam, on the stage, and even on the dance floor.
"The technique works well if you're doing something meaningful while, at the same time, walking the route in your mind; it only takes a couple of milliseconds. For actors and opera stars, this means picking out keywords from a script and organizing the rest of the text around them. Then you place the keywords along your route. The more of an expert you become, the fewer keywords you need to remember the material; understanding the material helps you remember it better. Many memory techniques work better if you already know some of what you are about to learn."
Even experts sometimes use memory techniques. Solomon Shereshevsky, the man who couldn't forget, gradually turned to the method of loci. In the beginning, he used his own self-made method, whereby he simply visualized the things he had to remember positioned along the streets of Moscow. He didn't need to create particularly distinct pictures because he remembered well without them. But sometimes he missed something because he had placed a memory in the shadow between two lampposts. He simply walked on by without noticing the unassuming little egg he was supposed to remember; it had faded into the background because his imagination was almost too vivid. When this happened, he realized that he had to structure his memories better, along a single route, using symbols.
In addition to the method of loci, you can use memory rules: for example, first-letter rules, creating a word from the first letter of each thing you want to remember. You can use the orange trick: put an orange in your bed when you need to remember something important. When you return home, you'll see the orange and remember why it's there. There are, of course, mind maps. Then there are flashcards—index cards with information on each side; countries might be on one side, capital cities on the other. Go through the pile. Those you know, you put to the side; others you drill through again until you know them.
In order to benefit from these methods, you often need to understand the topic at hand. You can't make mind maps without having familiarized yourself with the material and mastered it. The methods are basically all about making learning easier. They provide motivation. Cramming becomes unnecessary when you can learn in a more memory-friendly way. But you can't get around the fact that learning, as a rule, takes some effort. Take, for example, the periodic table, anatomical names in medicine, Latin names in botany, mathematical formulas, grammar rules in languages. Before they become part of you, you have to hammer them into place—or walk them through a memory palace.
"Mastering memory feels good, even more so for people with memory problems," By concludes.
Before we leave, he is going to demonstrate one of his tricks: memorizing a list of numbers. At his best, he was ranked ninth in the world at this. He asks us to read a random list of thirty-five numbers, one number per second, paced as evenly as possible. For us, no memory champions, the natural thing to do would be to repeat in our heads as many numbers as possible, right away, before they disappear. It's likely we'd remember only a few from the beginning and end of the list. People with average memories can remember six or seven numbers; that's how much our short-term memories can store. When we finish reading the numbers to Oddbjørn By, though, there is silence.
The Norwegian memory champion leans forward, his hands over his mouth and nose and a distant look in his eyes. Has he forgotten all the numbers already? A minute passes; two minutes. Then he begins to list them off. The first numbers are correct; he asks to skip a few numbers that he saves for last, and goes on to recall more numbers from memory. He is like a magician, pulling one rabbit after the other out of his top hat. He is so quick that we have trouble keeping up with him. In the end, he manages thirty-four of thirty-five numbers correctly. It is almost magical; it shouldn't be possible. But his method is to arrange the numbers, in pairs, into the shapes of creatures, which he then places in a memory palace. Two by two, the numbers become zebras and goblins, people and animals along his route. In principle, this is a method anybody can use, but if you want to be the best in the world, you have to practice a lot and stay focused. Perhaps you also need a certain amount of talent, as in sports. Those of us without talent can remain happy memory amateurs.
"Working with memory has changed me. When I read a book, there are more images in my mind. I have become much more visual," By says.
Anders Fjell, whom we met earlier, and Kristine Walhovd together lead the Centre for Lifespan Changes in Brain and Cognition at the University of Oslo, where they are involved in a number of research projects. Their goal is to reveal what influences memory throughout life.
One of their projects is a comprehensive study of the effects of memory training. Their subjects don't include any exceptional taxi drivers. Instead, they're training the memories of two hundred senior citizens. Do memory techniques make a difference in a group of seventy-year-olds?
"After ten weeks of memory training, the group of seventy-year-olds remembered as well as people in their twenties who had not learned any memory techniques," Walhovd tells us. Because the older participants are so determined, they usually make a solid effort. They get more out of the training than one might expect.
"They know they must make an effort and take the task seriously, perhaps more so than the younger ones," she asserts.
The changes in their memory skills are also visible in their brains. Just like Eleanor Maguire, Walhovd and her colleagues scanned the brains of the volunteer memory trainees and saw physical differences. But even if our brains change, improving our overall memory is still elusive, because it doesn't look as if training helps us to remember more broadly.
"If what you practice is memorizing one hundred words in the right order, then that's what you become good at: memorizing words in the right order," Kristine Walhovd says.
But what about people whose memories are poor due to brain injury? Completely regaining your memory after a serious brain injury is too much to hope for, especially if the hippocampus is affected, or if there are large and long-lasting injuries to the brain. The goal of rehabilitation is typically managing everyday activities better. Sometimes this means using aids (like a day planner, diary, or calendar with an alarm function), implementing steady routines, writing shopping lists, and recording messages. Changing the way one remembers things can be a long process for someone with a brain injury; sometimes it is also upsetting. Having memory problems means spending a lot of extra time and energy mastering tasks and learning new skills. Sometimes rehabilitation is as much a process of figuring out one's own limits as it is active memory training. For someone with a brain injury, memory techniques can help regain a sense of control.
According to research—that of both Eleanor Maguire and the research duo Walhovd and Fjell—memory training is not the same as improving memory in general. But remembering better with the help of certain techniques is nothing to sniff at if you can make it work.
Mastering memory techniques makes the brain better equipped—at using memory techniques. This is true for the taxi drivers, whose spatial memory improved while their hippocampus got bigger, as well as the grand masters of chess, who are better than everyone else at remembering chess positions, but not much else.
CHESS GRAND MASTER Jon Ludvig Hammer leans over the chess board. Then he bounces up.
"Are you kidding me? Are you frigging kidding me?" he says and laughs, astonished. "The next time, you have to give me a warning!"
It's just as if we held a glass of sour milk under his nose—the reaction is that intense. We have shown him one of the nonsense boards. He instantly saw what it was, and now he fumbles to place two correct pieces on his board, shocked and overwhelmed by the chaos we have shown him. But when he gets to the next nonsense board, he has developed a strategy and focuses on a limited number of pieces; he ultimately manages to get nine points on the last one.
On the proper boards, he makes a maximum of four or five mistakes. The Carlsen–Anand board is immaculate; he gets all twenty-three pieces correct after studying the board for five seconds.
In the amount of time it takes us to say "Viswanathan Anand, Hikaru Nakamura, and Garry Kasparov," the time it takes to glimpse a seahorse in the water or decide to turn left at a confusing intersection in London, the time it takes to walk through Oddbjørn By's mental barn, Jon Ludvig has managed to identify all the pieces on the board, where they belong, and also what game of chess this board is from. It is superb.
But for some of the boards, some pieces do end up in the wrong places. He did, after all, have only five seconds.
Jon Ludvig refuses to leave. He remains sitting there. He is obviously tortured by the fact that he wasn't completely right the first time and insists on one more chance.
"I'll set out the four real boards correctly in the right order, and this time I will get all of them right. Without looking at the boards again, of course," he says.
We realize we can't stop him.
He is very fast now. When board number one is completed, he doesn't bother to stop or take the pieces off the board—he just continues, as if in a trance, like a spiritual medium of chess, channeling kings and queens. He sprinkles all the pieces into place. On the four boards, he places ninety-six pieces. All are correct, except one, a pawn.
"The pawns make up the skeleton. I build everything around them. I structure the board logically, starting with the pawns," he explains.
His strategy for remembering the board does not remind us of Olga's, for whom the middle row was the most important.
Jon Ludvig Hammer is a full-time professional chess player. He can spend ten to twelve hours a day practicing opening moves in chess; that's his job. He has read all the books Simen Agdestein showed us. He has crammed attack moves and response moves so they are all available to him when he is in a tournament, ready to deliver. Further into the tournament, memory may play tricks on him as he becomes tired.
"Sometimes I forget what strategy I was using, because I have been thinking so hard about an alternative strategy in the meantime," he says. And, because working memory doesn't have the capacity to hold that many things, just going to the bathroom can make him lose his whole train of thought.
Jon Ludvig stares at his last board. His hand darts over a white pawn. He picks it up, puts it down again.
"There is a piece missing," he says. "But it wasn't there when you showed me the board the first time. There should be a pawn here, to defend the knight. This whole area is now open in a weird way."
We do a double take and check again. We had simply forgotten to place a white pawn on c2. The game has most definitely turned. It is checkmate.
— 6 —
**THE ELEPHANT'S GRAVEYARD**
**_Or: The art of forgetting_**
I stand amid the roar
Of a surf-tormented shore,
And I hold within my hand
Grains of the golden sand—
How few! yet how they creep
Through my fingers to the deep,
While I weep—while I weep!
O God! can I not grasp
Them with a tighter clasp?
O God! can I not save
_One_ from the pitiless wave?
Is _all_ that we see or seem
But a dream within a dream?
**EDGAR ALLAN POE _,
"A Dream Within a Dream"_**
BERLIN, 1879. THE city's most prominent citizens promenade beside the river Spree. Along Unter den Linden, they sit at outdoor cafés, enjoying the warm weather and the blossoming linden trees. They rearrange their dresses and their top hats and breathe in the spring smells: horse manure in the street and fresh-baked pretzels. The abundant foliage casts shadows on the ground.
"What a wonderful time!" these bourgeois may be thinking beneath the tree canopy in Berlin. "I wonder if this particular moment will stay with me for life. Will I remember the breeze making the linden trees sway, when I think back on this a year from now, five years, twenty years? How much of this will I forget?"
Meanwhile, in a laboratory at the University of Berlin, a lone researcher is about to begin a groundbreaking experiment. He is going to attempt something never before tried in history. He is not going to conquer a mountain, invent the lightbulb, or travel to the Moon. Nobody in high school history class will read about what he is going to do. But in the history of psychology, he will be hailed as a great hero, a man who walked where no one had walked before. Hermann Ebbinghaus will be remembered forever for his efforts to do something completely ordinary—forget. While Berlin's upper classes stroll the river in the spring sun, Ebbinghaus feeds his memory with meaningless syllables. BOS—DIT—YEK—DAT. He studies them intensely and tests himself, hour after hour, day after day, until he can repeat every list of twenty-five nonsense words in the right order. While life unfolds outside the University of Berlin, Ebbinghaus immerses himself in syllables. He's chosen to study empty combinations of letters because they are completely free of the troublesome contamination of emotions, ideas, and his own life. He tests how much he can still remember after a third of an hour, an hour, nine hours, a day, two days, six days, and thirty-one days.
He wants to find out how fast he forgets; it's as simple as that. Sure, outside of psychology circles, this may not seem like an accomplishment worthy of much celebration. We can plant a flag on the South Pole, but we can't do the same with the act of forgetting—we can't discover it and declare, _Here it is!_ While Solomon Shereshevsky could make a living and earn applause by remembering superhumanly long lists of words and numbers, nobody would pay a nickel to see Ebbinghaus stand onstage and _forget._ It's safe to say that he had undertaken an unglamorous task. Though what he did wasn't particularly exciting on the surface, it was actually quite sensational. Psychology was a brand-new field of research; nobody had researched memory like this before. Up to that point, measuring thoughts wasn't something anyone could have imagined. But Ebbinghaus performed such a significant feat that scientific society was forced to take him seriously.
It was a demanding task to document forgetting. Ebbinghaus didn't want to leave anything to chance, so he did all the experimenting on himself—and, really, who else would have agreed to the job? That way, he could trust that he was in full control of all variables. It meant he also had to keep his own personal life in check, so no sensational memories could influence the impersonal, scientific building blocks he was memorizing. After several years of intense and one could say _ascetic_ work memorizing and forgetting, Ebbinghaus published the book _Über das Gedächtnis_ (About memory). Up until 1885, memory had belonged to the realm of philosophers, writers, and alchemists. Never before had science focused on forgetting. How, then, do we measure a vanishing memory?
If Ebbinghaus memorized a list of nonsense words and after a while—let's say after one day—could come up with only a little more than half of them, had the rest been forgotten? Yes, there and then, some words were forgotten, and the difference could be measured and called forgetting. But this was not thorough enough for Ebbinghaus. It could have been that the words were still stored in the brain and only the access to them had been weakened, so that he couldn't reach them by will. It could be that, deep down, there were remains of memory traces that could be wrung out like water from a wet cloth.
"We cannot, of course, directly observe their present existence, but it is revealed by the effects which come to our knowledge with a certainty like that with which we infer the existence of the stars below the horizon," he determined.
He chose to approach forgetting from another angle. If he had forgotten a list of meaningless words, how long would it take for him to relearn them after some time had passed? For every new learning effort, he measured how many repetitions, or seconds, were required for him to remember the list again. If the list had been completely forgotten, so that not a single strengthened synapse remained, relearning the list would take him as long as it did the first time around. But if he'd retained anything, it wouldn't take as long to relearn it. In this way, he calculated the natural course of forgetting and discovered that our memories disappear most quickly in the first hour. After a day, more has been lost, but the process of forgetting quickly slows down, so that after a month, we've forgotten only slightly more than after a week. His research led to what we today call the _forgetting curve_. Shown as a graph, it descends quickly in the beginning and then tapers off.
Never has any researcher exposed his own weakness—his forgetfulness—for the benefit of humanity with such intense dedication as Ebbinghaus. For several years, he wrote page after page about what he had forgotten and tracked forgetting with tables and numbers, satisfied to have contributed to the science of psychology. Maybe he would have preferred to be in the streets of Berlin enjoying the spring sun, sipping a cup of coffee with friends, and strolling slowly along the river. But he wrote nothing about his personal memories from the time of the experiments—except that he strove to keep personally meaningful experiences to a minimum, in the service of science.
What Ebbinghaus proved was that memories, when they don't have anything to do with ourselves or what we care about, gradually wither. But he had no way of understanding exactly _what_ crumbles in our brain. The creation of memory traces was, as we've said before, not proven until the 1960s by Terje Lømo. Memory traces probably weaken over time. It seems as though, unless we practice and maintain knowledge until it's become firm in memory, the neurons involved in remembering eventually return to their original state. This is probably a good thing. It gives the brain space for new memories. The other thing Ebbinghaus revealed was that the brain begins tidy-up work shortly after new experiences have entered memory. This too is probably a practical trait in memory. It's better to clean up sooner rather than later. And it ought to be obvious fairly early on whether or not an experience is important enough to be stored. When Ebbinghaus researched forgetting by measuring learning, he also made it clear forgetting and remembering go hand in hand. They are two sides of the same coin.
If we don't forget, the storage space in our brain fills up (Solomon Shereshevsky and his like notwithstanding). For most of us, some memories have to depart to make room for new, perhaps more important ones.
"If we remembered everything, we should on most occasions be as ill off as if we remembered nothing. It would take as long for us to recall a space of time as it took the original time to elapse, and we should never get ahead with our thinking," William James pointed out in 1890.
Still, forgetting is something we fear. Forgetting is aging; it's decay and impermanence, a memento mori. When the days pass and we cannot remember them, it means we're one step closer to the end of life, without anything to show for it.
That's why blogger and author Ida Jackson has kept a diary since she was twelve. "It feels like it's helping. I lose fewer things that way. If I look up a certain day in my diary and see that we had dinner with friends, then I remember more of that dinner, even if I didn't write down any details." Ida is a collector of memories, scared to death that the moments will be gone forever.
Generally speaking, forgetfulness reminds us that we are not in full control. It _is_ , after all, impractical to forget appointments, friends' birthdays, phone numbers, and everyday experiences. Forgetting names can be embarrassing. But forgetting is much more common than the most intense hypochondriacs like to believe, and it is seldom a sign of dementia or early Alzheimer's. Lack of sleep and general exhaustion are enough to cause important things to slip.
Even when our brains work perfectly, most of us forget more than we'd like to. We forget names, because they usually don't have a logical connection to the person they belong to. Among the Vikings, a thousand years ago, it was not uncommon to get named after one's physical characteristic or personality. Some common Norwegian names still in use today originally meant "cockeyed" or "spinning"—fitting of someone with more energy than the average person. Some family names, like Smith, originally described a profession. Today, though, names are often random labels without a clue to the physical person they designate. Only through repetition and association are the names attached to the person in our memory.
We forget faces, because they are complex and difficult to describe. The small part of the cortex that specializes in perceiving and remembering facial features helps us navigate our social worlds by quickly processing the faces that we meet. But much like other brain functions, this doesn't work perfectly. When we first recognize a face, we don't necessarily remember who it belongs to. We forget where we know someone from because when we first see them, we haven't activated the memory network we originally placed them in.
Faces and names and appointments and telephone numbers, your sister's birthday or a bill that's past due: Where does all this everyday forgetfulness come from? Forgetting isn't just the process by which memory traces fade away. Forgetting takes place at all stages of memory: encoding, storing, and retrieval. Often experiences never make it into memory at all. In order to get to the stage where memories are stored and consolidated, experiences first have to go through a screening process.
The first obstacle is attention. Magicians and pickpockets thrive on exploiting attention, because they know it can focus on only one thing at a time. While you're looking at the map the thief pushes into your face to ask for directions; his hand sneaks, unnoticed, into your bag.
In 1970, a Norwegian TV reporter stopped people in the street and asked them some pointless questions in front of the camera. In the middle of the interview, someone walked between the reporter and the interviewee, carrying a large plywood sign. While the reporter was out of sight, a comedian, Trond Kirkvaag, took his place, wearing either fangs or a king's crown. The people being interviewed didn't seem to notice that anything had changed. One of them even pointed out a mistake in the interviewer's question, even though the person he told was someone entirely different from the person who asked the question in the first place. This was, of course, a comedy show on television, but it revealed a truth. If you are interviewed on TV, your attention is on the microphone in front of you. With all the adrenaline flowing through your body, you might not even notice if the person interviewing you is suddenly replaced with someone else.
Approximately twenty years later, Harvard researcher Daniel Simons did a similar experiment, which later made him famous in psychology circles and won him an Ig Nobel Prize. He made a movie—perhaps the world's most boring movie, if you're used to Hollywood fare. It shows six people passing a basketball. Those watching the film were asked to count how many times the ball was passed by the people wearing white. Half of those who watched the movie proudly reported that the ball was passed fifteen times, but when they were asked if they had seen a gorilla, they were insistent that they had not. Still, if you watch the film, you'll see a man in a gorilla suit slowly strolling among the basketball players, stopping and beating his chest, before showily spinning on his heel and exiting to the left. Our attention is like a camera lens; everything outside its focus is blurry and ends up in the background. We can hardly call this sort of thing forgetting; the only way the experience affected our mind was via a brief burst of sensory stimulation that went unnoticed by the rest of the brain.
The next obstacle standing in the way of something becoming a lasting memory is our working memory, aka short-term memory. It may be memory's weakest link, and its most critical one too. There is only limited room here, and memories can stay for only a short time, about twenty seconds. Henry Molaison still had a working memory and could maintain a conversation as long as he had a meaningful connection to the topic. As soon as his thoughts wandered, the conversation was over. This was the healthy part of Henry's memory. But his memories never got any further, into long-term memory. More often than not, our experiences end up like Henry's short-term memory, eluding further storage.
When psychology professor Alan Baddeley performed his now-famous diving experiment off the coast of Scotland, he had already started on another research project. It was actually this _other_ project that made him a giant in psychology and has made waves ever since. It involved trying to understand what happens to the fragile, volatile memories of the here and now.
In the 1960 s, Alan Baddeley had worked for the General Post Office in Britain, creating a memory-friendly system for postal codes. Unfortunately, the system was never adopted, but knowing how memory allows us to retain random numbers for the short time it takes to write them on an envelope raised many questions for Baddeley. It inspired him to research the topic of short-term memory further, together with his colleague Graham Hitch.
You'd think short-term memory would be easy to understand. Either we remember something for a short time, or we remember it for a long time. In the 1950s, researchers figured out that our short-term memory has room for seven units of information at a time. They called it the "magic number seven" (later revised to the not-quite-so-catchy "magic number seven, plus or minus two," taking into consideration normal variation in individuals). But Baddeley and his colleague soon discovered that short-term memory is much more complex; it is an active process, _working_ memory, not a magical container. They also found that working memory contains several stores, each with its own specialty: linguistic information, images, episodes from life—perhaps even more layers, each tied to a sensory modality, such as smell, taste, and touch.
"I remember one of our earliest experiments, one that led us to draw up our model of working memory, the topic that has occupied my mind for the past forty years," Alan Baddeley shares with us.
"We asked volunteers to remember sequences of five words that were similar in sound, such as man, cat, mat, can, and hat, and then we compared their performance with that of having to remember dissimilar-sounding words; for example, pit, day, hen, pot, bun. There was a clear difference: the dissimilar-sounding words produced up to 90 percent correct responses, as compared to only 10 percent of the similar-sounding word sequences!"
They had discovered that working memory has a separate store for spoken language, called the _phonological loop_ (try remembering _that_ till the end of the chapter!), whose only task is to store linguistic units.
"This is the part of working memory that allows us to learn a foreign language, for instance," he says.
Our ear picks up on new, not yet understood words, which our cortex interprets as language sounds and sends to the phonological loop, where they are held automatically for a few seconds. From there, these sounds can be repeated, in a loop (a process that is automatic but can also be voluntary). If we manage to repeat them for a long enough time, they may stick in our memory and we can say we have learned something new. Things we hear from teachers, spouses, customers on the telephone, or TV advertisements enter the phonological loop and compete for space. They say that messages can go in one ear and out the other, and this is an apt description of working memory. It is the place where our stream of consciousness is trapped and held, for a brief moment, in front of our inner eye and ear.
Visual information is processed by another part of our working memory, and the two systems can function fairly independently of each other.
"Regretfully, there has been less research on the visual part of working memory," Baddeley admits, "although it's currently a very active area."
Several of his experiments have shown that when subjects simultaneously absorb visual stimuli and words, their ability to remember words is less compromised than when they see several words at the same time. In other words, we can juggle several types of information without our memories suffering. Everything is handled by a _central executive_ , which steers the attention to where it is needed, prevents awareness from drifting, and keeps undesired information out of working memory.
During the forty years Alan Baddeley has been researching working memory, some new discoveries have changed the model for how here-and-now memories work. One of the latest additions to the model is the _episodic buffer_. It acts as an intermediary between our attention and our memories and thoughts, fetching them from our long-term memory and presenting them to us in the here and now.
"Think of it as a TV monitor, where thoughts, memories, and images are being shown to us," Alan Baddeley explains. "It's a passive monitor that plays a multidimensional show, a show that has been prepared for us elsewhere in the brain and then projected on the monitor."
Behind the curtain, the brain busily works to prepare the show for the screen. Working memory is where we think, solve problems, do math. It is also where memories are acted out before our inner eye.
The working memory model is useful for understanding how and why certain things never enter our memory at all. Forgetting in working memory is something completely different from forgetting in long-term memory.
Working memory is set up to hold information for a very short time; it provides only temporary storage. It's like a mail shelf, where employees are supposed to pick up today's mail so there's room for new deliveries. The only difference is that on this mail shelf, if you don't pick up your mail on time, someone throws it out. It is normal to forget in this way. It's a natural part of having a human brain.
"Forgetting is an important aspect of memory—it helps us see what's important," Baddeley reminds us.
Forgetting is so central to remembering that we almost take it for granted. Still, many complain about their poor memory, even though their ability to store new memories is totally normal. They are just victims of their own natural working-memory screening. The situation is worse for people with attention deficit hyperactivity disorder (ADHD), whose problems with attention make it harder for them to focus on things long enough to store them.
We often forget things when other thoughts demand space in our working memory. Worries are a classic example. Things we worry about are things that are important to us; they overflow with emotion, crying for attention. That's why they are sent directly into working memory.
Here's an example: you are studying for an exam; you're afraid of flunking. You are trying to focus on maritime ecosystems, but it's a hard struggle because you're so worried, and your worries are clogging up your working memory. The life cycle of plankton competes with thoughts like "If I don't pass the exam, I'll have to do the class over again, I'll lose half a year of studies, I won't get to go to Greece this summer, I'll have to find a summer job, I'll be broke, I'll never get a job, my parents will worry and nag, my friends will think I'm a loser, and they will go to Greece without me!" How many millions of plankton have to step aside to make room for these worries? The plankton lose. Even if you start off with a passion for plankton and their significance to ecosystems and the climate crisis, they're now flushed out to sea, far beyond your reach.
Working memory may also be to blame when we don't remember people's names the first time (maybe also the second and third). As we're shaking hands, the name we are supposed to remember competes with all the other thoughts going through our minds: how we look, what we'll talk about after the handshake, whether we grabbed their hand too hard or too soft. Many of us are afraid we'll appear impolite if we don't immediately remember a name. It may, however, actually be a sign of interest in the person. It is above all the individual and what they stand for—not their name—that occupies our working memory during that first handshake and the minutes that follow.
Even those with extremely good memories may sometimes succumb to the failures of working memory. Compared to most people, Norway's memory champion Oddbjørn By has a completely different standard when it comes to forgetting. What if he forgets just _one_ of the numbers he is supposed to remember in the exact right order? It would be disastrous! During the World Memory Championships in 2009, he was at the top of his game. Beside him, though, sat another contestant, a Chinese memory master with a throat infection. He was coughing loudly. Noise is something By trains to handle by sitting in noisy cafés. On the day of the competition, though, his nerves got the better of him. A cough from the competitor after digit number thirty-seven sealed his fate. Even though he missed only that one number, the thirty-eighth in the row, he wound up with thirty-seven points out of a possible one hundred, his life's most disappointing placement.
Yet another form of forgetfulness becomes evident when we're retrieving something from memory. To remember, we normally rely on cues to take us to the exact memory. They make it possible for us to find the right memory network, the particular fishnet of memories, and haul in the catch. Sometimes the cues get mixed up. We latch on to the network of something else that looks similar and steals our cue. It is a bit like googling: we must use the correct search term to get a relevant hit in our memory. And when the results of the search appear, we have to choose one among many.
Mnemonist Solomon Shereshevsky could remember meaningless lists of numbers and words for an almost immeasurable length of time. Yet he still had a memory problem: he was afraid that all the things he couldn't forget would disrupt his ability to remember other things during his performances. In other words, he was afraid of remembering the wrong list of words! Even if after every performance he wiped clear the board where an audience member would write the list of words, they were still almost permanently etched into Solomon's mind. He made repeated tries to forget the list, but the more he tried, the more the words stuck. His solution was to imagine the words on a piece of paper and, in his mind, crumple it up and throw it in the garbage. We're uncertain if this actually helped him forget, but at least it tagged the list, separating it from the new lists he was trying to repeat, onstage, with everyone's eyes on him. Ironically, he had used his amazing memory to help him forget.
Forgetting names and messages in droves is one thing. All of life's little experiences running like sand between our fingers is something else. Remembering the important things in life is what really matters, isn't it? What's the point of spending a bunch of money on a vacation if we can't remember any of it afterward? Forgetfulness is a friend, sifting through everything to reveal the high points, the pearls in our necklace of memories. Most of what we experience does disappear. All those times we've waited for the bus, the trips to the store, the afternoons on the sofa; they aren't supposed to remain in our memory. Forgetting even touches memory's shiniest pearls. It leaves behind only an outline; the rest is reconstruction. It's how our memory remains flexible.
The most widespread kind of forgetting, the kind that affects our personal memories to the highest degree, is the one we all experience after childhood. Researchers call it _childhood amnesia_ (or _infantile amnesia_ ).
Most of us have a boundary, somewhere between the ages of three and five, that marks the beginning of life as we remember it. Some remember further back, from around the age of two; others may have very few memories until the age of seven. Up to that point, it's a complete blank. We remember our first years only through stories our relatives tell us. Why do we forget our early childhood like this? How can that boundary appear at a certain age? It's a mystery, one researchers have struggled with for well over a century—and a riddle humans have probably pondered as long as we've philosophized about our own awareness. It is, after all, a universal, obvious gap in memory.
There have been many theories. Does it have anything to do with the development of language? In the 1980s and '90s, many suggested that childhood amnesia could be blamed on children's lack of language to express their experiences to their parents and to themselves, making them unable to attach their memories to words. This assumes that language, when developed enough, is what makes it possible for us to remember things. But children who have just learned to string words together in sentences are able to tell us about things that happened earlier in their lives, before they had language skills, so this cannot be true. Perhaps when our language skills reach a certain maturity level, this reorganizes our memories? Is everything shuffled and moved into new linguistic shelves and drawers? Memories are stories, and proper stories provide structure to memories, right? But this doesn't ring true either, because then there would be a sharp difference between the character of memories before and after the linguistic reorganization.
Up until the 2000s, the question wasn't being asked the right way. From another angle, you can ask: When do our first childhood memories _disappear_ , becoming part of our childhood amnesia? Earlier, people speculated about how, as adults, we remember childhood. However, that's not where we'll find the solution to the mystery. Our memories go through too much as we grow up for an adult perspective to be useful in understanding small children's memory.
At Emory University in Atlanta, psychology professor Patricia Bauer has set up a kind of children's memory lab, which proudly bears the nickname "Memory at Emory." Bauer wants to follow the natural course of children's memories, which demands patience and effort. To achieve her goal, she has to standardize the children's memories so the memories can be compared across age. When children come to the laboratory, they're given a certain set of toys that they don't have at home and are shown how they work. When they return to the laboratory a couple of months later, the children usually start playing with the same toy if they remember their last visit. This way, the researchers don't need the children to tell what they remember; they show it. As they grow older, their memory is measured by what they tell the researchers.
Patricia Bauer has completed many studies following the children's memories over time. Starting from the moment a memory is made, she can watch it take shape from the other side of the childhood amnesia boundary. The memories don't suddenly disappear when the child turns four. When you think about it, this is obvious. We know that three-year-olds can tell us about their summer vacation half a year later. Even two-year-olds are able, using their limited vocabularies, to talk about things that happened several months ago. Childhood amnesia doesn't just suddenly appear in a four-year-old who can still recall what happened a year ago. What Bauer discovered was that memories that later disappear into childhood amnesia are still accessible for children several years after the age of four, before they gradually fade away. To understand the process, we need to study the life span of a memory created in a two-year-old, a three-year-old, a four-year-old, and so on. A two-year-old's experiences become memories that last for a shorter period of time than those of a three-year-old. It seems as if our earliest memories come with a best-before date. They are perishables and degrade quickly. As a child grows older, their memories come with more generous best-before dates. Finally, as they mature, their memories reach the almost unlimited durability of canned goods. In hindsight, childhood amnesia sets in around the same point that our memories achieve adult durability. The memories made before that age become weaker and weaker until, at about nine years of age, they completely disappear in most children. The way language reorganizes memory doesn't explain why memories vividly described by a six-year-old vanish by the time that same child has turned nine. But language does have some effect. Bauer has seen a clear connection between how parents talk to their children about their experiences and how well those memories stick. Anecdotes parents bring up over and over again become part of a child's life story and come to life with the help of constructive memory.
"Everything you want your children to remember, you must talk to them about," brain researcher Kristine Walhovd says. "As parents, we of course emphasize the positive experiences of our children."
This is how parents can contribute to their children remembering a good childhood.
"They say 'it's never too late to have a happy childhood.' A lot depends on how you weigh the episodes in your child's life," Walhovd adds.
There is great variation in how far back our earliest childhood memories go. Some are undoubtedly glimpses of real experiences. Bright flashes of light, sound, and, most often, a certain mood. Some claim that they have vivid childhood memories from before the age of two. Many have childhood memories that can be traced back to photographs they've seen or stories they've heard from family members. Our memory's reconstructive process takes these stories and images and brings them to life, even when there is no trace left of the original memory. In that way, a "false" memory is created of a real-life experience. These constructions may appear early on in life, stay with us, and feel like "real" memories. Over the years, we may easily forget that we were once told the anecdote. The act of listening isn't as memorable as the story we hear. If your mother told you about a family vacation you went on at, say, the age of two—and you are now five—it may well happen that you pictured it vividly and remembered the reconstruction, without remembering that it came from your mother. Your mother may well have forgotten herself that she told you the story. In this way, reconstructions sneak in seamlessly among our childhood memories. People often insist that their childhood memories couldn't possibly originate from other people's descriptions or photos. And it's impossible for us to tell.
Let's dive back through the cortex to visit the seahorse in its temporal lobe. Could it hold the key to the riddle of childhood amnesia? One theory is that the hippocampus isn't mature enough in early childhood to consolidate memories for good. Because not only does the hippocampus have to grow and develop, it also has to build a network with the cortex. This happens at the same time the cortex is going through a growth spurt. All this chaos probably results in memories that are less securely stored compared to how they will be when everything in the brain is properly in place.
Some newer, more sensational theories look at other aspects of the hippocampus's development, theories that are more speculative. Some claim that place and grid cells, which we know are central to our spatial memory, aren't ready to map the environment until a child starts to move around independently, and even after that, that it still takes some time before the system is done "calibrating." Still others speculate that the solution lies in a microscopic layer of protein called the _perineuronal net_ that gradually envelops neurons and synapses. This fine-meshed protein net may protect the links between neurons, allowing the memories to more easily adhere. More and more netting is added to the brain throughout life. The downside may be that people's mindset hardens, so to speak, as the perineuronal net solidifies around the neurons. Our first memories can't get as firm a grip, because the perineuronal net hasn't been developed yet. However, this research has, so far, looked only at the brains of mice and rats.
Later in childhood and early adulthood, most of us are blessed with an observant personal memory that, as we've said, preferentially collects experiences in the reminiscence bump: many of the significant, new, exciting, sad, and transformative experiences that become part of our personal autobiography. Impressive as memory may seem, there's no denying that it goes hand in hand with obliviousness. Sometimes, it feels as if the days slide into a black hole as time passes. Is it possible to stop this? Can't we prevent forgetting from devouring all those little experiences? Think back on the last six months: perhaps, at first, there is only a vague outline, punctuated by holidays, birthdays, and trips. Then there is a virtual parade of the most prominent unique events. Everything is shortened, compressed. The air has been squeezed out, like clothes you roll tightly into a carry-on to avoid extra fees.
What happens if you fight natural forgetting? If you put effort into remembering all the unique moments that make up your life? Can the parade get longer? Can we put a lid on the black hole of forgetfulness, using memory techniques to remember the important events?
The thought is so absurd that it _has_ to be tested. So one of us sets about trying to fight forgetting. For several months, we have interviewed memory researchers and actors and chess players, but the two of us each have our own approach for remembering these events. One of us submits to the organic nature of forgetting, while the other one tries to nail each day to memory in order, for one hundred days.
Let us, the authors, invite you to our memory theater for a short performance—we'll set the stage for a talk show!
Hilde will play the role of the talk show host. Ylva is the main guest who will entertain viewers with the tale of how she pretended to be Ebbinghaus for one hundred days and conducted an experiment on herself.
_The lights come up. Applause_.
HILDE: So, Ylva, you've been experimenting on yourself! What were you hoping to achieve by memorizing the events of one hundred consecutive days?
YLVA: I thought of how magnificent it would be to be able to remember such a large chunk of a year. It would almost be like an archive. But mostly I wanted to be able to remember more of those magical everyday moments. By memorizing the main events of each day, I hoped they would latch on, like the associations in a memory network. That would be the great bonus.
HILDE: But one hundred days! That's a lot of everyday moments! What exactly did you do to make it work?
YLVA: At first I kept a diary, but that didn't work at all. I know it works for Ida Jackson; maybe she has a very good memory. I don't. I seldom remember what I did last weekend, even if I write it down. So I thought I would do it like Oddbjørn By: envision a spectacular image for each day. By's method for memorizing a deck of cards in the right order, all fifty-two of them, involves imagining each single card as a distinct image. I only needed thirty-one images, one for each day of the month. It took some time to come up with this, because it had never been done before in memory research. People have memorized decks of cards and the periodic table, but never one hundred days of their own life.
HILDE: Some researchers think that people who are depressed should try to memorize the positive moments of their lives. Since they have trouble remembering these moments, and their memories are often very general, they could use the memory palace technique to remember the good stuff. Is that what you mean?
YLVA: Not quite. For remembering past episodes and keeping them for later, it's all about memorizing events using the method of loci (the memory palace technique), where you place each image along a route. But I didn't use this method because the order for my images is already determined by the dates. So I made up a meaningful image which I attached to each date. I simply manipulated my memories; I was almost creating false memories. The first of the month, as an example, is a lamppost because it resembles the number one and is a distinct object. Then I placed it in my memory even if I hadn't encountered a lamppost on that day in real life.
HILDE: Are there a bunch of people and things hanging out around your lamppost, then? There's a first day in every month, and you memorized one hundred days, so there was more than one first to remember. How did you separate them?
YLVA: I used my real memories, too, and got some help from related events. We both remember the interview with Asbjørn Rachlew in March; it is somehow connected to the rest of the events that month. I imagined an elephant in the conference room, and it now signifies the eleventh of the month. But I also remember what else happened in March and can navigate according to that, even though I have two other elephants to keep track of. Well, I also have a fourth elephant that snuck in. It was the eleventh of May and the experiment was actually over. I was jogging at Ekeberg and became spellbound by the beautiful sunset over Oslo—the same view as in Edvard Munch's painting _The Scream_ , actually. I wished I could remember it forever! And then, out of nowhere, there was an elephant in a treetop. I mean—try _not_ to think of an elephant! It's impossible!
HILDE: That was perhaps not the beautiful and poetic moment you wanted to remember! So you remember your days by placing a rather vivid image in a memory. Swans, Princess Leia, and tigers, for example. These images don't have an obvious significance, do they?
YLVA: I make a logical association between the date of the month and the image. The fourth is Princess Leia because I like _Star Wars_ , and there's a well-known play on words—" _May the fourth_ be with you," based on the line "May the force be with you."
HILDE: Doesn't the image mess up the memory?
YLVA: That's the nature of memory reconstruction. There are more layers whenever I look back. One is the memory itself. The other layer is an imaginary world, where the swan or the elephant belongs. Then the memory also has a semantic component, the story of what happened when we interviewed Asbjørn Rachlew and his daughter was sitting with us, for example. Other episodes may also attach themselves to the memory, like running into my friend Gro on the way there. But why are we talking about everything I remember from these hundred days? We were supposed to be talking about forgetting!
HILDE: I'm just thinking that all this memorizing... perhaps it says more about forgetting than remembering.
YLVA: What do you mean?
HILDE: I mean, don't you get a little bit tired of remembering all this stuff? Don't you wish you could forget a lot of it, as you would normally do?
YLVA: Hmm, yes, it's crazy to think, "Oh no! I don't remember the third of March; I have _lost the third of March!_ " and feel the same panic as when I put a hand in my pocket and realize my wallet isn't there. I thought that remembering this much meant I was taking control of my memories, but maybe it's the other way around—the memories have taken control of _me_. It becomes more apparent to me how prominent the act of forgetting is in everyday life, especially when you contrast it with this manic struggle to remember it all. Normally, I wouldn't have cared if I didn't remember one day, but suddenly it is so important.
HILDE: Has your conception of time changed, now that you suddenly remember so much?
YLVA: It has given a bit more structure to my life. Since I can remember one hundred days in order, it's like I've captured a sequence of my life, rescued it from transience in a way. As if life's account book has memories on the plus side and things forgotten on the minus side.
HILDE: But it's also similar to when a tree falls in the forest and nobody hears it! If a day has passed and nobody remembers it, it still happened.
YLVA: But still, it can be really frustrating not to remember what happened last fall, for example. I find myself thinking, "When I was on holiday last fall, what did I actually do?" And I draw a blank. It's scary, in a way. Even though my memory is quite normal.
HILDE: Maybe the forgetting is an illusion, because when we talk and get onto a specific subject—running, for instance—you do remember that you ran a half marathon last fall!
YLVA: Yes, that's not easy to forget! As a rule, there are many events we don't forget; they just won't appear at the moment you summon them. Memory processes the event and places it in our life script, and makes it context dependent.
HILDE: After a year, when you haven't rehearsed the hundred days in a while, what will happen?
YLVA: That's the exciting part; I have, after all, "Ebbinghaused," so what will remain after a year? Will I beat the forgetting curve? We will see. But how much of the last hundred days will _you_ remember?
HILDE: Hmm, I think I'll remember a fair amount. The most important things, and the ones with the greatest emotional impact, I'll probably remember those best. I don't remember things in order, which you have forced yourself to do. But the important stuff stays. And a lot of what I remember should really be forgotten. Buttering a slice of bread one boring day in February, what's the use of remembering that?
YLVA: I could easily forget the days when I just hung around. Much of what we experience is supposed to get absorbed into the general atmosphere of life. Remembering one hundred days in a row really proves how much we actually forget, despite memory techniques.
HILDE: And if you were to remember every single little detail, it would take a hundred days to remember the hundred days! What's the point of that?
YLVA: I have no need to go back and relive the hundred days exactly as they were. It was really difficult to remember the day I was at home sick, or when I was at home on a Sunday, doing nothing. Or the days we sat at our local café working on this book, like we had done so many times before. According to the laws of memory, those moments are supposed to team up and become a cumulative memory—"writing" or "being sick" or "doing nothing." But I do think that my recollection technique now and then improved things. The seventh of the month was supposed to be the golden day, because my own mild synesthesia makes the number seven sound gold to me. On April seventh it rained, and even though it was a fairly boring and gray day, it rained gold in my mind!
HILDE: As if you were a memory alchemist and transformed the day into gold!
YLVA: It was actually a bit magical. It made my day. But I also appreciate remembering the parts of that memory that didn't include gold. That's what everyday magic really is: knowing that you're alive, letting it rain. But, of course, making up cues is a forced way to access memories. Normally, memories appear via natural association, when we talk about things or hear music.
HILDE: Now the experiment is over. How does it feel?
YLVA: It's wonderful not having to label events all the time. Finally, I can begin to live in the present. Even if it is a bit hard to let go. It is May fifteenth today, and fifteen is always a seahorse. There were a bunch of seahorses hanging by their tails from the beautiful cherry tree outside your door when I arrived.
HILDE: Oh, how symbolic!
YLVA: Yes, but now... it will be such a relief to forget.
_The audience applauds. The credits roll. Hilde throws her cue cards over her shoulder and looks knowingly into the camera_.
We conducted this little experiment of trying to remember one hundred days to have some fun with forgetting. But for many, forgetting is no fun. People suffer from memory problems in all stages of life and for many different reasons.
One common disease that affects memory is, perhaps surprisingly, depression. Lots of people who suffer from depression worry that their memory is bad. Worrying is a natural part of being depressed; there is so much to worry about when you feel down. You doubt your own abilities. As we know, remembering is characterized by an enormous amount of forgetting and daily mistakes, and this is completely normal. But when you are depressed, you notice only the negative. The glass is seen as half empty, and you believe that you forget differently from happy and optimistic people, who blindly trust what they think of as their own infallible memory. To fill your working memory with worries also limits the space for other things. "I'm worried that I can't remember things" takes the place of "Remember to call Gerda."
Psychology professor Åsa Hammar at the University of Bergen knows very well how depression can tamper with memory. She has tested many depressed individuals and found that they have a normal learning capacity when they're given several attempts to memorize lists of words. But they struggle to remember them after having heard them only once. When the words are repeated, they remember normally. It's as if they're overwhelmed by the first round. Part of the explanation for memory problems associated with depression has to do with attention and working memory, not the actual storing of the memories.
"That's the way it is with most things we try to remember on a daily basis," Hammar says. "Usually, we have only one chance to catch a message." Friends tell us what they did during their vacation just once. We have that one chance to consolidate the information into long-term memory. It isn't strange, then, that individuals with depression feel forgetful, since they need repetition to remember.
"Generally speaking, patients who are depressed also struggle to remember in the aftermath, when they no longer are depressed. They don't remember messages, what to buy in the store, and they miss central elements of conversations. Many may be afraid that they have some brain damage. My studies show, however, that depressed individuals remember as well as others; they just have to allow themselves more time and more attempts to do so."
In collaboration with Yale University, Hammar's research team has discovered another effect of depression on working memory. Individuals who had been depressed were shown several pictures of faces in a row and then got to see one of them again. They were supposed to say where in the row that picture had appeared. They were asked to do this with rows of sad faces and rows of happy faces. This is a relatively simple task, but those with depression struggled disproportionately with the task when the faces were smiling. It was as if they didn't "see" the happy faces. Hammar's explanation is that depressed people have a tendency to be drawn to the negative and almost overlook the positive. Then the complexity of the task was increased, and the subjects had to point out where in the row the face was shown—if the rows were in the reverse order. Their ability to remember the sad faces better made them perform poorly—with both happy and sad faces.
"The bias toward the negative made the sad faces take up more space in working memory, so that they weren't able to implement a reversal of the row," Hammar explains. The effect of bias is clear when people are presented with a difficult task. A particularly interesting finding is that difficulty performing this sort of task can help predict who is at risk of recurring depression. The more difficulty someone has, the greater their risk of recurring depressions. These results suggest that this failure of working memory may be a vulnerability that people with depression unfortunately carry with them, making it harder to keep depressions away.
An incredible number of people, upwards of 12 percent of the population, suffer from depression, which consequently limits their memory. One percent of the population is affected by epilepsy, making it one of the most common neurological disorders. Henry Molaison had epilepsy, but epilepsy wasn't the main cause of his poor memory; it was surgery that left him with such severe amnesia. Epilepsy itself can cause milder memory problems, though, both in children and adults. Epilepsy is a disturbance in the way the brain functions. Epileptic seizures are caused by uncontrolled electrical activity in the brain; it's like an electrical storm. During a major seizure, a person, who is often unconscious, experiences violent spasms in their arms and legs. The seizure usually doesn't last more than a couple of minutes. But there are other types of seizures, depending on the type of epilepsy. Some have seizures that are so short they are almost undetectable; people just get a distant look in their eyes for a few seconds. These are called absence seizures, because people are "absent" for a few seconds. As mentioned, Henry suffered from these absence seizures as well as major seizures. Even if the seizures last for no more than twenty seconds, they can be enough to disrupt attention and memory formation. Many with absence seizures have attention difficulties extending beyond the seizures, which can make it more difficult for them to learn things at school. Both major seizures and absence seizures are accompanied by epileptic activity in large parts of the brain.
Epilepsy can also stem from a more defined region of the brain. One type of such focal epilepsy is temporal lobe epilepsy, which begins in the temporal lobe. That's where the hippocampus is too. Here it is sometimes a dysfunction, a disruption in normal wiring of neurons, or an injury that causes a focal epileptic seizure. During these seizures, people often feel a sinking feeling in their stomach or a strong feeling of déjà vu, the feeling we all sometimes have that what we're experiencing now has happened already. The only difference is that these feelings of déjà vu are stronger and more frequent in people with epilepsy. Following the déjà vu or the strange gut feeling, the seizure may spread to a wider area of the brain, causing the person to seem "absent" for several minutes, often making smacking noises with their mouth and fidgeting with their hands. Since this type of epilepsy is often caused by damage or dysfunction in the hippocampus, it can also be accompanied by everyday memory problems. People may also forget their seizures, sometimes even the period before and after. Even today, temporal lobe resection is offered as a surgical treatment to some of these people—but only on one side. As long as we have at least one hippocampus left, our memories are safe, relatively speaking.
One person who has tried this surgery is Terese Thue Lund. After dealing with epilepsy for years, without much success with medication, doctors suggested brain surgery. In 2015, surgeons removed about the front inch of her right temporal lobe, including most of her hippocampus, in the hope that it would cure her epileptic seizures.
The jury is still out on the result of the surgery for her epilepsy, but one thing is clear—Terese's memory, which was bad before the surgery, has not been made worse. If anything, it may be better.
If you didn't know, you wouldn't suspect that anything was missing in her brain. We are visiting her at her apartment in Oslo, and she is friendly and hospitable, laughing easily. Her living room is spotless, and on the table are home-baked cupcakes. She tells us she is busy planning her wedding. There is a lot to remember, but she doesn't want it to be stiff and formal.
"I obviously know that I forget things. I have to make a note of all appointments, for example," she begins.
"All of us have to do that."
"Yes, but I have to check my book at least three times a day, and I still don't remember my appointments. When I take the bus, I don't remember what stop I'm getting off at. I never remember people I've met, unless they're wearing unusual clothes or have a strange hair color. I wish people could wear the same clothes all the time!"
"Will you remember us?"
"I could easily walk right by you in the street. I didn't recognize you, Ylva, but I remember now that we had a very good conversation before the surgery. It was in the white building at the hospital...?"
"My office is not in the white building. That's where the occupational therapists and social workers are. Perhaps you talked to a social worker?"
"Oh, I see. Sorry, then it probably wasn't _you_ I had that nice conversation with, at least not the conversation that I remember!"
Even though Terese deals with her memory problems with a lot of humor and laughter, it's still difficult for her.
"The worst thing is when people bring up things we've experienced together. Most people know what I'm like, but the fact that I can't remember shared experiences with friends hurts them. My maid of honor remembers all the parties we've been to, in detail. And I remember nothing, although I know we've had fun!"
Terese does not remember her first date with her boyfriend. She doesn't remember if she vacationed with him last year or the year before. She worries a bit about her wedding speech, because she won't be able to charm the audience with stories of the sweet, romantic moments she has shared with him. Her surgery was in December, and over Christmas that year she was convalescent. She remembers that.
"After the surgery, it felt as if the fog lifted a bit. I clearly remember spending Christmas at my in-laws'. I remember that they poked their heads in my room and told me the weather was awful. And I rejoiced! They drove me to the sea, and I stood there and got soaked! I stood there and breathed it all in. With the cold rain on my face I just feel so alive; it's fantastic!"
Terese loves weather, she says, and by that she means bad weather. A wild storm, the sea beating the breakwater in Bodø, the northern city where she's from. She doesn't actually remember what she did during her trip south with her boyfriend, but she remembers in detail how they almost froze to death during a winter camping trip once.
"Perhaps discomfort helps you remember things better? The more uncomfortable you are, the better you remember it, it seems!"
She is laughing. We all find the idea of memory therapy based on being uncomfortable a bit amusing.
Terese's memory is seriously damaged, we know—the three of us sitting around her coffee table, where pictures of the most important things in her life sit under a sheet of glass. There are photos of her with her boyfriend, of northern Norway, and of her dog, as well as comic strips. Undergoing brain surgery where you can potentially lose your memory—what little there is of it—has not been easy for her. She has endured many years of examinations and tests, electrodes both outside and inside her head to measure epileptic seizures, MRIs, memory tests. It wasn't till the surgeon was certain she would not suffer a great further loss of memory that he felt confident enough to cut into her temporal lobe to remove the seahorse and the surrounding brain tissue.
Terese can't study because she forgets everything she reads. She is on a leave of absence from work and has to organize her day in a way that is meaningful to her. She works out, walks the dog, plans her wedding, and meets up with friends. She was diagnosed with epilepsy in 2008. But doctors believe she has had epilepsy since she was a child, when she had nocturnal seizures.
"I'll still have a good life, even though there are many things I can't do. I have a future with a husband and kids before me, and friends and family," Terese says while gently petting her dog, Prudence.
It will be a few years before she knows for sure that her surgery was a success. If she has no more seizures, she can gradually stop taking medication. Epilepsy drugs can also hinder memory as they have a bit of a slowing effect on the brain. Many people have to take several different epilepsy drugs to keep their seizures at bay, while at the same time struggling with side effects. But the alternative—not taking medicine—can also damage memory, especially if the seizures are severe and frequent.
Epilepsy, ADHD, and depression are some of the most common disorders threatening memory from within. But memory can also be damaged from the outside. Head injuries, like the ones you can get in traffic accidents or as a result of sports trauma, are among the most serious threats to the brain, and they mostly affect young people. Falls and accidents can happen to people of all ages, but while older people experience stroke and dementia as natural consequences of the aging brain, young people pretty much have only head injuries to worry about, at least in regard to memory loss. Head injuries often lead to memory difficulties. While ADHD affects memory by way of derailing our attention, and temporal lobe epilepsy causes memory loss by damaging the hippocampus, head injuries attack memory from many directions. Attention, working memory, storage, and recall can all be affected, to a greater or lesser degree. On top of all that, many head injury sufferers experience fatigue. They get worn out easily and therefore have difficulties staying focused. Even though many head injuries are isolated incidents after which victims improve during the first couple of years, there are also many that cause permanently impaired memory. Head injury is a chronic disorder, even if it was initially caused by an acute incident.
When the memory of a young person is affected, it often happens unexpectedly, because we take memory for granted. Then old age sneaks up on us, and we forget more and more. Throughout our adult life, the cortex shrinks a tiny bit for every year that passes. When we reach old age, it shrinks faster. Brain cavities gradually grow as the brain's white matter disappears. For most people, that's all that happens. We have a difficult time learning new things, and things that are easy to forget, like names, go missing more often than before. But one thing that aging doesn't diminish is the wisdom we have accumulated over a lifetime. Our memories and life experience, even if things gradually take longer to assimilate, become part of one large knowledge bank. Young people may think faster, learn faster, and have a more efficient memory, but old people have an advantage in life experience. Growing old is not about decay, but about change.
With age comes a greater risk for developing brain diseases. The most feared variety of forgetfulness in the present day is Alzheimer's disease. The front pages of major newspapers often report new, small breakthroughs in research. It is one of our era's greatest health challenges, and the hunt for an answer is as complex as the search for a cure for cancer. Julianne Moore won the 2015 Oscar for Actress in a Leading Role for _Still Alice_ , in which she portrays a woman afflicted by early-onset Alzheimer's. The desperation the character, a world-renowned linguist, feels when she realizes that she may forget her own children is something very familiar. We could write a whole book on the subject: what happens in the brain, how the disease is experienced by the afflicted person and their family. How nursing homes help by playing music from the patient's youth, awakening something in their reminiscence bump. We cannot do justice to the subject of Alzheimer's disease in a book that's supposed to contain so much else. We have to make do with a couple of paragraphs.
As we live longer than in times past, the task of maintaining the structure and function of our bodies grows bigger. The structure in this case is the brain. Getting wrinkles and liver spots, needing a walker, having a hunched back, losing muscle mass—those are things we can live with. But to lose our memory, and thus lose our grip on existence, is scary. It sneaks up on us. In the beginning, it's difficult to remember names, messages, what we did yesterday. But this is quite similar to what everyone experiences as they age. Memory loss comes with age. It's easy to chuckle when old people start to become a bit forgetful. However, at a certain point it turns into something more serious. As the disease spreads to the whole brain, we need help with everything, and we grow more and more distant. Before it gets that far, though, we've experienced a gradual loss of memory. The hippocampus is affected first, which means that new memories can't be consolidated the way they were before. Alzheimer's patients can tell detailed stories from their own childhood and youth but won't remember that you visited last week. It is a little like the amnesia Henry Molaison had, only not as bad—to begin with. Before we reach the stage of amnesia Henry had, large parts of the brain are affected. In addition to memory problems, Alzheimer's patients struggle with a range of symptoms including language difficulties, emotional disorders, and problems making plans.
No one knows the exact cause of the disease. Some _think_ they have found it, while other researchers disagree. So far, the most popular explanation is that waste accumulates around neurons, creating what they call an _amyloid plaque_ , and disrupts neurons to the point that they commit suicide (neuronal suicide, that is). This is, of course, not good news for the brain. We all lose a bunch of neurons on a daily basis, but in Alzheimer's patients it happens much faster. Both the ability to consolidate new memories and, gradually, the memories themselves, stored in various places around the cortex, dissolve. Another change in a brain with Alzheimer's is an increase in what is called _tau_ protein within neurons, leading to a buildup of damage inside the cells. Researchers disagree on whether it is tau or amyloid plaque that causes the disease. Or perhaps there's an undiscovered culprit? But where do the amyloid plaque and tau come from? Is there anything we can do to prevent them from accumulating in the brain? At the moment, we don't have the answers. However, we do know that the process leading to Alzheimer's starts several decades before the disease is detectable. If we have any chance of halting the disease in the future, we probably have to intervene early, long before we're certain that we're going to get Alzheimer's at all. If we're going to find a treatment that stops Alzheimer's disease before it is too late, it is important to understand exactly how it works. This will require continued, massive effort by thousands of researchers around the world.
What's it like not to remember anything? Do we even know what we're forgetting? That's the definition of amnesia: not remembering, and not knowing what we forget. It's a diagnosis assigned to very few people.
Our friend Henry Molaison from chapter 1 suffered from amnesia, maybe the most severe form. Since he was unable to store memories from moment to moment, everything that happened after his surgery was an isolated moment, trapped in the present. He had his life story, but everything that happened to him after the age of twenty-five (including the two years prior to the surgery that were also gone) didn't remain. He had what is called _anterograde amnesia_. In order to get this form of amnesia, both hippocampi would have to be seriously injured. Damage to other parts of the brain can also result in this type of amnesia if those parts are closely linked to the hippocampus. Stroke, encephalitis, and sometimes even severe heart attacks can all impair both hippocampi.
For some—very few—their whole lives are defined by the inability to remember anything, from the day they were born. They have a rare form of hippocampal dysfunction, something which will affect their development and change the course of their lives. This condition is called _developmental amnesia_ , since it begins before a child develops into an adult. The cause isn't always known, but in some cases it is blamed on a difficult birth or respiratory problems in premature babies. The hippocampus is very fragile, and a lack of oxygen can affect it especially severely. This form of amnesia is special because those with it aren't completely unable to form memories, like Henry Molaison—they manage to learn a great deal in school, although they need a lot of help. But what they lack is personal memories. An anonymous English patient whom researchers refer to as Jon is among them. He has an IQ of 114, well above average. He is smart, but he _remembers_ nothing! He is married and lives as normal a life as possible. He has probably acquired factual knowledge slowly, through repetition and a meaningful context, but he has no memory of going to school to learn anything. He _knows_ that he is married, in the way he knows any other fact, but he has no actual memories of the wedding, first meeting his wife, or their first kiss. He doesn't even know what it's like to recall memories—he's like someone born blind, not knowing what it's like to see.
Most people with any type of amnesia retain memories from earlier in life but struggle to consolidate new experiences. But there's a small subset of people who suffer from another form of severe memory impairment: _retrograde amnesia_. For these people, all earlier memories vanish—they're erased from the hard drive, so to speak. This is one of the greatest mysteries when it comes to forgetting. Since our memories are distributed throughout the brain, how can all of them suddenly disappear? It's hard to imagine that every memory from an entire life could be erased. Nobody has been able to explain how it could be caused by brain damage, either. Sometimes individuals with retrograde amnesia have been discovered far away from home, without any knowledge of who they are. Even in Norway, there have been some famous examples. In December 2013, a man was found lying in a snowbank on the side of a street in Oslo. He didn't remember who he was or where he came from, but he understood several eastern European languages and spoke good English, albeit with an eastern European accent. He was bruised, with cuts all over his body, but the police couldn't figure out what had happened to him. There was likely some criminal context. The man was eventually reunited with his family in the Czech Republic, and the family connection was confirmed by DNA analysis.
For some people, a serious psychological reaction may be the reason for their amnesia. It's as if their entire personality is switched off so they can start over again. The way it often begins is that they will go into a daze and then take off on a trip, apparently without a goal or a reason, typically without identification papers. Some regain their memory through therapy. For others, it's as if the label "I," tied to all personal memories, is erased for good. For some, brain injury (such as from cardiac arrest) may be to blame, but it's still a mystery to memory researchers how memories from an entire life can be gone, as if suddenly deleted. Perhaps the hippocampus is the key here too. The hippocampus ties everything together, all our experiences, the places we've been, and the feeling of connectedness between our memories and our self.
On November 28, 2000, Øyvind Aamot (who now goes by the first name Wind) sent an email from China to his mother. This was the last sign family and friends received that he was alive before he was found three weeks later in a village, with ID papers and plane tickets. He remembered nothing from the previous twenty-seven years, his whole life to that point. He didn't remember who he was, where he came from, or anything he had experienced up to that point. A third of an average life span. Most of us have memories from early childhood, but what is Wind's first memory?
"It's not what people think. Many want to believe that I woke up on a train in China without any memories, because it makes sense based on what they know and understand. But I _didn't wake up_ in that way, and I don't think it is that easy to turn what I experienced into a linear story," Wind says.
This is what we know: Wind was twenty-seven years old, working as a freelance journalist, and had developed an interest in anthropology. While on a sailing trip around the world, he told his friends he was going to travel into the Chinese mountains to study equestrian nomads. A month later, no one had heard from him.
He can remember being on a train. He knows that he was found unconscious and sent to the doctor in a car. However, it's difficult to establish when he took the train and when he was at the doctor's. Twice he was found unconscious and helped by villagers in the province of Hunan. It's possible that these episodes have something to do with the matter. A diving accident sustained during his sailing trip could also be the cause, perhaps combined with the fact that he had meningitis as a child. Doctors speculated that some sort of poisoning could have caused the amnesia. Or maybe something completely different had happened. Ten psychology specialists examined Wind afterward without finding the answer.
It took a long time before he became aware of himself again and realized the situation he was in. He just followed others; he was in a passive state. He didn't answer when people asked him questions, he didn't reach out to anyone, he didn't know where he was going. When he saw people standing in line, he joined them. When they reached into their pockets, pulled out something, and handed it over, he did the same, at the same counter. Then he was given food, without having any notion about lineups, stores, or money. Twenty-seven years were completely gone and with them all awareness of how the world works. He had become a man without a memory, a person with retrograde amnesia.
It's a very rare state. There are likely only a few hundred people in the world (we don't know exactly how many there are) with this experience: losing all their memories except for language and motor memories.
Unlike Henry Molaison, people with retrograde amnesia can create new memories. Coincidentally, Henry lost the ability to create new memories at age twenty-seven, while Wind started his life from scratch when he was that age. Twenty-seven-year-old Henry's life extended backward in one direction, while Wind's stretches in the other—combined, the two men have memories of a full life.
"I was helped by so many in the beginning, but I didn't understand the concept of helping. It took a long time before I realized what people were doing for me, and then I was filled with enormous gratitude. I cried long and hard then. In the same way, I didn't know what a friend was, but it was a word I heard all the time, so I noticed it and remembered it. It was always when something good was happening... I started to see everybody that reached out a hand or sent me a friendly glance as a friend," Wind says today.
He has learned to live with his first twenty-seven years being gone. He has reconnected with friends and family. The now more than forty-year-old man has smile lines bearing witness to four decades of laughter, but he has only fifteen years of pleasant memories. But maybe this is an oversimplification.
"You are asking if I miss what I don't remember?" he says and laughs. "How would that be possible? Like you, I have gaps in my memory that I fill in, only my gaps are probably a lot bigger than yours. When someone tells me what I have experienced before, I can visualize it, and it evokes emotions. I call these emotional memories. Immediately following my amnesia, I had no contact with these memories."
Wind has picked up these stories about himself and linked them to the part of his memory which is subconscious, but which reminds him of who he is, of his emotions. When a friend told him about the time he threw a cheese sandwich in his face in elementary school, Wind could picture it, and he could recognize the emotional reaction and the humor between them. That's how he has reconstructed a good deal of his past. It is no longer a large, black abyss of nothingness. He has established continuity with the person he was before he lost his memory—a man with a sparkle in his eye.
How can we determine what's actually true when amnesia devours the memories of the original events? Wind Aamot has filled his past with reconstructions of what he has experienced. They are, in a way, false memories about real events. But it doesn't bother him. He has a feeling of continuity, identity, and truth, even though his life up to the age of twenty-seven is a mixture of reproductions from others and voids in his memory. But everything is linked to the emotional core of Wind's personality.
Which of our memories are true and which are not is something we may never know. It doesn't change who we are. The truth about forgetting is that we are forced to live with it, embrace it, and let it do the job of chiseling out the most important things that will stand out like monuments in our memories, even if that means forgetting all those little things we wish we could remember.
— 7 —
**THE SEEDS OF SVALBARD**
**_Or: Traveling into the future_**
Our revels now are ended. These our actors, As I foretold you, were all spirits and Are melted into air, into thin air:
And, like the baseless fabric of this vision, The cloud-capp'd towers, the gorgeous palaces, The solemn temples, the great globe itself, Ye all which it inherit, shall dissolve And, like this insubstantial pageant faded, Leave not a rack behind. We are such stuff As dreams are made on, and our little life Is rounded with a sleep.
**WILLIAM SHAKESPEARE _,
The Tempest_**
LIKE PART OF a set from a science fiction film, a building protrudes out of a snowy plateau on Svalbard, an archipelago in the Arctic Ocean. The front of the tall, narrow concrete structure is illuminated by a piece of art that sparkles like snow crystals during the day and northern lights during the night. Otherwise, the structure is completely unremarkable, and most days of the year it stands solitary in this majestic landscape. Through the door there's a corridor that leads to three concrete chambers. Inside these the future of the world's food supply rests in little plastic packets containing various seeds: black, yellow, oblong, round, striped, hairy. Here they wait, side by side.
Svalbard's Global Seed Vault was opened in 2008. Inside, the permafrost keeps the temperature at a steady minus eighteen degrees Celsius all year. The seeds are deposited here from countries all over the world in an international effort, operated by the Norwegian government in cooperation with the Global Crop Diversity Trust. All deposits belong to the countries that made them and can be withdrawn at any time. Hundreds of rice and wheat varieties—each country's agrarian heritage—are kept here. While the seasons turn and winter storms rage, while wars are fought on the other side of the globe and temperatures rise, the seeds lie in the cold, quiet concrete, waiting for the future.
It has been nicknamed the Doomsday Vault. Some have, throughout the process of developing the Seed Vault, envisioned Earth's future, the nuclear wars, climate changes, fields where nothing grows because of drought and new invasions of pests. If the worst happens and the continents look like an uninhabited Mars landscape, the seeds can be withdrawn and give humanity new hope. There has actually already been one withdrawal, after seeds from Syria's national seed bank were destroyed in their civil war. Svalbard's Global Seed Vault is not really meant to be saved for doomsday; it's a running backup for all the depositing nations, for the benefit of Earth. Doomsday is not a single event looming in the distance; it's happening now in the form of natural catastrophes and wars. It's coming gradually, so slowly that we hardly even notice it. Climate change and mass migration are continuously changing our world little by little, every day. The Seed Vault itself has recently been affected by melting permafrost.
But where does the changing future begin? Where do new ideas about the future sprout? In our own seed bank, our memory.
All of us reminisce, more often as we age. Maybe it starts in our twenties, as we read old assignments from elementary school, and ends in a deck chair outside the old folks' home, a photo album in our lap. But reminiscing itself has no evolutionary function. Our flexible, unreliable memories are changeable for one reason: they are supposed to be used; they are not museum objects. Why would nature invest in such an expansive—albeit deceptive—memory if we weren't supposed to use it for something essential? This is where past meets future. One wouldn't be possible without the other. They lie at opposite ends of the dial of our internal time machine. Turn it to the left, and you travel backward in time. Turn it to the right, and you travel forward. Our memories are the prerequisites for mental time travel into the future, for our plans, dreams, and fantasies. It can't be the prospect of an ever-increasing stack of memories to look back on that makes us yearn for eternal life, or at least a very long one. Rather, it must be the thought of always having a future ahead of us. Visions of the future are a natural part of past memories, not only because the past helps us predict the future, but because the process that gives us vivid memories _is the same_ as the one that we use to imagine the future.
Counting future thinking among the core functions of memory has not always been the case within memory research. It wasn't something researchers cared much about until the 2000s. One of the pioneers in this regard is Thomas Suddendorf at the University of Queensland in Australia. He speaks to us via the internet from the other side of the globe. Even this is a form of time travel, where eight o'clock in the morning in Oslo meets four o'clock in the afternoon in Australia. In a way, Thomas is speaking to us from the future—just eight hours into the future, but still.
"During all these years, memory researchers have been preoccupied with how people remember correctly, ignoring the important question: Why do we have a memory in the first place?" he says.
In 1994, he and Michael Corballis submitted a paper on the human capacity to imagine the future to a number of psychology journals and were rejected.
"Finally, we were published in a small journal that hardly anyone read," he tells us. The journal has since folded.
"Memory has traditionally concerned what can be measured as correctly remembered. Naturally, future thinking cannot be measured in that way," he suggests as an explanation for the initial lack of interest.
Ten years later, the tables had turned. _Science_ magazine named research into mental time travel and episodic future thinking as one of the scientific breakthroughs of 2007. Suddendorf and Corballis's article, "Mental Time Travel and the Evolution of the Human Mind," published in 1997, is one of the most important cornerstones in today's research into episodic future thinking.
"It's a poor sort of memory that only works backwards," says the White Queen in Lewis Carroll's children's classic _Through the Looking-Glass_. It may be that the Queen was quite right: proper memory works both ways.
According to Thomas Suddendorf, the explanation for our fallible memory lies in the evolution of our species. Throughout the history of human evolution, about six million years of it, our environment has changed and forced adaptations in our genetic material. Natural selection does not only favor physical characteristics like opposable thumbs and upright walking, features that aided survival and reproduction among early humans. The human mind was also shaped by evolution. From the perspective of evolutionary psychology, we must always ask what a particular mental function means to survival and reproduction, if it's something universal to humans, not just a local, cultural variation. We can safely say that memory is universal.
"If, for some reason, it was important to humans to preserve an exact copy of the past, then that is what our memory perhaps would give us. But why would we need a replica of the past? It is the future that matters the most. The future holds potential partners and perils. Most of us have a tendency to remember our successes better than our failures. This biases our self-image. What if this is more advantageous when meeting a new potential partner?"
The evolutionary advantage is the strongest argument in favor of a memory system that houses both past and future mental time travel, according to Suddendorf. Or rather: it is actually an argument in favor of memory being a byproduct of the evolution of future imagination. The past is useful only inasmuch as it helps us predict the future. Our malleable, unpredictable, yet vivid memory would not have evolved had it not been for its usefulness in creating vivid, insightful scenes of the future.
"It's the same for all memory functions. Take Pavlov's dogs as an example. They produced stomach acid and drooled when they thought they'd be fed, and when Pavlov repeatedly rang a bell before he gave them food, the dogs began to drool and produce stomach acid at the sound of the bell. This has been used as a prime example of memory, but isn't it more accurate that the dogs drool in anticipation of the food that's coming in the future?"
Pavlov's dogs didn't have to look into their own future, though; they were more like passive recipients of a new connection between sensory impressions in their brain, called _classical conditioning_ —a kind of memory without any conscious awareness or will. This type of learning happens in all members of the animal kingdom, from amoebas to humans. But even this primitive form of memory is the product of a need, in all living beings, to be able to predict the future and thereby ensure survival.
"The human way of creating future scenarios and retrieving vivid memories must have had a huge evolutionary advantage. Having an open-ended and flexible memory system allows for an endless set of possible future scenarios that are being constantly evaluated in our minds," says Suddendorf. His book _The Gap: The Science of What Separates Us from Other Animals_ takes us on a journey back in time, to when Earth was populated by early hominins: _Australopithecus_ species, _Homo erectus_ , _Homo neanderthalensis_ , and, eventually, _Homo sapiens._ The traces they have left behind actually offer some clues to how their minds must have worked. The emergence of sophisticated stone tools suggests that they were increasingly capable of not only acquiring food, but preparing themselves for the future. "Consider _Homo erectus_ , who lived on Earth from around 1.8 million years ago up until as recently as perhaps 27,000 years ago; they developed a kind of handheld axe, useful for cutting meat, among other things. These are elaborate tools, not for throwing away after use. They have carried them along with them—they were armed, so to speak," Suddendorf says.
_Homo erectus_ envisioned a future need for food and protection from predators. Early hominins were scavengers, not hunters, and their need for weapons was for protection—a future-oriented need as much as anything else. Being prepared for perils that may appear at any time in the future is highly advantageous for a creature in the middle of the food chain. As the early humans became increasingly carnivorous, planning for hunting and storage became useful.
An even more convincing argument for a future-oriented _Homo erectus_ mind is the discovery of what seem to have been workshops—places where they practiced making axes. They're a powerful clue to understanding ancient future thinking, according to Suddendorf.
"We have found remnants of a number of stone axes in certain locations, as if individuals gathered there to practice making them and teach each other. Consciously honing skills is also something that has made humans very flexible when it comes to preparing for the future. By learning the _art_ of making an ax, _Homo erectus_ was reassured that he would always have an ax, even if he lost one!"
_Homo erectus_ would be able to face the future equipped for whatever might happen. The ability to imagine future danger and make an ax to defend oneself against it was one of the first steps toward modern humans' spectacular visionary abilities. Telephones and trains, computers and airplanes: none of these would have existed if we hadn't dreamed of them first.
This ability has accompanied humankind across continents, then thousands of years later through a large-scale industrial revolution, all the way to planning an expedition to Mars. Artists, philosophers, and scientists have imagined helicopters (the universal genius Leonardo da Vinci), robots (the author Karel Čapek), spectacular future cities (the filmmaker Fritz Lang), and brain scanning for thoughts (the filmmaker Wim Wenders)—the last not unlike what modern fMRI researchers are approaching today. These dreams have, in many cases, predated the technology by hundreds, and sometimes thousands, of years. Even the ancient Egyptians dreamed of traveling to the Moon.
All humans are visionaries, and the basis for their visions lies in their memory. Our memories are the fuel for our imagination. Imagination, in turn, is the energy that brings memories to life. Remembering is actually imagining what happened. Of course, many of the details of a memory are actually stored somewhere. But the moment the memory enters consciousness, in a wave of reexperiencing, it is already reconstructed—the fragments taken from memory are transformed into a coherent experience and story.
Looking at it this way, there's not much difference between reconstructing something that _has_ happened and constructing something that has never happened—or hasn't happened _yet_. As with memories, future thoughts aren't built from completely random details. The more we know about the world—the more experiences we've had—the easier it is to picture them as part of the future. Future scenarios are less detailed and less lifelike the further into the future they get. Today's NASA researchers, planning a Mars expedition in the 2030s, can envision more realistic scenarios when they base their projections on pictures they have seen of Mars's surface. Their vision might combine the photos from previous Mars expeditions and perhaps their own experience of climbing a mountain. In the 1700s and 1800s, people imagined Mars in totally different ways. There was no lack of fantasies about who might live on Mars and what the surface of the planet might look like. Its imagined appearance was based on a few sometimes inaccurate images glimpsed through telescopes. What prior experiences caused people to imagine little green men, we will never know.
The best part of this natural time machine is that access isn't restricted to a few lucky people. All of us have it. You may not have noticed it before, but try to think of how much of your day you spend in the future. Are you thinking about what you will have for dinner later today? Are you looking forward to your vacation in two months? You picture it for a few seconds: the plane ride, the warm Jamaican sun bathing your face, the beach and the waves.
There are some situations where it is easier to imagine the future than others—like when you are about to go on a first date. Never are you as engrossed in the future as during the days before the two of you meet. You plan what to wear, where you're going to meet, how you'll greet your date (with a hug or a handshake), what you'll talk about, what you'll do. Internally, you act out the dialogue between the future you and your possible future partner. Sometimes it can seem so real that your feelings are aroused. The synesthetic Solomon Shereshevsky, the man who could not forget, had an almost overpowering imagination. Once, as a schoolboy, he didn't want to leave bed for school, and so he imagined himself going down to have breakfast and leaving for school. The vision was so realistic that he stayed in bed, actually believing he was already at school. For most of us, though, imagining the future is just a natural part of our daily mind wanderings, part of our stream of consciousness, which can just as easily take us back in time as forward. We are all time travelers, all the time.
As far as our brains are concerned, the past and future are almost the same. Only when we consider what the mental time machine actually provides us, in the form of future time travel, can we truly understand the essence of memory, with all its faults and lies. So how do we research the connection between memory and future imaginings? The usual memory tests don't work. Memorizing lists of words can't measure thoughts of the future. For a long time, the future seemed too hard to control, too subjective for research. Envisioning the future was largely the domain of poetry and literature—it has certainly been the cornerstone of the whole science fiction genre. Not until psychology was revolutionized by technology and the invention of fMRI scanning was mental time travel into the future a real interest to researchers. Just as brain imaging made our personal memories "visible," it also suddenly made it possible to see what happens in the brain when we look forward in time.
The opportunity provided by fMRI made Harvard researchers Daniel Schacter and Donna Rose Addis jump on the bandwagon. In 2007, they published an essay in the journal _Nature_ titled "Constructive Memory: The Ghosts of Past and Future," which has become an important reference. Through several experiments, they have pointed to a striking similarity in brain activity when people reminisce and when they imagine the future. Their volunteers are typically presented with a cue word and asked to retrieve a memory, or imagine something that may happen in the future. As they commence their time travels, a set of overlapping brain regions stand out.
Imagine taking part in one of these experiments. You lie down in the scanner, holding in each hand a button to press as responses. A small cage-like device is placed over your head, with a mirror allowing you to look out through the tunnel of the MRI machine to where instructions are presented on a computer screen. While the machine makes all the possible types of clicks and bumps you can imagine (yes, it is a noisy affair), you see cues on the screen, like "beach," triggering a memory or a plan for the summer ahead. For a few minutes, the big, noisy magnetic tunnel is transformed into your own personal time machine, taking you to your summer house where you put your luggage down, kick off your sandals, and open the dusty curtains and the door to the terrace, letting the warm sea breeze embrace you.
After a couple of rounds back and forth in time, the experiment is over, and the researchers can start tracing the time travels in your brain. What are the internal mechanics of this time machine? The hippocampus seems to be involved, but it's not alone. There is also an area in the front and toward the middle of the brain that appears important. An area farther back, also along the midline, looks to be active—it's probably some kind of network hub. Other areas take part too. Time travels make a distinct pattern in the brain, suggesting a network with its own special function. What surprised the researchers perhaps the most was that this network looks suspiciously similar to the so-called default mode network, which is activated when people are asked to try not to think of anything.
We talked about this default mode in the chapter about personal memories—do you remember? Probably not, so we'll do it again. In most fMRI studies of everything from linguistic understanding to working memory, a resting state is used as a control condition—the baseline state of activity we compare the task activity to. That's how researchers are able to show that, compared to not thinking of anything in particular, we largely activate areas in the outer layer of the frontal lobe and the back of the brain when we solve complicated working memory tasks. Relatively speaking, that is. The whole brain is, after all, active at all times. It is the differences between activities that show how we use different areas of the brain more or less.
The default mode, however, isn't just a blank state. What do we normally do when we think of nothing in particular, when we don't focus on a task? We let our thoughts wander. There is a symphony of the past and the future playing in our heads—yes, in yours too—while we are waiting for our next task. We think about what we will do when we are done with the experiment, what we will do later that evening, what we did the previous weekend, and perhaps something fun that happened on the way to the experiment. There's a lot of evidence that the default, basic state consists of a free flow of memories and future thoughts. According to calculations, people spend more than half their waking time letting their minds wander between memories and future thoughts; what has happened to them and what _might_ happen.
"Just think about it," Suddendorf says, "how similar memories and future scenarios feel in our minds. The phenomenology—that is, the quality of the experience—is almost the same."
With a biological footprint in the brain, so to speak, there is no longer any doubt that episodic foresight can be studied scientifically. But the future is studied in other ways as well. The contents of our future time travels can't be measured by fMRI. They're typically measured using questionnaires or interviews, designed to capture the richness of sensory experience as well as its coherence and vividness; it can be as flat as a news story, or as lively as a real experience.
An interesting feature of both memories and episodic future thinking is that their point of view can vary. Are you the "I," or an observer watching yourself from above? Sometimes, you see the events approximately as you did see them, or will see them: through your own eyes. You see the restaurant table sitting between you and your date, your potential future partner on the other side. Other times, you see yourself from the outside: from afar, you see yourself and your date looking at each other across the table—and this feels more distant.
Sometimes, asking people to describe their future thoughts in detail can reveal how they experience imagining it. Some of the story will concern the narrative, how things will unfold. Other details hint at what they experience thinking about it: the emotions, sensory impressions, and personal evaluations. As with memories, future thinking can be either semantic or episodic, factual elements or experiences. To some extent, we can predict what may happen in the future, without picturing it in vivid detail. "Semantic memory is a much older form of memory, in terms of evolution," Suddendorf tells us.
According to him, animals who cache food remember it in a semantic way, not as vivid episodes. It seems impressive when after a long delay, a bird who has hidden away a larva and a nut chooses to ignore the larva and seek out the nut. It may be argued that the bird has an episodic memory of having hidden the larva at that particular place at a specific time and, because of this, now knows that the larva is no longer edible. But according to Suddendorf, it could just as easily be that the bird can tell if the memory has decayed. It has a memory of the larva being in that location, but that memory feels decayed and so is ignored in favor of the memory of the nut, which the bird knows will be edible in spite of the decayed memory.
Even within the span of a human life, the semantic memory appears before the episodic.
"In my research, I have found a convincing overlap between the emergence of episodic memory and the ability to imagine the future in children."
From around age four, kids can relate their past experiences vividly and in detail, as well as plan for the future. They can talk about specific plans and show that they understand that the future may hold different scenarios than the present, including changes in their own needs and states. For example, they may plan on bringing a favorite teddy bear or blanket in case they need comforting.
"The evidence for a unified system where the past and the future go together stems from brain-imaging studies, studies of the similarities in how they are experienced, and from the fact that they develop in parallel in children," says Suddendorf.
An even more convincing argument comes from people with amnesia. It is evident that people with anterograde amnesia (like Henry Molaison, who couldn't store new memories) have only a vague vision of their own future, despite having memories from before the injury. They do have a past, but they can't use it to see the future. It's as if the engine of the time machine is simply not working, even though the fuel of past memories is there. This clearly demonstrates that the future is more than simply learning from past experiences. In 1985 Canadian psychology professor Endel Tulving described an amnesia patient, N.N., who lacked the ability to envision both memories and future thoughts. He asked his patient about the next day:
E.T.: "Let's try the question again about the future.
What will you be doing tomorrow?"
(There is a 15-second pause.)
N.N. smiles faintly, then says, "I don't know."
E.T.: "Do you remember the question?"
N.N.: "About what I'll be doing tomorrow?"
E.T.: "Yes. How would you describe your state of mind when you try to think about it?"
(A 5-second pause.)
N.N.: "Blank, I guess."
When asked to elaborate on the "blankness," N.N. said, "It's like being in a room with nothing there and having a guy tell you to go find a chair, and there's nothing there."
There are exceptions, though. Future thoughts don't always depend on the hippocampus and don't necessarily use the same machinery as episodic memories. People with developmental amnesia, those born without the ability to create episodic memories, can still imagine the future. You may remember Arne Schrøder Kvalvik, our friend the musician, who could recall hardly any real memories from his childhood? He still worries about frightening mishaps that could befall him or his children, so the ability to envision the future is not missing for him, at least in a semantic way.
Eleanor Maguire and colleagues speculate that this ability may be due to the brain adjusting to a lack of memories by changing which network contributes to future thinking. It's similar to the way that children born with damage to the brain's language center can still learn to talk, because the brain moves the language center to the healthy half of the brain. Those who develop amnesia as adults can't reshape their brain that drastically; it takes a natural malleability that only the developmental potential of childhood can offer. Those born with a damaged hippocampus can develop new brain networks to take over the vital ability to plan the future. Why, then, can't other parts of the brain take over creating episodic memories in developmental amnesia patients? The answer must be that the hippocampus holds a unique position in binding experiences together in time, at the exact moment they happen. The future has of course not happened yet, and so hasn't been encoded by the hippocampus.
People with depression also have difficulties envisioning the future. For them, the future isn't just gloomy—it's also blurry. Researcher Mark Williams examined a group of individuals with depression in 1996 and found that both their memories and their future thoughts were very fuzzy and general. They did not contain as many specific details as those of happy people. There are consequences to this lack of detail. Seeing the future can present solutions to problems. Imagining a pleasant get-together with friends could mean reaching out to those friends, breaking the isolation that contributes to depression.
Nobody has spent much time researching how depression affects the mental time machine. Only a few studies have been done since Williams's, and they were done in the 2000s. Williams, in turn, has more recently studied depressed patients' future visions of something far worse—suicide. These thoughts are far from fuzzy in people with depression. On the contrary, they are sometimes experienced in a similar way to flashbacks in patients with PTSD. Williams calls them flash-forwards. He and his research team interviewed previously depressed and suicidal individuals about their perceptions of their own deaths. At their most desperate, their suicidal thoughts were very strong and clear. When correlated with a questionnaire that measured the seriousness of suicidal thoughts—in other words, how imminent potential suicide was—there was an obvious connection with the intensity of the suicidal fantasies. The more lucid the fantasy, the more serious the suicide risk. Williams and his research team urge professionals assessing suicide risk in their patients to focus more on the significance of potentially deadly future thoughts. Within clinical psychology and psychiatry, just like in memory research, the phenomenological aspect has been overlooked.
This neglect may be due to the fact that we undervalue the role of fantasy in determining people's actions. Vividly imagining the future: Isn't that a pointless, self-indulgent activity? Isn't knowing what our options are enough? We think of the future in semantic terms too: we consider the likeliness of possibilities to make predictions about our plans for the weekend, what level of education we might get (at least when we have begun studying), how the climate will probably change. Figuring out what the future may hold is of course useful, but do we need to _feel_ it? Does immersing ourselves in the future actually have a function, or is it only a side effect of the memory we have? Suddendorf is convinced that visualizing future scenarios does have a point.
"Imagining something before it happens is like a simulation where we can test how the action will affect us and feel different outcomes before we make our choice. For instance, if I want to take a bone from my dog, I can base my actions on past knowledge of how the dog might react. I want to avoid getting bitten, so I picture different scenarios for myself: Should I throw a cat at it to distract it, should I shoot the dog, or should I simply try to calm it before I go for the bone? All these options have different consequences. It would certainly not be very beneficial to kill the poor dog—simply thinking of it is immoral. But in my mental simulations, I can evaluate all of this. The simulation makes all the little details come to life so that they can be scrutinized."
Suddendorf prefers to call future thoughts _episodic foresight_ , to use a direct parallel to episodic memory.
So far, we know very little about how important episodic foresight is to shaping our future behavior. We have to remember that there wasn't much interest in future thinking until around 2007. However, a few studies have shown that the episodic system may have a direct influence on problem-solving and creativity. The Harvard professor we mentioned earlier, Daniel Schacter, showed through experiments that when manipulating people into using their episodic memory system more elaborately, they also performed better on a test measuring creativity.
He and his colleagues assigned people to one of two groups and showed all of them a film, which they had to recall later. One group was interviewed thoroughly about the film's details using the interview techniques of modern police investigations—the investigative interview described in the chapter about false memories, the one Asbjørn Rachlew helped introduce to Norway.
The other group received a math assignment simply to pass the time, and to make sure their brains were equally engaged before the creativity task.
Then, during the creativity task, both groups were asked to come up with as many different usages of common objects as they could. (Try it for yourself: How many different things can you do with a pencil?) Those who had gone through the investigative interview were far better at this than the other group. It's as if the interview set their mental time machine into motion, making it useful for creative problem-solving as well.
Another useful aspect of episodic future thinking is that the future can hold rewards for the actions we consider here and now. Imagine that you've just been working out: you're sweaty, you're short of breath, and your legs feel wonderfully heavy as you sink into your couch with a good conscience. Based on previous experiences with working out, you know that this feeling is a treat. By imagining it before you work out again in the future, you get a taste of it, a preview. That motivates you to go and actually work out. We call it _reinforcement_ , those good feelings that motivate us to do more of the same. Such future reinforcements help shape our behavior more than we think. In experiments where people are asked to estimate the attractiveness of a larger, distant reinforcement, as compared to a smaller, more imminent reinforcement, they usually favor the more imminent one. But when they are prompted to imagine the distant reinforcement in vivid detail, the difference between the imminent and distant reinforcements in terms of attractiveness here and now is decreased or even eliminated. That actually makes it easier to postpone an immediate need in favor of a later one. Think of this as the cornerstone of human society and civilization. Some argue that these mental previews of future rewards are what made it possible to develop morality. From an evolutionary perspective, human morality originated from the evolution of an ability to postpone selfish immediate needs in favor of the social reward that is the feeling of being part of the group. Experiencing this reward before committing to the socially appropriate behavior makes it more likely that you will actually stick to it. And being part of the group was certainly highly advantageous, both millions of years ago and now.
This supposed advantage for survival and reproduction isn't in itself proof of anything. That's how evolutionary psychology works: it provides us with speculations and assumptions that may bind clues from the past (bones, stones, cave paintings) and the present (how we seem to use our brains) together in a meaningful way. Thomas Suddendorf goes as far as to claim that mental time travel into the future may help explain the most fundamentally human attribute of all: language.
A vision of the future is most useful when you can share it with others; otherwise you'd need to pursue it alone. Our flexible minds require a flexible communication system. These two needs—seeing the future and communicating it—have gone hand in hand during evolution, together pushing the human mind onward. This hasn't just been a dance for two; there's a third partner, our instinctual need to share and bond with each other. While our closest living relatives, the great apes, strengthen their bonds by picking lice from each other's fur, we humans prefer to gossip. We talk with each other, sharing stories and future ideas. Sharing stories is part of what has kept us together in groups, giving us ample opportunities to share our experiences of the past and thoughts about the future. "We don't know for how long, but certainly humans have had a particular drive to tell each other stories. The oldest recorded story that we know is a cave painting in Lascaux in France, dating back seventeen thousand years. It shows a man lying on his back, in front of a bison. The bison's entrails are spilling out, perhaps as a result of the man's spear, or from a hit from a hairy rhino depicted nearby. We don't know exactly how the story goes, but it is obviously a dramatic one, something that was worth telling," Suddendorf says.
Suddendorf believes such stories are crucial to the human capacity to deal with the future. Through stories, we develop our ability to predict the future and come up with plans to face it.
"Through other people's stories, we learn alternative solutions to common problems in life. Most stories, either traditional fairy tales or modern novels, are about people solving problems. They all have a specific moral: if you do what the main character of the story does, the outcome will be like _this_. It increases your repertoire for solving similar problems in your own life in the future. Learning from each other like this is inherent in us. We don't need to invent the wheel over and over again. But most importantly: we exchange visions of the future."
Psychologist and writer Peder Kjøs believes stories are crucial to living our lives and negotiating alternative life paths. If we feel trapped, we can always go to the library and discover between the covers of books other people's thoughts, feelings, and actions, possible parallel worlds to our own. If we don't want to do that, we can turn on the TV, go to the movies, or read news articles. Stories are such important pillars of our society. How come we're drawn to them so strongly?
"We read novels to be able to imagine other ways to live. Each individual's life and fate is an object of intense interest in our culture," he says.
He thinks the story of the individual hero has been reinforced in this way because these days, people are less attached to religion and an all-encompassing relationship with God. What's sacred is an individual's relationship with other individuals, not their relationship with a deity. Stories of personal destinies become guiding stars in our lives. TV series, movies, blogs, newscasts, Facebook updates, and novels, all the stories from around the world and our world history, become a universe of endless possible ways to lead our lives, each something we can choose or choose not to follow. One thing is for sure: if we can't _imagine_ something happening, we can't possibly do our part to _make_ it happen. Without the impulse to do something new, nothing new will happen.
Suddendorf also maintains that creative writing is made possible by future thinking.
"Imagining fiction is basically the same as imagining oneself in the future. The simulations you perform in your mind can similarly be simulations of different lives. And you can simulate how your story may relate to other people, how relevant and realistic it may be. It is the same brain processes that are at play when you imagine being another person. The memory theater is actually more like a mind theater, where the show can be about yourself in the past or present, or with someone else in the lead role."
In Greek mythology, the goddess of memory, Mnemosyne, was the mother of the nine Muses, inspirational goddesses who ruled over the arts, including several forms of literature. The idea that our ability to imagine—or create—is closely related to memory is not so new after all.
"Memory is the base for everything I write, I think," Linn Ullmann tells us. "Of course, a memory doesn't qualify as art in itself. What sets literature apart from being a simple retelling of a dream you just had is the way you work with memories to transcend the personal moment here and now. I have no obligation to the truth when I write; my only obligation is to fiction itself. That holds true even when I am basing my stories on personal memories."
Her memories may appear unreliable, like memories in real life, without detracting from the emotional strength of her story. Something new emerges: a peephole into other people's lives and fates, feelings and thoughts.
"In my work with memory, I discovered that it borders on imagination," she says.
In her experience, fragments of memories can build something that we would call fiction. When you read a novel, it activates your mental time machine. This time, though, it takes you into the heads of the characters in the book and transports you to the places where they live.
Someone else who believes in the power of storytelling is futurist Anne Lise Kjær, who provides companies, organizations, and nations (she is just back from a consulting trip with the Icelandic government) with tools for building future scenarios that can be used in long-term strategies and marketing work. Her client list includes, among others, brand names like Sony, IKEA, Disney, and several universities.
"My secret is that I am a good storyteller; I bring the future alive in my clients' minds, so that they can see it for themselves," Kjær says.
With an education in design she acquired in Denmark, she is now the CEO of a large, London-based international firm, Kjær Global. When she explains her work as a futurist to us, it is clear that, for the most part, she uses _language_ to build the future scenarios. She assembles her stories using the building blocks of stored knowledge and future probabilities. She helps build a _trend atlas_ , a map of values and ideas that together may shape the future. This atlas helps shape the semantics of the future. It's a kind of mental Lego. Using these trend analyses, she helps her clients sketch out their own futures. For instance, a typical question to consider for a future vision is whether people are drawn more toward their leisure time than toward earning more money, or how topics of climate change and mindfulness may influence our choices.
"I work with connecting the dots so that the future may appear. But there are many ways the dots can be combined, so we work with parallel visions simultaneously." She tries to see patterns in what is already there.
"Sometimes you need a wild card to make it all fit. These are scenarios that may not be very likely—like green snow! But sometimes they are needed to bring the vision forward," she says. "The future cannot be seen in a crystal ball. I can only provide a road map," she says. Her ability to generate stories about the future has made her a successful entrepreneur. Like Suddendorf, she knows that we shape our own future by recognizing possibilities and following routes that lead to specific outcomes. A futurist is not a fortune-teller; knowledge about the future is mostly a tool her clients can use to influence their own futures themselves.
While Kjær Global is paid to help clients envision a positive future, others imagine a global future that most wouldn't enjoy. There's even a small group of people who deny that these visions could come true.
The Intergovernmental Panel on Climate Change (IPCC), a scientific body guided by the United Nations, works with our globe's future every single day. Katharine Mach of Stanford University is one of the climate researchers responsible for the panel's fifth report, which was released in 2014. The report outlines humankind's past impact on the planet, and the risks we face in the future.
"Picturing ice floating in the water is the easy part. The ice from the melting poles. That is tangible," she tells us.
And that is part of the challenge. Images of polar bears swimming for their lives in the Arctic, far away from us, don't provoke an immediate fear of the climate crisis. We all picture it, the ice floating on the Arctic waves, polar bears swimming desperately as hunting grounds melt away. But that's Svalbard and the Arctic. How will it look for us, where we live?
"The climate panel works with two alternate future scenarios," Chris Field explains. He was the chair of the second working group of the fifth report. As founder of the Carnegie Institution's Department of Global Ecology and director of the Stanford Woods Institute for the Environment, he is without doubt one of the leading experts on world climate change.
"The first scenario is one of ambitious mitigation. The other is a scenario with continued high emissions."
He admits that climate researchers have, for a long time, been reluctant to offer compelling scenarios of how climate change is likely to impact our lives.
"We haven't talked enough about how the future may unfold, and we have not taken into account the psychological aspects of envisioning these future scenarios."
Doomsday visions are the easiest to imagine. However, they are more paralyzing than helpful for most people. If the planet is going under anyway, what's the point of even trying to stop it now?
"It is frustrating to know that we could have achieved the goal of limiting the global rise in temperature if the global community had reacted sooner," he says.
It is impossible not to share his frustration. It feels to us as if he and the UN climate panel carry the future of the entire planet on their shoulders. Isn't it horribly depressing to stare into the abyss climate change represents? Katharine Mach is a young senior researcher, yet she is already all too familiar with it. When she first learned of the gravity of climate change as a much younger scientist, it affected her dramatically.
"It made a strong impression; it was scary, really. It was like going from zero to one hundred very fast; from not knowing to knowing. Now, after so many years of research behind me, it has grown into more of a passion, something that I turn to with the eager curiosity of a scientist."
In Chris Field's and Katharine Mach's vision for the future, there is no room for Hollywood's idea of dystopia. There is no pretentious score, no George Clooney or Tom Cruise in a hero's role.
"The future has three time frames—the immediate future, the near future (the next decade), and the distant future—all three of which depend on what we do here and now. Our job is to draw all these scenarios," Mach says.
We can already see signs of climate change in the form of drought in certain parts of the world and more extreme weather in general. The recent increase in dramatic forest fires, as seen in British Columbia and California, and the overwhelming flooding of Houston, Texas, caused by hurricanes like nothing we've seen before, are only a couple of notable examples. Even in the safe haven of Norway the weather is changing, with less snow in winter and more stormy weather.
For Field, it is important to always keep an eye on the distant future, even though the changes are most visible in the near future. He has a different perspective than what you see in the doomsday visions, though—one that surprises us. Even though the changing climate will bring failing crops, heightened international conflict, and an increasing number of refugees, he insists there are also reasons to be optimistic.
"The ongoing changes in the climate will inspire development. New solutions for green energy will be pushed forward, bringing positive changes, especially for the world's poorest. Climate change may open up possibilities that will make the world a better place, creating stronger and more vibrant communities. This could be our chance to make some substantial changes," Field says.
"Just imagine what the coastal landscape could look like with buildings that have accommodated to rising sea levels," Mach says, explaining that dikes to keep water at bay could also be incorporated into the city's landscape. They could house residences and offices. We imagine a version of the Netherlands, which famously employs dikes to keep it dry, on steroids. Is this the future?
"We have to picture the future within a specific context, to create visions that can be used for people to provoke actual development," she says.
The future isn't just ice drifting with the current until it melts and becomes one with the rising sea, but also cities built from new thinking.
For the IPCC, conveying optimism has been difficult. Their image is one of our shared guilty conscience; they are Hollywood dystopia personified, dressed in nice suits, holding press conferences, and receiving the Peace Prize medal in Oslo City Hall. But they have a commitment to make us aware of all the possibilities, to inspire change. They urge us to take in the future in smaller portions, each possible to swallow, each inspiring new changes as we move along into the near and distant future. For this is the truth about the future: it is not on the other side of an abyss of time, it is right in front of us all the time, like stepping stones in the river (or rather, like floes of ice in the ocean, if that's what it takes to make you picture it). Seeing two weeks into the future may lead to a path that continues on toward the distant horizon. Businesses may find solutions that are beneficial to them here and now; their leaders may picture the economic rewards, their pride at accomplishing something new, the way they can talk about their business at dinner parties to feel good about themselves. They may not picture the fields of golden barley swaying in the wind, an Earth rescued. Money and personal satisfaction are, after all, what drive most people's intentions. Nevertheless, that first small change may lead to the next stepping stone, and then the next. "We are determined to take into account the psychological future; it really concerns us," Field says, and Mach concurs.
Perhaps grandiose Hollywood films featuring "ambitious mitigation" aren't the right direction to follow, but Field and Mach may be on board with the idea of video games that could allow people to take part in more realistic simulations.
For Thomas Suddendorf, climate change and human evolution are intertwined. Because of our ability to make new tools and envision the future, we have outsmarted _Homo erectus_ , the Neanderthals, and a whole array of other hominin species. Our highly developed visionary skills have taken us to the top of the food chain. Now we are about to outsmart ourselves with our own civilization-creating, adaptive mind. "It's our ability to envision the future that got us into this mess; let's hope it can deliver us out of it too. To do this, we must envision alternative versions of the future. We can picture the consequences of our actions, so we'd better take responsibility for them."
To make change possible, the future must be transformed into something tangible and meaningful. It must be relevant. Future ways of saving the planet work only insofar as they are related to people's personal goals and preferences, Suddendorf says. For him, personally, the preservation of the rainforest is highly important. He is an eager supporter of work to sustain the gorillas of West Africa and the orangutans of Indonesia. Working in evolutionary psychology, he has spent a lot of time in the presence of these great apes, both in zoos and in the wild. "We all have different motives. For some people, the extinction of species is alarming. We know that using palm oil from plantations in areas that used to be the forest homes of orangutans will mean the end of orangutans as a direct consequence. And that's upsetting. Others, perhaps, couldn't care less about orangutans—some people don't even believe in man-made climate change. But most people can relate to visible pollution, like smog in the air, garbage all around, that sort of thing. When there is filth all around you, it is hard not to take that seriously. So to reach these people, one must appeal to that aspect of environmental problems. For others, economic incentives are more important. Climate change may impact people's economy directly in various ways. We have to build models of the future that mean something to people personally. Our ability to envision the future is, after all, flexible, so it should be possible to mold it into something that fits with people's motivation."
Knowledge is a seed, simultaneously carrying past experience and future potential. The library of Alexandria was once a seed vault, a carrier of a vast amount of wisdom and knowledge, serving the whole Mediterranean civilization until it burned down some two thousand years ago. A new library now resides in Alexandria, like a bridge between ancient culture and present life. The Bibliotheca Alexandrina was designed by the Norwegian architectural firm Snøhetta.
"I'm a production designer for the future. Wherever I go, I see new possibilities, new spaces," Kjetil Trædal Thorsen tells us. He is one of the founding architects of Snøhetta, a now internationally renowned architectural firm.
To be an architect is to envision future cities—or parts of them, especially public buildings, like libraries, theaters, city halls, and opera houses. How they fit into the landscape and the possibilities they reveal will determine the fate of the area surrounding them. Certain solutions for the climate crisis exist within the architecture of the future: we can design buildings that produce more energy than they use, or that are positioned to optimize the sunlight flowing in through windows, or that inspire new ways of thinking about our civilization. Thorsen is involved in making Chris Field's and Katharine Mach's dreams of a positive future a reality.
In addition to the Bibliotheca Alexandrina, Snøhetta is behind the entry pavilion of the 9/11 Memorial & Museum at Ground Zero in New York, where the World Trade Center towers once stood. They designed the new museum in Lascaux, the place in France where some of the world's oldest and most beautiful cave paintings are hidden in a mountain. Spreading out into the Oslo Fjord, the glacier-like marble building that is the home of the Norwegian National Opera & Ballet invites the whole city to its rooftop, like nothing else in the world. The Snøhetta architects work with our shared memory—memories of places—and they do it with their future-oriented design philosophy.
"Of course we as architects don't decide what the future will be. We're simply projecting our wishes for the possible future onto buildings we create," Thorsen says.
With the opera house in Oslo, it all started with values: the Norwegian ethos of equality, open access to nature and the sea, social democracy, closeness with the environment. The architects talked about how buildings can be either authoritarian or inclusive, about high culture versus popular culture—and then, how they could turn something that is traditionally considered an authoritarian, high-culture institution, as represented by grand opera houses around the world, into something that represents the Norwegian spirit of down-to-earthness. When the building was finished, it represented many of these aspects of openness and usefulness to the general public. They thought of a mountain in the middle of the city. Mountains hold a special place in Norwegian people's minds; they are free for all to experience and represent traditional outdoor activities. And so the opera house stands, rising partly out of the sea, with a continuous white surface taking visitors up to the top in a short walk that may feel like climbing a glacier.
"In order to succeed with a project, we have to hit on something that is already a developing tendency in society—our ideas must resonate with something that's already there. Otherwise the ideas will not develop into a real project. Timing is everything, and the jury and the commissioners must believe in it. Actually, there is a series of particular events that must line up for a building like this to finally be realized," Thorsen explains.
At the beginning of this series of remarkable things are stories and ideas—not a lot of drawings. Echoing the futurist Anne Lise Kjær, Thorsen thinks ideas built with language are the departure point for a successful building.
"Architecture is all about telling stories. We are like authors. If we put our designs down onto paper, it closes any further creativity in the other team members. We need to evoke open possibilities, open images, and ideas. That is why we only use words in the beginning of a process. Sometimes, a stray sentence uttered during a brainstorming session triggers an idea that leads to something great."
Collective visions are fostered at Snøhetta. Kjetil Trædal Thorsen never talks about his achievements; he always refers to "our" achievements.
"It is better being part of the Beatles than being Frank Sinatra. We always work together."
The way architects consider the future they're creating in a social context resonates with what we've heard from Thomas Suddendorf, his idea of language and social unity driving the evolution of the human species, giving us the basis for civilization.
Snøhetta now has offices in New York, San Francisco, Innsbruck, Singapore, Stockholm, and Adelaide, employing more than 180 people from thirty different nations. When they won the competition for the opera house, they were located in a shabby street just behind the city's hospital emergency room and had only thirty employees.
"Every assignment is important to us. But the main project, the vision I stick to at all times, is Snøhetta itself, this office, what it will become," Thorsen says.
Not long ago, something happened that moved the architects to tears, something far beyond what anyone could have envisioned for a building they had worked on. It was the dawn of the Arab Spring. The battle against censorship was being fought in the streets of Cairo. With its special status as an international research and cultural center, the Bibliotheca Alexandrina had been exempt from the strict laws of censorship in Egypt. It now became a symbol of the fight for free speech and human rights. As the demonstrations reached a crescendo, the protesters, holding hands, formed a protective circle around the library.
"It's among the greatest things an architect can experience, when people—not the military, but civilians—protect what we have built. We always do our work with humility. We change people's physical environment, so we have to respect humanity. When we build movie theaters in Saudi Arabia, we do it because we feel architecture can be a tool to facilitate something more democratic than what the country stands for today."
Perhaps a building can be so steeped in democratic values that it can change a totalitarian society? The opera house in Oslo has, without doubt, changed people's relationship with an art that was previously associated with the economic and cultural upper classes.
Snøhetta's main office is situated in an old warehouse on the harbor in Oslo. Inside the old walls, the office is a large and open space. From the ceiling, hundreds of small plastic bags filled with water hang in a circle. They catch the light reflected from the fjord and slowly rotate. For a moment, we can almost imagine a tiny seahorse in each bag.
"We made this cheap version of a chandelier for a party once and decided to keep it. Initially, someone had an idea of putting a goldfish in each of them, but that would really just be unethical," the publicist tells us.
She's as relaxed and enthusiastic as everyone else we've met here. We want to stick around; the architects are all open and curious.
Only a few hundred feet down the harbor, the opera house awaits as we stroll along the waterfront. The water is glimmering, almost blinding us with the rays of sun that hold the promise of upcoming summer. Not many months ago, the same water swallowed our diver friends, as they descended fifty feet to perform our memory experiment. Back then the fjord was black with a layer of gray, reflecting the cloudy sky. Rain was pouring over us, and the wind was almost unbearable. Now that June has begun, it all seems so far away: our paper cups of coffee soaked with rain, the divers in their neoprene suits waving optimistically from the water as they prepared for diving while we were left behind on land, shivering in the February rain. How soon experiences that we expect to stay with us fade into vague memories.
The tall windows of the opera house catch the sunlight. Inside, warm oak covers much of the walls, along with colorfully lit origami-like panels made by the Icelandic artist Olafur Eliasson, the same artist who made the rainbow tunnel on top of ARoS in Denmark, in the city where Dorthe Berntsen does her research on autobiographical memory.
The opera house is crawling with tourists and regular Oslo citizens, people wearing jeans or saris, kids listening to music, a father and his daughter taking pictures with a selfie stick on the rooftop, children running and laughing with joy. The fjord embraces it all with its glittering light.
YLVA: So what have you learned about memory, Hilde? I mean, while we've been writing this book.
HILDE: A lot of things have surprised me. I've realized that memory has little to do with identity. Personality tests don't measure how much we remember. At the same time, I feel trapped by my memories. They don't become weaker as I get older. It's more like I'm looking at my memories through a prism. From certain angles, I see different colors, but the original colors never disappear. Things have greater depth now than they did in the past.
YLVA: When you talk about it like that, how can memories _not_ have anything to do with who we are?
HILDE: No, that's true. I am my memories too. Then I think of the unimaginable number of moments my life contains. So many unique things that have only happened to me, exactly at this point in history. I can't relive any of my life's moments, and only I have experienced them. It's like I'm carrying a whole galaxy of memories inside me!
YLVA: Yes! There are trillions of galaxies out there in space, and it's the same with our memories. There are an unfathomable number of moments. That's why I wanted to study psychology, to learn more about how our inner universes work.
HILDE: And that's why I wanted to be an author. I believe we're all pretending to be normal, orderly, and rational, when in reality we're guided by thoughts, dreams, and wishes we don't even know we have. I've thought a lot about how memory is the core of how we tell stories; we get our storytelling techniques from memory itself. When I write, I have two modes: either "it used to be a certain way" or "then something new happened." In Hollywood films, they always present an initial situation of normalcy, which gives us a feeling of familiarity—which comes from what we in the book refer to as cumulative memory—before something unbelievable happens, usually after twenty minutes, nowadays even faster. This corresponds to those unique, pivotal moments that stand out in our memory. And then there's foreshadowing and flashbacks; that's what we do all the time in life as well. We travel into the future and into the past. And then there's the cliffhanger, that exciting moment in a story when someone's life is in danger and we won't find out what happens until much later. This is life. We seldom figure out the answer to a riddle until some time has passed. We all live with cliffhangers all the time.
YLVA: Yes, the life story, the existential part of memory. The whole time, we live in the story about ourselves and the world, and _that's_ what memory is all about. In fiction, there are metaphors and signs, and we look for those in real life too. We're looking for coherence. After an event has passed, we may hang on to an image that's symbolic for the situation or story.
HILDE: But what have _you_ learned? Probably nothing, since you're the memory expert?
YLVA: When I did my hundred days experiment, I finally realized how it feels to be one of my own patients. I had to fight to remember each of those hundred days, which of course is ridiculous compared to the kinds of memory problems my patients have. But the struggle to keep on top of it all, to keep track of all that one has to remember, is quite similar, I imagine.
HILDE: I would happily forget some of the negative experiences in life. I wouldn't mind if they could disappear forever. It's a relief to get rid of certain things, to just let go. Forgetfulness is underrated.
YLVA: Sad memories can be pearls on the necklace too. Things don't get better just because we forget the bad things. But I want to stand up for everyday forgetting. It's nice to just live life and give up trying to remember everything the whole time. I will remember this particular day. I'm not sure I will remember in a week exactly what date it was, but that doesn't matter. People seem to be obsessed with memory, thinking remembering better will make them smarter. I understand the obsession. I myself am passionately devoted to thinking about memory and using it the best way. But there is another side to it too. Worrying about our memory is a symptom of society's ridiculous standards of perfection. Not only are we supposed to look good, we're supposed to think perfectly too. It's okay not to remember everything. Memory cannot be perfect.
HILDE: Imagine if we lived forever. Nothing would be important any longer. No moment would be considered remarkable or unique.
YLVA: True. Then it would be even more obvious how important the future is—the whole future would lie in front of us, eternally. But these unique moments we have talked so enthusiastically about, I don't know if I agree anymore that that's where the magic of life can be found. I don't remember my son's first steps, and when I think about it, that makes me sad. Shouldn't I remember his first steps? At the same time, one of my best memories of him, when he was little, is actually a cumulative memory. It is the memory of all the times I lay beside him in bed and sniffed his hair and snuggled his small body. Why is that memory worth less than the moment when he started to walk?
HILDE: Isn't that memory just as nice?
YLVA: Regardless, it is reconstructed. That one moment, a baby's first steps, is as much a reconstruction as is the sum of many moments. We yearn so much to preserve individual moments: something beautiful and precious that will last forever. That doesn't happen. Maybe that's why you write?
HILDE: The fantastic part about writing is being able to preserve precious moments.
YLVA: Or not-so-precious moments?
HILDE: Yes, those too. When I write, memories become hyperrealistic. They become so vivid that I feel like I can touch them. I believe memories are artifacts, meant to be used—like when I retrieve a happy moment and let it linger in consciousness.
YLVA: There is something I've been thinking about a lot lately: mindfulness has given future thinking a bad name. It's like mind wandering has become something bad, something we must take control of! But wandering freely with our thoughts is very natural. We need time to ponder the past, and we need time to look forward, without forcing it. The natural state of the resting mind is wandering back and forth in time.
WHILE WE CONVERSE, a yacht approaches the opera house. It seems to have come out of nowhere, because all of a sudden it's just there. It's filled to the brim with people dressed to party. They have apparently rented an evening on the fjord with drinks and dancing. The speakers are thumping with a song by the Swedish rapper Timbuktu; the artist is spitting the words out in contempt, describing a world where no one wants to plant any seeds or think of anyone but themselves. The boat makes a turn right in front of the opera house. It's almost as if it's doing it just for us. It's easy to visualize the yacht filled with everyone we have talked with for this book: Edvard Moser and Terje Lømo; Eleanor Maguire, busily planning a year of travel; the taxi drivers of London; epilepsy patient Terese Thue Lund and her little dog, sitting so obediently by her feet; Utøya survivor Adrian Pracon, dreaming of a future as a terror researcher; trauma researcher Ines Blix; psychologist Peder Kjøs; writer Linn Ullmann, preparing her next novel; climate researcher Chris Field, currently trying to prevent the temperature from rising two degrees. We can see our sister Tonje, who has since quit skydiving; and Wind Aamot, who moved to Austria; Henry Molaison; opera singer Johannes Weisser, rehearsing _Onegin_ ; and criminal investigator Asbjørn Rachlew and his daughter by the gunwale. All of these people, and many others, who have helped us better understand memory and shared their research, their opinions, and their life stories.
The music keeps pumping its depressing message out into the summer air. Maybe we'd like a different song playing as the credits roll for this book, not Timbuktu's rap hit. And perhaps our memory deceives us. Perhaps it was rather the quiet Beatles song "In My Life" we could hear across the Oslo Fjord that June evening, four British musicians singing about all the beautiful moments that can fill the memory, and of all the people you love and lose during a lifetime.
The boat turns away from us, out into the fjord, toward the sunset. You, the reader, can decide on your own credit-roll music, choose what sounds best. What reminds you of the sea? What music moves you? Retrieve that music from your memory!
The music fades, and the yacht disappears over the hazy summer evening's horizon. All those who have been trapped within the pages of this book: we're letting them go now. They're sailing out into the world and into the future. Everything they know, all the memories and experiences they have, they'll use to shape the world and make it better, different, new.
And now it's your turn.
**NOTES**
_Quotations not cited here come from interviews that the authors personally conducted between November 2015 and May 2016._
**Chapter 1**
Page 2. The discovery of the hippocampus: Shyamal C. Bir, Sudheer Ambekar, Sunil Kukreja, and Anil Nanda, "Julius Caesar Arantius (Giulio Cesare Aranzi, 1530–1589) and the Hippocampus of the Human Brain: History behind the Discovery," _Journal of Neurosurgery_ 122, no. 4 (2015): 971–75, doi: 10.3171/2014.11. JNS132402.
Page 4. Henry Molaison's surgery: William Beecher Scoville and Brenda Milner, "Loss of Recent Memory after Bilateral Hippocampal Lesions," _Journal of Neurology, Neurosurgery, and Psychiatry_ 20, no. 1 (1957): 11–21.
Page 6. Scoville's confession: Ibid.
Page 7 and on. Henry's life and the scientific discoveries: Suzanne Corkin, _Permanent Present Tense: The Man with No Memory, and What He Taught the World_ (London: Allen Lane/Penguin Books, 2013).
Page 7. Henry's ability to perceive time: Ibid.
Page 8. The maze experiment with Henry: Ibid.
Page 9. "I thought this would be difficult": quote from Henry Molaison reported by Brenda Milner on several occasions, including in "Memory as a Life's Work: An Interview with Brenda Milner," interview by Maria Schamis Turner, The Dana Foundation, March 18, 2010, <http://www.dana.org/News/Details.aspx?id=43060>.
Page 11. "It's a funny thing... I'm living and you're learning": quote from Henry Molaison in Corkin, _Permanent Present Tense_ , 113.
Page 12 and on. Solomon Shereshevsky: Alexander R. Luria, _The Mind of a Mnemonist: A Little Book about a Vast Memory_ , trans. Lynn Solotaroff (Cambridge: Harvard University Press, 1968).
Page 15. "We believe that the enormous attention": Jacobo Annese, "Welcome to Project H.M.," Brain Observatory, accessed May 20, 2014, <http://brainandsociety.org>. For further information on Project H.M. and H.M.'s Brain Web Atlas, see <https://www.thebrainobservatory.org/project-hm/>.
Page 16. Maguire's research has allowed her to "see" memories (Maguire is a coauthor): Martin J. Chadwick et al., "Decoding Individual Episodic Memory Traces in the Human Hippocampus," _Current Biology_ 20, no. 6 (2010): 544–47, doi: 10.1016/j.cub.2010.01.053.
Page 18. The infamous "memory wars," review and further research: Lawrence Patihis et al., "Are the 'Memory Wars' Over? A Scientist-Practitioner Gap in Beliefs about Repressed Memory," _Psychological Science_ 25, no. 2 (2014): 519–30. doi: 10.1177/0956797613510718.
Page 18. Some argue that the hippocampus has only temporary hold of our memories: Larry R. Squire, "Memory Systems of the Brain: A Brief History and Current Perspective," _Neurobiology of Learning and Memory_ 82, no. 3 (2004): 171–77, doi: 10.1016/j.nlm.2004.06.005.
Page 19. Others believe that the hippocampus is active every time we remember: Morris Moscovitch et al., "Functional Neuroanatomy of Remote Episodic, Semantic and Spatial Memory: A Unified Account Based on Multiple Trace Theory," _Journal of Anatomy_ 207, no. 1 (2005): 35–66, doi: 10.1111/j.1469-7580.2005.00421.x.
Page 19. "What memory goes with": William James, _The Principles of Psychology_ (New York: Henry Holt and Company, 1890), 651, <https://archive.org/details/theprinciplesofp01jameuoft>.
Page 20. Discovery of how neurons are connected (quite a while before the polar expeditions): Fridtjof Nansen, _The Structure and Combination of the Histological Elements of the Central Nervous System_ (Bergen: J. Grieg, 1887).
**Chapter 2**
Page 22. The original diving experiment: Duncan R. Godden and Alan D. Baddeley, "Context-Dependent Memory in Two Natural Environments: On Land and Underwater," _British Journal of Psychology_ 66, no. 3 (1975): 325–331, doi: 10.1111/j.2044-8295.1975.tb01468.x.
Page 25. Only thirty-six of one hundred psychology experiments were re-created successfully: Open Science Collaboration, "Estimating the Reproducibility of Psychological Science," _Science_ 349, no. 6251 (2015): aac4716, doi: 10.1126/science.aac4716.
Page 27. Memory as magic in the 1500s and 1600s: Frances A. Yates, _The Art of Memory_ (Harmondsworth: Peregrine Books, 1969).
Page 31. Tim Bliss and Terje Lømo's first descriptions of memory trace in the brain: T.V.P. Bliss and T. Lømo, "Long-Lasting Potentiation of Synaptic Transmission in the Dentate Area of the Anaesthetized Rabbit following Stimulation of the Perforant Path," _Journal of Physiology_ 232, no. 2 (1973): 331–56, doi: 10.1113/jphysiol.1973.sp010273.
Page 32. O'Keefe's discovery of place cells in the hippocampus: J. O'Keefe and J. Dostrovsky, "The Hippocampus as a Spatial Map: Preliminary Evidence from Unit Activity in the Freely-Moving Rat," _Brain Research_ 34, no. 1 (1971): 171–75, doi: 10.1016/0006-8993(71)90358-1.
Page 33. The discovery of grid cells in the entorhinal cortex, right outside the hippocampus, is described here, among other places (the Mosers are coauthors): Torkel Hafting et al., "Microstructure of a Spatial Map in the Entorhinal Cortex," _Nature_ 436, no. 7052 (2005): 801–6, doi: 10.1038/nature03721.
Page 35. California researchers found memories connected in memory networks in the hippocampi of mice: Denise J. Cai et al., "A Shared Neural Ensemble Links Distinct Contextual Memories Encoded Close in Time," _Nature_ 534, no. 7605 (2016): 115–18, doi: 10.1038/nature17955.
Page 37. Eleanor Maguire's "mind-reading machine": Chadwick et al., "Decoding Individual Episodic Memory Traces."
Page 38. Memories are not static: Heidi M. Bonnici, Martin J. Chadwick, and Eleanor A. Maguire, "Representations of Recent and Remote Autobiographical Memories in Hippocampal Subfields," _Hippocampus_ 23, no. 10 (2013): 849–54, doi: 10.1002/hipo.22155.
Page 42. The story about the elephants Shirley and Jenny who found each other after more than twenty years has been widely reported in the media, by, among others, Sophie Jane Evans, "Elephants REALLY Never Forget," _Mail Online,_ March 12, 2014, http://www.dailymail.co.uk/news/article-2579045/Elephants-REALLY-never-forget-How-freed-circus-animals-Shirley-Jenny-locked-trunks-hugged-played-met-time-20-years.html.
Page 45. Slime mold that remembers: Tetsu Saigusa et al., "Amoebae Anticipate Periodic Events," _Physical Review Letters_ 100, no. 1 (2008): 018101, doi: 10.1103/PhysRevLett.100.018101.
Page 45. Slime mold solves U-shaped trap problem: Chris R. Reid et al., "Slime Mold Uses an Externalized Spatial 'Memory' to Navigate in Complex Environments," _Proceedings of the National Academy of Sciences of the USA_ 109, no. 43 (2012): 17490–94, doi: 10.1073/pnas.1215037109.
Page 47. Henry Molaison had only semantic memories of his own past: Sarah Steinvorth, Brian Levine, and Suzanne Corkin, "Medial Temporal Lobe Structures Are Needed to Re-Experience Remote Autobiographical Memories: Evidence from H.M. and W.R.," _Neuropsychologia_ 43, no. 4 (2005): 479–96, doi: 10.1016/j.neuropsychologia.2005.01.001.
Page 50. Medical students remember well outside learning environment: Andrew P. Coveney et al., "Context Dependent Memory in Two Learning Environments: The Tutorial Room and the Operating Theatre," _BMC Medical Education_ , 13 (2013): 118, doi: 10.1186/1472-6920-13-118.
**Chapter 3**
Page 54. Marcel Proust, _Remembrance of Things Past_ [later translated as _In Search of Lost Time_ ] vol. 1 _, Swann's Way_ , trans. C.K. Scott Moncrieff (New York: Henry Holt and Company, 1922), epub edition at <http://www.gutenberg.org/ebooks/7178>.
Page 56. _After Life_ (original title _Wandafuru raifu_ ), directed by Hirokazu Kore-eda (Japan, 1998).
Page 57 and on. Dorthe Berntsen sums up the research on personal memories in her book _Erindring_ [Recollection] (Aarhus, Denmark: Aarhus Universitetsforlag, 2014). In English, see Dorthe Berntsen and David C. Rubin, eds., _Understanding Autobiographical Memory: Theories and Approaches_ (Cambridge: Cambridge University Press, 2012).
Page 57. The reminiscence bump: Ibid.
Page 60. Karl Ove Knausgård, _My Struggle_ , 6 vols. (5 vols. published in English to date), trans. Don Bartlett, various publishers. Originally published as _Min kamp_ (Oslo: Forlaget Oktober, 2009–11).
Pages 62–63. Aldrin recalls the Moon landing: Buzz Aldrin and Ken Abraham, _Magnificent Desolation: The Long Journey Home from the Moon_ (New York: Harmony Books, 2009), 33–38 passim.
Page 64. How to capture people's spontaneous memories in daily life: Anne S. Rasmussen, Kim B. Johannessen, and Dorthe Berntsen, "Ways of Sampling Voluntary and Involuntary Autobiographical Memories in Daily Life," _Consciousness and Cognition_ 30 (2014): 156–68, doi: 10.1016/j.concog.2014.09.008.
Page 65. Murakami describes how music awakens memories: Haruki Murakami, _Norwegian Wood_ , trans. Jay Rubin (New York: Vintage Books, 2000), 3.
Page 68. "I wanted to see what would happen": Linn Ullmann, _Unquiet_ (New York: W.W. Norton, forthcoming).
Page 69. " _To remember_ is to look around": Ullmann, _Unquiet_.
Pages 71–72. Two brothers, each with their perspective of memory: William James, _Principles of Psychology._ And Henry James, _A Small Boy and Others_ (1913, Project Gutenberg, EBook #26115, 2008), 2, <http://www.gutenberg.org/files/26115/26115-h/26115-h.htm>.
Page 72. The hippocampus assembles memory elements like a director of a play: Moscovitch et al., "Functional Neuroanatomy."
Page 74. An overview of fMRI studies of personal memories in the brain: Philippe Fossati, "Imaging Autobiographical Memory," _Dialogues in Clinical Neuroscience_ 15, no. 4 (2013): 487–90.
Page 75. "Default mode" in the brain: Randy L. Buckner and Daniel C. Carroll, "Self-Projection and the Brain," _Trends in Cognitive Sciences_ 11, no. 2 (2007): 49–57, doi: 10.1016/j.tics.2006.11.004.
Page 75. Pitfalls in connection with fMRI studies, elegantly served up with salmon for dinner: Craig M. Bennett et al., "Neural Correlates of Interspecies Perspective Taking in the Post-Mortem Atlantic Salmon: An Argument for Multiple Comparisons Correction" (poster presented at the 15th annual Organization for Human Brain Mapping conference, San Francisco, CA, June 2009), <http://prefrontal.org/files/posters/Bennett-Salmon-2009.pdf>.
The study is summarized in an excellent _Scientific American_ blog post, "Ig Nobel Prize in Neuroscience: The Dead Salmon Study," September 25, 2012, <http://blogs.scientificamerican.com/scicurious-brain/ignobel-prize-in-neuroscience-the-dead-salmon-study/>.
Page 77. Individuals suffering from depression have less distinct personal memories: J. Mark G. Williams et al., "The Specificity of Autobiographical Memory and Imageability of the Future," _Memory and Cognition_ 24, no. 1 (1996): 116–25, doi: 10.3758/BF03197278.
Page 77. Turning on positive memories to "treat" depression in mice (Tonegawa is a coauthor): Steve Ramirez et al., "Activating Positive Memory Engrams Suppresses Depression-Like Behaviour," _Nature_ 522, no. 7556 (2015): 335–39, doi: 10.1038/nature14514.
Page 78. Emotional images for use in student assignments/experiments about sad (and in other ways emotional) memories: Elise S. Dan-Glauser and Klaus R. Scherer, "The Geneva Effective Picture Database (GAPED): A New 730-Picture Database Focusing on Valence and Normative Significance," _Behavior Research Methods_ 43, no. 2 (2011): 468–77, doi: 10.3758/s13428-011-0064-1. The (depressing) material can be downloaded from <http://www.affective-sciences.org/home/research/materials-and-online-research/research-material/>.
Page 79. Tulving's explanation of semantic versus episodic memory: Endel Tulving, "Episodic and Semantic Memory," in _Organization of Memory_ , eds. Endel Tulving and Wayne Donaldson (New York: Academic Press, 1972), 381–402.
Page 80. Susie McKinnon tells how she discovered that her memory was different: Helen Branswell, "Susie McKinnon Can't Form Memories about Events in Her Life," _Huffington Post_ , April 28, 2015, <http://www.huffingtonpost.ca/2015/04/28/living-with-sdam-woman-has-no-episodic-memory-can-t-relive-events-of-past_n_7161776.html>.
Page 80. Susie's state is described scientifically here (Levine is a coauthor): Daniela J. Palombo et al., "Severely Deficient Autobiographical Memory (SDAM) in Healthy Adults: A New Mnemonic Syndrome," _Neuropsychologia_ 72 (2015): 105–18, doi: 10.1016/j.neuropsychologia.2015.04.012.
Page 81. Arne Schrøder Kvalvik, _Min fetter Ola og meg: Livet og d_ ø _den og alt det i mellom_ [Me and my cousin Ola: Life, death and everything in between] (Oslo: Kagge Forlag, 2015).
Page 83. Extremely good autobiographical memory is described here: Aurora K.R. LePort et al., "Behavioral and Neuroanatomical Investigation of Highly Superior Autobiographical Memory (HSAM)," _Neurobiology of Learning and Memory_ 98, no. 1 (2012): 78–92, doi: 10.1016/j.nlm.2012.05.002.
Page 88 and on. All quotes from Adrian Pracon are from our interview with him. He has also told his story in his book, _Hjertet mot steinen: En overlevendes beretning far Ut_ ø _ya_ [Heart against stone: The story of a survivor from Utøya] (Oslo: Cappelen Damm, 2012).
Page 91. Flashbulb memories: Roger Brown and James Kulik, "Flashbulb Memories," _Cognition_ 5, no. 1 (1977): 73–99, doi: 10.1016/0010-0277(77)90018-X.
An update on the inconsistency of flashbulb memories in one of the most thorough studies ever conducted on the subject: William Hirst et al., "A Ten-Year Follow-up of a Study of Memory for the Attack of September 11, 2001: Flashbulb Memories and Memories for Flashbulb Events," _Journal of Experimental Psychology: General_ 144, no. 3 (2015), 604–23, doi: 10.1037/xge0000055.
Page 93. Trauma memories are like ordinary memories, just on maximum volume: David C. Rubin, Dorthe Berntsen, and Malene Klindt Bohni, "A Memory-Based Model of Posttraumatic Stress Disorder: Evaluating Basic Assumptions underlying the PTSD Diagnosis," _Psychological Review_ 115, no. 4 (2008): 985–1011, doi: 10.1037/a0013397.
Page 94. Questionnaire given to 207 government employees after the 2011 bombing: Øivind Solberg, Ines Blix, and Trond Heir, "The Aftermath of Terrorism: Posttraumatic Stress and Functional Impairment after the 2011 Oslo Bombing," _Frontiers in Psychology_ 6 (2015): article 1156, doi: 10.3389/fpsyg.2015.01156.
Page 96. Blix calls it centering: Ines Blix et al., "Posttraumatic Growth and Centrality of Event: A Longitudinal Study in the Aftermath of the 2011 Oslo Bombing," _Psychological Trauma: Theory, Research, Practice, and Policy_ 7, no. 1 (2015): 18–23, doi: 10.1037/tra0000006.
Pages 96–97. People with PTSD have smaller-than-average hippocampi, and twins have similar-sized hippocampi even when one isn't exposed to trauma: Mark W. Gilbertson et al., "Smaller Hippocampal Volume Predicts Pathologic Vulnerability to Psychological Trauma," _Nature Neuroscience_ 5, no. 11 (2002): 1242–47, doi: 10.1038/nn958.
Page 98. The possibility of worse general memory in the wake of PTSD: Claire L. Isaac, Delia Cushway, and Gregory V. Jones, "Is Posttraumatic Stress Disorder Associated with Specific Deficits in Episodic Memory?" _Clinical Psychology Review_ 26, no. 8 (2006): 939–55, doi: 10.1016/j.cpr.2005.12.004.
Page 99. Treatment methods for PTSD: Jonathan I. Bisson et al., "Psychological Therapies for Chronic Post-Traumatic Stress Disorder (PTSD) in Adults," _Cochrane Database of Systematic Reviews_, no. 12 (2013): article CD003388, doi: 10.1002/14651858. CD003388.pub4.
Page 99. _Tetris_ as a "vaccination" against traumatic memories: Emily A. Holmes et al., "Key Steps in Developing a Cognitive Vaccine against Traumatic Flashbacks: Visuospatial _Tetris_ versus Verbal Pub Quiz," _PLOS ONE_ 5, no. 11 (2010): article e13706. doi: 10.1371/journal.pone.0013706.
Page 100. PTSD symptoms in the survivors from the Utøya attack: Petra Filkuková et al., "The Relationship between Posttraumatic Stress Symptoms and Narrative Structure among Adolescent Terrorist-Attack Survivors," _European Journal of Psychotraumatology_ 7, no. 1 (2016): article 29551, doi: 10.3402/ejpt.v7.29551.
**Chapter 4**
Pages 106–7. The False Memory Archive: Selected Submissions, A.R. Hopwood's False Memory Archive Website, <https://www.falsememoryarchive.com>.
Page 110. Memory is fallible and (re)constructive: Daniel L. Schacter, "The Seven Sins of Memory: Insights from Psychology and Cognitive Neuroscience," _American Psychologist_ 54, no. 3 (1999): 182–203, doi: 10.1037/0003-066X.54.3.182.
Page 110. The witness who saw two Oklahoma bombers is mentioned in this article, among other places: Daniel L. Schacter and Donna Rose Addis, "Constructive Memory: The Ghosts of Past and Future," _Nature_ 445, no. 27 (2007), doi: 10.1038/445027a.
Page 111. People with good autobiographical memories remember more incorrect details (Elizabeth Loftus is a coauthor): Lawrence Patihis et al., "False Memories in Highly Superior Autobiographical Memory Individuals," _Proceedings of the National Academy of Sciences of the USA_ 110, no. 52 (2013): 20947–52, doi: 10.1073/pnas.1314373110.
Page 112. Solomon Shereshevsky's vivid childhood memories: Luria, _Mind of a Mnemonist._
Page 113. Implanted memories in mice: Gaetan de Lavilléon et al., "Explicit Memory Creation during Sleep Demonstrates a Causal Role of Place Cells in Navigation," _Nature Neuroscience_ 18, no. 4 (2015): 493–95, doi: 10.1038/nn.3970.
Page 114. The less pleasant experiment, using optogenetics: Steve Ramirez et al., "Creating a False Memory in the Hippocampus," _Science_ 341, no. 6144 (2013): 387–91, doi: 10.1126/science.1239073.
Page 116. Staged robbery on TV: Robert Buckhout, "Nearly 2,000 Witnesses Can Be Wrong," _Bulletin of the Psychonomic Society_ 16, no. 4 (1980): 307–10, doi: 10.3758/BF03329551. The TV broadcast itself aired on December 19, 1974.
Page 117. The famous asparagus and its way into the memory of unsuspecting volunteers (Loftus is a coauthor): Cara Laney et al., "Asparagus, a Love Story: Healthier Eating Could Be Just a False Memory Away," _Experimental Psychology_ 55, no. 5 (2008): 291–300, doi: 10.1027/1618-3169.55.5.291.
Page 117. False memories about food poisoning by egg salad led to changes in food habits in connection with eggs (Loftus is a coauthor): Elke Geraerts et al., "Lasting False Beliefs and Their Behavioral Consequences," _Psychological Science_ 19, no. 8 (2008): 749–53, doi: 10.1111/j.1467-9280.2008.02151.x.
Page 117. Loftus's classic car crash experiment: Elizabeth F. Loftus and John C. Palmer, "Reconstruction of Automobile Destruction: An Example of the Interaction between Language and Memory," _Journal of Verbal Learning and Verbal Behavior_ 13, no. 5 (1974): 585–89, doi: 10.1016/S0022-5371(74)80011-3.
Page 118. Loftus made people believe they had once been lost at a shopping mall: Elizabeth F. Loftus and Jacqueline E. Pickrell, "The Formation of False Memories," _Psychiatric Annals_ 25, no. 12 (1995): 720–25, doi: 10.3928/0048-5713-19951201-07.
Page 119. Edgar Allan Poe's hot-air balloon hoax was published in the _New York Sun_ April 13, 1844.
Page 119. Aloft in a photoshopped hot-air balloon (Maryanne Garry is a coauthor): Kimberley A. Wade et al., "A Picture Is Worth a Thousand Lies: Using False Photographs to Create False Childhood Memories," _Psychonomic Bulletin and Review_ 9, no. 3 (2002): 597–603, doi: /10.3758/BF03196318.
Page 127. A critical review of the existence of false memories after manipulation: Chris R. Brewin and Bernice Andrews, "Creating Memories for False Autobiographical Events in Childhood: A Systematic Review," _Applied Cognitive Psychology_ 31, no. 1 (2017): 2–23, doi: 10.1002/acp.3220.
See also this blog post for a critical review of the critical review! Henry Otgaar, "Why We Disagree with Brewin and Andrews," _Forensische Psychologie Blog_ , June 1, 2016, <https://fpblog.nl/2016/06/01/why-brewin-and-andrews-are-just-completely-wrong/>.
Page 129. How a careless mistake by the police can create false memories (Loftus is a coauthor): Kevin J. Cochrane et al., "Memory Blindness: Altered Memory Reports Lead to Distortions in Eyewitness Memory," _Memory and Cognition_ 44, no. 5 (2016): 717–26, doi: 10.3758/s13421-016-0594-y.
Page 130. The Innocence Project: http://www.innocenceproject.org. Referenced in: Elizabeth F. Loftus, "25 Years of Eyewitness Science... Finally Pays Off," _Perspectives on Psychological Science_ 8, no. 5 (2013): 556–57, doi: 10.1177/1745691613500995.
Page 130. Svein Magnussen's important overview of witness psychology, with examples from Norwegian jurisprudence: _Vitnepsykologi: Pålitelighet og troverdighet i dagligliv og rettssal_ [The psychology of eyewitness testimony: Reliability and credibility in everyday life and the courtroom] (Oslo: Abstrakt Forlag, 2004).
Page 131. Memories of serious traumas seldom appear out of the blue: Gail S. Goodman et al., "A Prospective Study of Memory for Child Sexual Abuse: New Findings Relevant to the Repressed-Memory Controversy," _Psychological Science_ 14, no. 2 (2003): 113–18, doi: 10.1111/1467-9280.01428.
Page 133. Elizabeth Loftus (coauthor) deprives people of sleep and makes them "confess": Steven J. Frenda et al., "Sleep Deprivation and False Confessions," _Proceedings of the National Academy of Sciences of the USA_ 113, no. 8 (2016): 2047–50, doi: 10.1073/pnas.1521518113.
Page 133. False memories of having committed serious crimes in youth: Julia Shaw and Stephen Porter, "Constructing Rich False Memories of Committing Crime," _Psychological Science_ 26, no. 3 (2015): 291–301, doi: 10.1177/0956797614562862.
Page 140. Gisli Gudjonsson discusses false confessions in _The Psychology of Interrogations and Confessions: A Handbook_ (West Sussex, UK: Wiley, 2003).
Page 142. Asbjørn Rachlew's doctorate: "Justisfeil ved politiets etterforskning: Noen eksempler og forskningsbaserte mottiltak" Failures of justice within police work: Some examples and research-based interventions] (PhD diss., University of Oslo, 2009), [http://urn.nb.no/URN:NBN:no-23961.
Page 142. The description of the perpetrator is from Rachlew's doctorate.
Page 145. Jørn Lier Horst, _Ordeal_ , trans. Anne Bruce (Dingwall, UK: Sandstone Press, 2016).
Page 150. Elizabeth Loftus has delivered a TED talk: "How Reliable Is Your Memory?" TEDGlobal, June 2013, <https://www.ted.com/talks/elizabeth_loftus_the_fiction_of_memory>.
**Chapter 5**
Page 152. The great taxi experiment (London cab drivers have different hippocampi from the rest of us): Eleanor A. Maguire et al., "Navigation-Related Structural Change in the Hippocampi of Taxi Drivers," _Proceedings of the National Academy of Sciences of the USA_ 97, no. 8 (2000): 4398–403, doi: 10.1073/pnas.070039597.
Page 155. Maguire's Ig Nobel Prize description: "The 2003 Ig Nobel Prize Winners," Improbable Research (website), <https://www.improbable.com/ig/winners/#ig2003>.
Page 156. The great taxi experiment, part 2 (training for the Knowledge changes the brain): Katherine Woollett and Eleanor A. Maguire, "Acquiring 'The Knowledge' of London's Layout Drives Structural Brain Changes," _Current Biology_ 21, no. 24 (2011): 2109–14, doi: 10.1016/j.cub.2011.11.018.
Page 159. Neurons are being "born" in parts of the brains of both mice and men: Peter S. Eriksson et al., "Neurogenesis in the Adult Human Hippocampus," _Nature Medicine_ 4, no. 11 (1998): 1313–17, doi: 10.1038/3305.
Page 159. Newborn neurons in the hippocampus: Leonardo Restivo et al., "Development of Adult-Generated Cell Connectivity with Excitatory and Inhibitory Cell Populations in the Hippocampus," _Journal of Neuroscience_ 35, no. 29 (2015): 10600–10612, doi: 10.1523/JNEUROSCI.3238-14.2015.
Page 159. Researchers have measured activity in new neurons while rats navigate a maze: Ibid.
Page 160. Retired taxi drivers get "normal" brains again: Katherine Woollett, Hugo J. Spiers, and Eleanor A. Maguire, "Talent in the Taxi: A Model System for Exploring Expertise," _Philosophical Transactions of the Royal Society B: Biological Sciences_ 364, no. 1522 (2009): 1407–16, doi: 10.1098/rstb.2008.0288.
Page 162. The chess experiment was conducted for the first time in the 1940s but was not published in English until later: Adriaan D. de Groot, _Thought and Choice in Chess_ (The Hague: Mouton, 1965).
Page 163. The experiment was then repeated under similar conditions, but with more chess champions: William G. Chase and Herbert A. Simon, "Perception in Chess," _Cognitive Psychology_ 4, no. 1 (1973): 55–81, doi: 10.1016/0010-0285(73)90004-2.
Page 171. Oddbjørn By explains how we can learn memory techniques in his book _Memo: The Easiest Way to Improve Your Memory_ , trans. Håkon By (Double Bay, Australia: Lunchroom Publishing, 2007).
Page 173. The Globe as one big memory machine: Yates, _Art of Memory_.
Page 175. Giulio Camillo and the idea of the memory theater: Yates, _Art of Memory._
Page 175. Robert Fludd considered the theater to have magical connections with our memories: Yates, _Art of Memory._
Page 175. "Give me my Romeo": William Shakespeare, _Romeo and Juliet_ , in _The Globe Illustrated Shakespeare_ , ed. Howard Staunton (New York: Gramercy Books, 1998), 188.
Page 178. Solomon Shereshevsky gradually turned to the method of loci: Luria, _Mind of a Mnemonist._
Page 181. Memory training benefits older individuals (Fjell and Walhovd are coauthors): Ann-Marie Glasø de Lange et al., "The Effects of Memory Training on Behavioral and Microstructural Plasticity in Young and Older Adults," _Human Brain Mapping_ 38, no. 11 (2017): 5666–80, doi: 10.1002/hbm.23756.
Page 182. Changes in seniors' memory skills are also visible in their brains (Fjell and Walhovd are coauthors): Andreas Engvig et al., "Effects of Memory Training on Cortical Thickness in the Elderly," _NeuroImage_ 52, no. 4 (2010): 1667–76, doi: 10.1016/j.neuroimage.2010.05.041.
**Chapter 6**
Page 187 and on. Ebbinghaus's travels into the kingdom of forgetfulness: Hermann Ebbinghaus, _Über das Gedächtnis_ (Leipzig: Verlag von Duncker und Humblot, 1885) _._ Translated by Henry A. Ruger and Clara E. Bussenius as _Memory: A Contribution to Experimental Psychology_ (New York: Teachers College, Columbia University, 1913), <https://archive.org/details/memorycontributi00ebbiuoft>.
Page 189. "We cannot, of course, directly observe their present existence": Ebbinghaus, trans. Ruger and Bussenius, _Memory_ , 1.
Page 191. "If we remembered everything": James, _Principles of Psychology,_ 680 _._
Page 194. Even gorillas can avoid being noticed, and then they are not lasting memories: Daniel J. Simons and Christopher F. Chabris, "Gorillas in Our Midst: Sustained Inattentional Blindness for Dynamic Events," _Perception_ 28, no. 9 (1999): 1059–74, doi: 10.1068/p281059. The original film clip with the basketball players and the gorilla can be seen here: <http://viscog.beckman.illinois.edu/media/ig.html>.
Page 196. Baddeley and Hitch's original model for working memory: Alan D. Baddeley and Graham Hitch, "Working Memory," _Psychology of Learning and Motivation_ 8 (1974): 47–89, doi: 10.1016/S0079-7421(08)60452-1.
An update is found here: Alan Baddeley, "Working Memory: Theories, Models, and Controversies," _Annual Review of Psychology_ 63 (2012): 1–29, doi: 10.1146/annurev-psych-120710-100422.
Page 199. ADHD and working memory: Michelle A. Pievsky and Robert E. McGrath, "The Neurocognitive Profile of Attention-Deficit/Hyperactivity Disorder: A Review of Meta-Analyses," _Archives of Clinical Neuropsychology,_ published ahead of print, July 6, 2017, doi: 10.1093/arclin/acx055.
Page 199. Worrying disrupts working memory performance: Nicholas A. Hubbard et al., "The Enduring Effects of Depressive Thoughts on Working Memory," _Journal of Affective Disorders_ 190 (2016): 208–13. doi: 10.1016/j.jad.2015.06.056.
Page 201. Solomon Shereshevsky's attempts to forget: Luria, _Mind of a Mnemonist._
Page 203. An overview of theoretical perspectives of childhood amnesia: Heather B. Madsen and Jee H. Kim, "Ontogeny of Memory: An Update on 40 Years of Work on Infantile Amnesia," _Behavioural Brain Research_ 298, part A (2016): 4–14, doi: 10.1016/j.bbr.2015.07.030.
Page 205. Bauer's theory of how early childhood memories gradually disappear: Patricia J. Bauer, "A Complementary Processes Account of the Development of Childhood Amnesia and a Personal Past," _Psychological Review_ 122, no. 2 (2015): 204–31, doi: 10.1037/a0038939.
Page 207. An undeveloped grid cell system, before a child begins to move around independently, may explain childhood forgetfulness: Arthur M. Glenberg and Justin Hayes, "Contribution of Embodiment to Solving the Riddle of Infantile Amnesia," _Frontiers in Psychology_ 7 (2016): article 10, doi: 10.3389/fpsyg. 2016.00010 _._
Page 207. Perineuronal nets and their role in memory development: Renato Frischknecht and Eckart D. Gundelfinger, "The Brain's Extracellular Matrix and Its Role in Synaptic Plasticity," in _Synaptic Plasticity,_ eds. Michael R. Kreutz and Carlo Sala, _Advances in Experimental Medicine and Biology_ 970 (2012): 153–71, doi: 10.1007/978-3-7091-0932-8_7.
Researcher Sakida Palida explains that the perineuronal net can be part of the explanation for childhood amnesia: Laura Sanders, "Nets Full of Holes Catch Long-Term Memories," _ScienceNews_ , October 20, 2015, <https://www.sciencenews.org/article/nets-full-holes-catch-long-term-memories>.
Page 217. Åsa Hammar's research on depression and memory: Åsa Hammar and Guro Årdal, "Cognitive Functioning in Major Depression—A Summary," _Frontiers in Human Neuroscience_ 3 (2009): article 26, doi: 10.3389/neuro.09.026.2009 _._
Åsa Hammar and Guro Årdal, "Verbal Memory Functioning in Recurrent Depression during Partial Remission and Remission—Brief Report," _Frontiers in Psychology_ 4 (2013): article 652, doi: 10.3389/fpsyg.2013.00652.
Page 218. Åsa Hammar and researchers from Yale University have discovered another effect of depression: Forthcoming publication.
Page 219. Epilepsy is one of the most common neurological diseases: Susanne Fauser and Hayrettin Tumani, "Chapter 15—Epilepsy," in _Cerebrospinal Fluid in Neurologic Disorders_ , eds. Florian Deisenhammer, Charlotte E. Teunissen, and Hayrettin Tumani, _Handbook of Clinical Neurology_ 146, 3rd series (2017): 259–66, doi: 10.1016/B978-0-12-804279-3.00015-0.
Page 224. Memory problems are common after traumatic brain injury: P. Azouvi et al., "Neuropsychology of Traumatic Brain Injury: An Expert Overview," _Revue Neurologique_ 173, no. 7–8 (2017): 461–72, doi: 10.1016/j.neurol.2017.07.006.
Page 225. A general overview of Alzheimer's disease and possible causes: Kaj Blennow, Mony J. de Leon, and Henrik Zetterberg, "Alzheimer's Disease," _The Lancet_ 368, no. 9533 (2006): 387–403, doi: 10.1016/S0140-6736(06)69113-7.
Page 225. _Still Alice_ , directed by Richard Glatzer and Wash Westmoreland (New York: Killer Films, 2014).
Page 227. A critique of the amyloid hypothesis, the dominating theory of what causes Alzheimer's: Anders M. Fjell and Kristine B. Walhovd, "Neuroimaging Results Impose New Views on Alzheimer's Disease—The Role of Amyloid Revised," _Molecular Neurobiology_ 45, no. 1 (2012): 153–72, doi: 10.1007/s12035-011-8228-7.
Page 228. Developmental amnesia—to be born without ability to create memories because of dysfunction in the hippocampus: Faraneh Vargha-Khadem, David G. Gadian, and Mortimer Mishkin, "Dissociations in Cognitive Memory: The Syndrome of Developmental Amnesia," _Philosophical Transactions of the Royal Society B: Biological Sciences_ 356, no. 1413 (2001): 1435–40, doi: 10.1098/rstb.2001.0951.
Page 229. Severe memory loss, called retrograde amnesia, is sometimes attributed to psychological mechanisms: Angelica Staniloiu and Hans J. Markowitsch, "Dissociative Amnesia," _The Lancet Psychiatry_ 1, no. 3 (2014): 226–41, doi: 10.1016/S2215-0366(14)70279-2.
... but can also be blamed on brain injuries, as in this case with cardiac arrest: Michael D. Kopelman and John Morton, "Amnesia in an Actor: Learning and Re-learning of Play Passages Despite Severe Autobiographical Amnesia," _Cortex_ 67 (2015): 1–14, doi: 10.1016/j.cortex.2015.03.001.
Page 231. Wind Aamot has contributed to a documentary about his amnesia, _Jakten på hukommelsen_ [The hunt for memory], text and direction Thomas Lien (Oslo: Merkur Filmproduction AS, 2009).
**Chapter 7**
Page 237. The Global Seed Vault has been affected by global warming: Amy B. Wang, "Don't Panic, Humanity's 'Doomsday' Seed Vault Is Probably Still Safe," _Washington Post_ , May 20, 2017, <https://www.washingtonpost.com/news/energy-environment/wp/2017/05/20/dont-panic-humanitys-doomsday-seed-vault-is-probably-still-safe/?utm_term=.763d10f71a68>.
Page 239. The article that formed the basis for research of future thinking: Thomas Suddendorf and Michael C. Corballis, "Mental Time Travel and the Evolution of the Human Mind," _Genetic, Social, and General Psychology Monographs_ 123, no. 2 (1997) _:_ 133–67.
Page 239. Future thinking named one of the year's scientific breakthroughs: The [ _Science_ ] News Staff, "The Runners-Up," _Science_ 318, no. 5858 (2007): 1844–49, doi: 10.1126/science.318.5858.1844a.
Page 239. "It's a poor sort of memory": Lewis Carroll, _Through the Looking-Glass_ , chap. 5 (1871; Project Gutenberg, 1991, updated 2016), <http://www.gutenberg.org/files/12/12-h/12-h.htm>.
Page 241 and on. Thomas Suddendorf, _The Gap: The Science of What Separates Us from Other Animals_ (New York: Basic Books, 2013).
Page 244. Solomon Shereshevsky imagined he was really at school: Luria, _Mind of a Mnemonist._
Page 245. A short and easily read essay about the relationship between memories and future thinking (previously cited in chapter 4): Schacter and Addis, "Constructive Memory."
Page 248. Half the time our minds are wandering off from the present, say these researchers, although with a rather dubious conclusion on happiness: Matthew A. Killingsworth and Daniel T. Gilbert, "A Wandering Mind Is an Unhappy Mind," _Science_ 330, no. 6006 (2010): 932, doi: 10.1126/science.1192439.
Page 250. Children develop episodic memory and future thinking parallel to each other: Thomas Suddendorf and Jonathan Redshaw, "The Development of Mental Scenario Building and Episodic Foresight," _Annals of the New York Academy of Sciences_ 1296 (2013): 135–53, doi: 10.1111/nyas.12189.
Pages 250–51. Tulving's amnesia patient who couldn't see the future: Endel Tulving, "Memory and Consciousness," _Canadian Psychology_ 26, no. 1 (1985): 1–12, doi: 10.1037/h0080017. The quotes are from p. 4.
Page 251. How people with developmental amnesia can still picture the future: Niamh C. Hurley, Eleanor A. Maguire, and Faraneh Vargha-Khadem, "Patient HC with Developmental Amnesia Can Construct Future Scenarios," _Neuropsychologia_ 49, no. 13 (2011): 3620–28, doi: 10.1016/j.neuropsychologia.2011.09.015.
Page 252. People with depression have difficulties envisioning the future: Williams et al., "The Specificity of Autobiographical Memory."
Page 252. Suicide thoughts as future thoughts (Williams is a coauthor): Emily A. Holmes et al., "Imagery about Suicide in Depression—'Flash-forwards,'" _Journal of Behavior Therapy and Experimental Psychiatry_ 38, no. 4 (2007): 423–34, doi: 10.1016/j.jbtep.2007.10.004.
Page 254. Influence of episodic thinking on creativity: Kevin P. Madore, Donna Rose Addis, and Daniel L. Schacter, "Creativity and Memory: Effects of an Episodic-Specificity Induction on Divergent Thinking," _Psychological Science_ 26, no. 9 (2015): 1461–68, doi: 10.1177/0956797615591863.
Page 256. Thinking about the future in detail makes it easier to choose delayed rewards: Jan Peters and Christian Büchel, "Episodic Future Thinking Reduces Reward Delay Discounting through an Enhancement of Prefrontal-Mediotemporal Interactions," _Neuron_ 66, no. 1 (2010): 138–48, doi: 10.1016/j.neuron.2010.03.026.
Page 261. The UN climate panel's fifth report: Chris Field et al., eds., _Climate Change 2014: Impacts, Adaptation, and Vulnerability. Part A: Global and Sectoral Aspects. Contribution of Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change_ (Cambridge and New York: Cambridge University Press, 2014).
Page 278. "In My Life," performed by the Beatles, songwriters Lennon–McCartney, track 11 on _Rubber Soul_ , LP, Parlophone, 1965.
**RECIPE FOR GOOD MEMORIES**
**_Or: Thanks to all involved_**
BY WRITING THIS book, we have created new memories together. We have in a way given ourselves a new, unique reminiscence bump. For this, we owe a whole lot of people our thanks, because such memories are not created in a vacuum.
When diving into the memory, it is absolutely an advantage to receive help from good divers. "How many divers do you need?" Caterina Cattaneo said when we asked her if she would help us re-create the famous experiment. Caterina, who is also a brilliant author and our good friend and support, has contributed a lot more than diving, but now it's all about diving. We also want to thank Tine Kinn Kvamme, Rune Paulsen from the Divestore at Gylte, and the ten fantastic men who took part that rainy, raw February day.
The four chess champions Simen Agdestein, Olga Dolzhikova, Aryan Tari, and Jon Ludvig Hammer deserve glory and thanks, even if their efforts probably mean less in their personal memory bank than real chess achievements. For the hot-air balloon experiment, we enlisted the help of our Norwegian editor's wife, Anita Reinton Utgård, who benevolently entered into an agreement of conspiracy and provided childhood photos of our skilled editor Erik Møller Solheim, whom we of course also want to thank! Erik knew what we were after from the beginning and has helped us make the best possible book.
We want to thank Adrian Pracon for our most precious memory from this time. He brought us to Utøya and showed us the places that mean so much to him, both the pleasant places and the places where terror attacked him so directly.
Thank you all who have contributed to this book in interviews! Thanks to each and every one of our interviewees, but perhaps particularly to Linn Ullmann, Peder Kjøs, Terese Thue Lund, and Arne Schrøder Kvalvik, who properly changed our lives just a little bit and made us wiser in our work on this book.
Beyond the pages of the book, we have had a large and varied support group, including among others Simon Grahl; Mia Tuft; colleagues and friends from the neuropsychology environment; Hilde's book club and author friends Eivor Vindenes, Tone Holmen, Hedda Klemetzen, and Vera Micaelsen; and fellow hiker Marit Ausland. The largest support group includes our families: Matt and Niclas, Liv, Heidar, and Eyvor.
Although not by means of hot-air balloon, the book has now traveled all the way over to Vancouver, Canada, with the generous help of Rob Sanders and all the great staff at Greystone Books, including Jennifer Croll and Dawn Loewen, and the translator Marianne Lindvall. Together, we made this book even better.
Finally, we want to thank our sister Tonje, not only for her generous sharing of her near-death experience, but for all the memories we share. Like the time we all got stuck in the swamp near our cabin in Bodø: Ylva got stuck first. Tonje came to rescue her and got stuck too. Then Hilde came to the rescue but wasn't exactly lucky either. There we stood, calling our father, who eventually pulled us out. This goes to show that we don't always learn from the immediate past. The experience, though, we can keep with us for the rest of our lives.
Copyright © 2018 by Hilde Østby and Ylva Østby
Originally published in Norway in 2016 as _Å dykke etter sj_ ø _hester: En bok om_
_hukommelse (Diving for Seahorses: A Book About Memory)_
English translation copyright © 2018 by Marianne Lindvall
First published in English by Greystone Books in 2018
Foreword copyright © 2018 by Sam Kean
18 19 20 21 22 5 4 3 2 1
All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior written consent of the publisher or a license from The Canadian Copyright Licensing Agency (Access Copyright). For a copyright license, visit www.accesscopyright.ca or call toll free to 1-800-893-5777.
Greystone Books Ltd.
greystonebooks.com
Cataloguing data available from Library and Archives Canada
ISBN 978-1-77164-347-4 (cloth)
ISBN 978-1-77164-345-0 (epub)
Editing by Jennifer Croll
Copy editing by Dawn Loewen
Jacket and text design by Nayeli Jimenez
Jacket illustration by H. L. Todd, U.S. National Museum
Excerpts from MAGNIFICENT DESOLATION: THE LONG JOURNEY HOME FROM THE MOON by Buzz Aldrin, copyright © 2009, 2010 by StarBuzz LLC, used by permission of Harmony Books, an imprint of the Crown Publishing Group, a division of Penguin Random House LLC, and by permission of Bloomsbury Publishing Plc. All rights reserved.
Excerpts from UNQUIET by Linn Ullmann, translated by Thilo Reinhard and Linn Ullmann, copyright © 2015 by Forlaget Oktober AS, Oslo, translation copyright © 2019 by Linn Ullmann, used by permission of W. W. Norton & Company, Inc.
Excerpt from the FALSE MEMORY ARCHIVE used by permission of A.R. Hopwood. All rights reserved.
Every attempt has been made to trace ownership of copyrighted material. Information that will allow the publisher to rectify any credit or reference is welcome.
Greystone Books gratefully acknowledges the Musqueam, Squamish, and Tsleil-Waututh peoples on whose land our office is located.
Greystone Books thanks the Canada Council for the Arts, the British Columbia Arts Council, the Province of British Columbia through the Book Publishing Tax Credit, and the Government of Canada for supporting our publishing activities.
1. Cover
2. Title Page
3. Contents
4. Foreword
5. 1. The Sea Monster
6. 2. Diving for Seahorses in February
7. 3. The Skydiver's Final Thoughts
8. 4. In the Cuckoo's Nest
9. 5. The Big Taxi Experiment and a Rather Extraordinary Game of Chess
10. 6. The Elephant's Graveyard
11. 7. The Seeds of Svalbard
12. Notes
13. Recipe for Good Memories (Acknowledgments)
14. Copyright Page
|
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\section{Introduction}
The integer quantum Hall effect (IQHE) refers to the remarkable properties of a non-interacting
electron gas in two spatial dimensions in the presence of a magnetic field $B$ and a disordered potential.
These properties are only observed under the extreme conditions of
strong magnetic field and very low temperature which explains why it was discovered relatively late \cite{vonKlitzing}.
Figure \ref{Data} shows some typical experimental data.\footnote{We found this image on the internet but could not locate
the article which presented this figure, which are numerous.}
The most striking feature is the exact quantization of the transverse resistivity on the ``plateaux":
\begin{equation}
\label{rhoxy}
\rho_{xy} = \inv{n} \, \frac{h}{e^2}, ~~~~n = 1, 2, 3, \ldots
\end{equation}
where $h$ is Planck's constant and $e$ the electron charge.\footnote{The exact quantization $n= 1,2,3, \ldots$ has been verified experimentally to
within $10^{-10}$.}
\begin{figure}[t]
\centering\includegraphics[width=1.0\textwidth]{Data.pdf}
\caption{Experimental data on the Hall resistivity $\rho_{xy}$ as a function of magnetic field at very low temperatures (red curve,
the green curve is the longitudinal $\rho_{xx}$.) }
\label{Data}
\end{figure}
The theoretical understanding of the IQHE is by now well-developed and there are many excellent reviews and books \cite{Girvin}.
Some early pioneering works were by Laughlin and Halperin \cite{Laughlin,Halperin}. Let us review some of the very basics.
The pure problem of a single electron in a magnetic field was solved long ago by Landau.
The eigenstates fall into Laudau levels with energy $\ELandau (n) = ( n + \tfrac{1}{2} ) \hbar e B/m$ where $m$ is the electron mass.
Each Landau level has a large degeneracy of states $N_{{\rm states}} = \Phi/ \Phi_0$ where $\Phi$ is the magnetic flux and $\Phi_0 = h c/e$.
These are all de-localized states.
The IQHE is instead a many body problem, namely a finite density electron gas at finite temperature with non-zero $B$,
{\it in the presence of disorder,} such as various kinds of random impurities or defects. The plateaux would not exist without this disorder
and a complete understanding involves Anderson localization. Since we will not be considering any detailed physically motivated
hamiltonian,
let us just give a rough and brief picture of the phenomenon. At energies approximately in the gap between the pure Landau levels the states are localized due to disorder and thus don't contribute to the conductivity and it remains constant on the plateaux. At certain critical energies $E^c_n$ near the original Landau levels, where by definition
$E^c_{n+1} > E^c_n$, there is a quantum phase transition where some states are delocalized and contribute to a change of the conductivity.
Let us write this in terms of the Fermi energy $E_F$:
\begin{equation}
\label{EFprop}
{\rm If} ~~ E^c_{n} > E_F > E^c_{n-1} ~~~~{\rm then } ~~ \rho_{xy} = \inv{n} \, \frac{h}{e^2}
\end{equation}
For the experiments it is easier to control the magnetic field, thus we define critical $B^c_n$ where $B^c_{n+1} < B^c_n$ and:
\begin{equation}
\label{Bprop}
{\rm If} ~~ B^c_{n} < B < B^c_{n-1} ~~~~{\rm then } ~~ \rho_{xy} = \inv{n} \, \frac{h}{e^2} .
\end{equation}
It will also be important to point out that the integer $n$ in the quantization of $\rho_{xy}$ was eventually understood as a topological invariant,
sometimes referred to as a Chern number \cite{Thouless}. This fact explains the robustness of the quantized plateaux in spite of
variable details of the sample, in particular the realization of disorder, which varies from sample to sample.
It is also known that the transitions between plateaux are infinitely sharp at zero temperature, and for the most part we assume we are in this situation.
We wish to also mention that the IQHE also exists in models without Landau levels \cite{Haldane}.
Although the theory of the IQHE is well-developed, the explicit calculation of $\rho_{xy}$ is a difficult problem since it is a transport property in the presence of disorder. One can attempt disorder averaging, however this is also notoriously difficult, especially at the critical transitions. In fact, the precise nature of the quantum critical points at the transitions remains unknown; even the delocalization exponent is only known numerically. We will consider this exponent in Section IV.
Inspection of Figure \ref{Data} indicates many complicated details, such as the following. The widths of the plateaux
vary considerably for a single sample, becoming smaller as $B$ is decreased. Apart from this, the critical values $B^c_n$ appear random,
and certainly depend on the realization of the disorder, of which there are infinite possibilities. The resistivity vanishes at $B=0$, where it is approximately linear.
In this paper, we will merely present an explicit mathematical function that has many of the same properties as the measured
$\rho_{xy}$. It is not such a simple matter to conjure up such a function, since the measured $\rho_{xy}$ has many detailed features.
Our proposed formula is relatively simple, being constructed from the gamma and zeta functions, and captures many of these salient features. Hence our terminology ``phenomenological", since we don't attempt to compute the resistivity for any specific many-body hamiltonian, which in any case is a very difficult problem due to the disorder. For these reasons, it will be left as an open question as to whether any specific model hamiltonian
for the IQHE has the transport properties that correspond to our formula, even approximately.
We wish to point out however that the zeta function has an integral representation involving the Fermi-Dirac distribution
$1/(e^\varepsilon +1 )$ which we recall in the Appendix \eqref{IntRepFermi}, and this provides some encouragement
that our formula may eventually be understood as a resistivity for a gas of fermions.
Clearly some guesswork is involved and this exercise will not necessarily prove to be fruitful since it is not based on methods used to compute transport, such as a Kubo formula.
However we wish to point out that this kind of guesswork has been proven to be successful for some well-known problems.
For instance, let us just mention Veneziano's guess of a scattering amplitude expressed only in terms of ratios of gamma functions led to the development of the huge field of string
theory\cite{Veneziano}. Of course we cannot promise such success here, however we feel it is still worth pursuing.
For our proposed formula, the non-trivial zeros of the zeta function play a crucial role, and thus can perhaps provide some new insights on
the Riemann Hypothesis (RH). As emphasized above, we do not know if any microscopic quantum many body model leads to a resistivity
that corresponds to our phenomenological formula. Nevertheless, if we hypothesize such a connection, then the RH can be interpreted in light of it. There are very few approaches to the RH based essentially on physics, and this may be new one.
We should mention approaches based on the Hilbert-P\`olya idea that perhaps there exists a single particle quantum hamiltonian whose eigenvalues
are equal to the ordinates of zeros on the critical line. This has been pursued by Berry, Keating, Sierra and others \cite{BerryK,BerryK2,Sierra}.
A very different approach is based on ideas in statistical mechanics, in particular properties of random walks, where the randomness arises from the pseudo-randomness of the prime numbers.
See in particular the most recent work \cite{Mussardo} and references therein.
To our knowledge a possible connection between the IQHE and the RH has not been explored before, and our hope is that this short
work may shed some light on at least one of them. We wish to mention though that a relation between the pure Landau problem and the Riemann zeros was proposed in \cite{SierraTownsend}, however without disorder this is not the same physics as the IQHE which involves transport rather than energy eigenvalues.
\section{A phenomenological formula for $\rho_{xy}$}
Let us straightaway present our formula. Let $s=\sigma + i t$ be a complex variable and first define the real function:
\begin{equation}
\label{thetaDef}
\theta(\sigma, t) = \Im \log \Gamma (s/2) - t \, \log \sqrt{\pi }+ {\rm arg} \, \zeta(s), ~~~~~(s = \sigma + i t).
\end{equation}
First a few words about the components of this function, which can in fact be interpreted as an angle, as we will explain.
$ \Im \log \Gamma\( \tfrac{1}{2} (\sigma+it) \)$ should be understood as ${\rm arg} \, \Gamma (s/2)$.\footnote{In Mathematica LogGamma[z] is a built in function.}
It is important here and elsewhere that in the above equation it is ${\rm arg}$ and not ${\rm Arg}$, where the latter by definition is the principal branch.
Remind that for any meromorphic function $f(s)$, away from a zero or pole one can always calculate
${\rm Arg} \, f(s) = \arctan \, \Im f(s)/\Re f(s)$ on the principal branch $-\pi < {\rm Arg} < \pi$.
On the other hand, ${\rm arg}$ keeps track of branches and needs to be defined differently, typically using piecewise integration
of $f'(s)/f(s)$ from some known point. ($ {\rm arg} (e^{i \alpha}) = \alpha$ for $-\infty < \alpha < \infty$.) For instance for ${\rm arg} \, \zeta(\tfrac{1}{2}
+i t)$ one standard definition is via the contour $\CC'$ in Figure
\ref{argFigure}.
In summary, if $s$ is neither a zero nor a pole, then
\begin{equation}
\label{args}
{\rm arg} \, f(s) = {\rm Arg} \, f(s) ~~~{\rm mod} ~ 2 \pi, ~~~~~~ -\pi < {\rm Arg}\, f(s) < \pi,
\end{equation}
however in the present context, the ${\rm mod} ~ 2\pi$ will be important.
The contribution from ${\rm arg} \, \Gamma$ is a smooth function that grows with $t$. Using the Stirling formula and its corrections one can easily show for large $t$:
\begin{equation}
\label{RS}
\Im \log \Gamma \( \tfrac{1}{2} (\sigma+it)\) - t \, \log \sqrt{\pi } =
\frac{t}{2} \log \( \frac{t}{2\pi e}\) + \frac{\pi (\sigma -1)}{4} - \frac{(3 \sigma^2 - 6 \sigma +2)}{12 t} + \CO(1/t^3) .
\end{equation}
On the other hand, ${\rm arg} \, \zeta (s)$ is a much more complicated quantity and where all the action is.
Some basic facts we need about the zeta function
are collected in the Appendix. There is no analog of Stirling's formula that would lead to anything as simple as \eqref{RS}. An important role will be played by $S(t) = {\rm arg} \, \zeta (\tfrac{1}{2}+it) / \pi$, and there is a large mathematical literature concerning it. Here let us just mention Selberg's central limit theorem \cite{Selberg}: $S(t)$ satisfies a normal distribution with zero mean
and standard deviation equal to$\tfrac{1}{\sqrt{2} \pi} \sqrt{ \log \log t} $ in the limit $t\to \infty$. Thus it grows very, very slowly with $t$ compared to the first terms in \eqref{thetaDef}. Thus to a high probability, ${\rm arg} \, (\tfrac{1}{2} + it)$ is nearly always on the
principal branch.\footnote{For instance, from Selberg's theorem one deduces that in the range $0<t<1000$ the probability that
${\rm arg} \, \zeta(\tfrac{1}{2} + it )$ is not on the principle branch is only $0.0014$. In practice this implies that in many cases one can use
${\rm Arg}$ in Mathematica to compute ${\rm arg}$, however this should be done with some care.}
Nevertheless it can attain infinitely large values, though very rarely, due to the tail of the normal distribution.
With these preliminaries, we present the phenomenological function we advertised.
Henceforth we work in units where $h=c=1$, we set $m=e=1$, and $B$ is expressed in dimensionless units, such as $B/B_0$ where
$B_0$ is a reference magnetic field strength.
We first present the simplest version,
and defer presenting some deformations to Section IV:
\begin{equation}
\label{rhoxyformula}
\rho_{xy} (B) = \frac{\pi}{\theta(\tfrac{1}{2}, 1/B) + 2 \pi } .
\end{equation}
In Figure \ref{rhoxyPlot} we plot the above function, and it certainly shows some resemblance to the data in Figure \ref{Data}.
\begin{figure}[t]
\centering\includegraphics[width=.7\textwidth]{rhoxyPlot.pdf}
\caption{Plot of the function \eqref{rhoxy}. We have shifted $\sigma = \tfrac{1}{2} \to \tfrac{1}{2} + \delta$ with
very small positive $\delta$ in order to smooth out the transitions. At $\sigma = \tfrac{1}{2}$, the transitions are infinitely sharp
as expected at zero temperature.}
\label{rhoxyPlot}
\end{figure}
For fixed $B$, the Fermi energy is a function of the number density of electrons. If the density is fixed, as in a specific sample, then the Fermi energy depends on $B$, thus one can observe the plateaux by either varying $E_F$ or $B$. The relation between these quantities
can be complicated. Note however that since the degeneracy of each pure Landau level is proportional to $B$, we roughly expect that
$E_F \propto 1/B$.\footnote{In two spatial dimensions one expects $E_F \propto \rho$ where $\rho$ is the number density of electrons. For instance, in natural units with $\hbar = c= 1$, a dimensionally correct relation is $E_F \propto \(\frac{\rho}{me \ell^2 } \) \inv{B}$ where $\ell$
a length scale characterizing the disorder. The present work does not rely on the specific relation between $E_F$ and $B$.}
Since we will not deal with any specific material, and we are not experts, as an oversimplification we will simply {\it define} for now
\begin{equation}
\label{EBprop}
E^c_n \equiv 1/B^c_n
\end{equation}
in appropriate units. Variations of the above formula will be considered in Section IV.
\bigskip
Let us list some of the main features of \eqref{rhoxyformula}:
\bigskip
$\bullet$ ~~ The values of the resistivity are exactly quantized as $\rho_{xy} = 1/n$ on the plateaux.
{\it If one assumes the RH, and all the non-trivial zeros are simple},
then this is explained by the well-known result that the number of zeros of $\zeta (s)$ inside the critical strip
$0<\sigma<1$ with $0<t<T$ is given by
\begin{equation}
\label{NofT}
N(T) = \theta(\tfrac{1}{2}, T)/\pi + 1 .
\end{equation}
This is a consequence of Cauchy's argument principle, and is reviewed in the Appendix.
\bigskip
$\bullet$ ~~ Let $\rho_n = \tfrac{1}{2} + i t_n$ denote the $n$-th zero of $\zeta$ on the upper critical line, where by convention
$n=1,2, \ldots$ and the first few are $t_1 = 14.134.., ~ t_2 = 21.022....$.
Again assuming the RH, the critical values are given precisely by these zeros:
\begin{equation}
\label{BcEc}
B^c_n = 1/t_n ~~ \Longrightarrow ~~ E^c_n = t_n .
\end{equation}
\bigskip
$\bullet$ ~~ The widths of the plateaux, $B^c_n - B^c_{n+1}$, become smaller and smaller as $B$ is decreased,
which resembles the experimental data.
Although we did not attempt a fit to the data in Figure \ref{Data}, one can check that the ratios $B^c_{n+1}/B^c_n$ are roughly equal to
$t_n/t_{n+1}$.
\bigskip
$\bullet$ ~~ The resistivity vanishes at $B=0$ nearly linearly:
\begin{equation}
\label{Bzero}
\lim_{B \to 0} \rho_{xy} (B) \approx \frac{2 \pi B}{ \log(1/ B) } .
\end{equation}
By replacing $B$ with $B |\log (B)| $ in \eqref{rhoxyformula}, $\rho_{xy} (B)$ is linear near $B=0$ up to much smaller $\log \log B$ corrections. We will consider
other kinds of deformations in Section IV.
\section{Interpretation in connection with the Riemann Hypothesis}
The RH is the conjecture that all zeros inside the critical strip $0<\sigma <1$ are on the critical line $\sigma = \tfrac{1}{2}$.
Whether these zeros are simple or not also remains a difficult open problem.
In the last section we already commented that our phenomenological formula \eqref{rhoxyformula} can only describe the IQHE if
the RH is true and all zeros are simple. Let us elaborate.
Suppose the RH is false such that there are zeros $\rho_\bullet$ off the line, which necessarily come in pairs
$\rho_\bullet = \sigma_\bullet + i t_\bullet, 1- \sigma_\bullet + i t_\bullet$. These zeros contribute to $N(T)$ with multiplicity $2$ or more.
This would imply that the transverse conductivity $1/\rho_{xy}$ does not always jump by $1$ at the transitions, but rather sometimes jumps
by $2$, or more depending on their multiplicity.
In other words not all integers $n$ in \eqref{rhoxy} would be physically realized. Furthermore,
assuming the RH, if the zeros were not simple, then $n$ would not always jump by exactly $1$, but rather by the order of the zero, and again some $n$ would be absent.
In our simplified physical picture thus far, the critical energies $E^c_n$ are identified as the Riemann zeros $t_n$ based on \eqref{EBprop}.
Whereas the quantization $n$ in \eqref{rhoxy} is robust, i.e. sample independent due to its relation to the Chern topological number,
the values at the transition $E^c_n$ are not universal. They depend in particular on the realization of the disorder, i.e. details of the
disorder, among other properties of the sample.
A famous conjecture is that the differences between Riemann zeros $t_n$ satisfies the GUE statistics of random hamiltonians \cite{Montgomery,Odlyzko}. In the present context this randomness is naturally explained as arising from the random disorder.
In fact random matrix theory has already been applied to quantum transport in disordered systems \cite{Beenakker}.
The actual Riemann zeros must then correspond to a special realization of disorder, just as the Hilbert-P\'olya idea involves some as yet unknown hamiltonian.
It is important then that our formula \eqref{rhoxyformula} can be deformed in order to accommodate for variable
$E^c_n \neq t_n$, and other variations such as finite temperature. This will be explored in Section IV.
It is interesting to note that extreme values of $|\zeta ( \tfrac{1}{2} + i t)|$ were studied from the perspective of the so-called freezing transition in disordered landscapes \cite{Fyodorov1,Fyodorov2}, and the latter is an important component of the physics of the IQHE.
Returning to pure mathematics, the angle $\theta(\sigma, t)$ contains all the information about the zeros although in a not so transparent way.
This was developed in a precise manner in \cite{Gui}.
Referring to the completed zeta function $\chi (s)$ in \eqref{chidef}, it is known that inside the critical strip $\chi (s)$ and $\zeta (s)$ have the same zeros.
Obviously at a zero $\rho_n$, the modulus $| \chi (\rho_n)| =0$, however such a formula is not very useful in enumerating the zeros.
Assuming the RH, one can in fact extract the actual exact zeros $t_n$ from $\theta (\sigma, t)$ in the following way.
First it is important that even though $| \chi (s) | =0$ at a zero, its argument $\theta(\sigma, t)$ is still well defined {\it once one specifies a contour indicating the direction of approach to the zero}. Let us provide a slightly different argument than the one presented in \cite{Gui}.\footnote{This version was found during discussions with Giuseppe Mussardo.}
On the critical line $\sigma = \tfrac{1}{2}$, by the functional equation \eqref{funceqn}, $\chi(s)$ is real. If the RH is true and the zeros are simple,
it must simply change sign at each zero. Thus, assuming the RH and the simplicity of the zeros, $\theta(\tfrac{1}{2}, t)$ must jump by $\pi$ at each zero. Approaching zeros along the critical line from below, one
finds
\begin{equation}
\label{frombelow}
\lim_{\epsilon \to 0^+} \, \theta(\tfrac{1}{2}, t_n - \epsilon ) = \pi (n-1).
\end{equation}
Rotating counterclockwise by $\pi/2$, one deduces
\begin{equation}
\label{fromright}
\lim_{\delta \to 0^+} \, \theta(\tfrac{1}{2} + \delta, t_n ) = \pi (n- \tfrac{3}{2} ) .
\end{equation}
The above equation was used in \cite{Gui} to calculate zeros to very high accuracy.\footnote{To our knowledge the above equation was first proposed by the author. See \cite{Gui} and references therein.}
It fact it was proven that if there is a unique solution to \eqref{fromright} for every $n$, then the RH is true and
all zeros are simple.
The importance of approaching the zeros from the right of the critical line is two-fold.
For so-called $L$-functions based on non-principal Dirichlet characters, there are strong arguments that
the Euler product formula (EPF) converges for $\sigma>\tfrac{1}{2}$ (See \cite{LM1}). For zeta itself, the Euler product formula is
\begin{equation}
\label{EPF}
\zeta (s) = \prod_p \( 1 - \inv{p^s} \)^{-1}
\end{equation}
where $p$ is a prime, and the EPF converges only for $\sigma > 1$, unlike what is expected for $L$-functions based on
non-principal Dirichlet characters.
To the left of the critical line, ${\rm arg} \, \zeta (s)$ behaves
quite differently than from the right: from equation \eqref{argrelations} one sees that to the left there are many more changes of branch compared with to the right. In conjunction with the EPF, one can use the latter to approximate
${\rm arg} \, \zeta (\tfrac{1}{2} + i t)$ and thereby compute the zeros $t_n$ directly from the prime numbers with a truncation of the EPF, at least approximately \cite{ALzeta}.
\defz{z}
\section{Deformations of the formula for $\rho_{xy}$: variable $B^c_n$ and modeling finite temperature}
As explained above, we interpreted the critical $E^c_n$ as equal to the exact Riemann zeros on the critical line.
In reality, for a specific experimental sample, these $E^c_n$ are not equal to the exact Riemann zeros $t_n$. It is thus important for our proposal that
the $E^c_n$ can be deformed away from the exact and known $t_n$ without spoiling the exact quantization of $n$ in \eqref{rhoxy}. One expects this is possible since $n$ is topological. This can be done in many ways, and in this section we explore a few.
\bigskip
\noindent $\bullet$ ~~ {\bf Deforming the functional dependence on $B$.} ~~
The most straightforward deformation is to change the function of $B$ inside $\theta(\tfrac{1}{2}, 1/B)$ in \eqref{rhoxyformula}, i.e.
to replace $1/B$ by a function $f(B)$. The resistivity remains quantized on the plateaux, i.e. equation \eqref{rhoxy} still holds.
However this modifies the critical values $B^c_n$ to solutions of $f(B^c_n) = t_n$.
For instance, changing
$1/B$ by a constant $\alpha/B$ simply rescales the $B^c_n$. More importantly, replacing $1/B$ with $f(B) = 1/B |\log B|$ makes the small $B$ behavior much more linear near $B=0$ as previously stated.
\bigskip
\noindent $\bullet$ ~~ {\bf Deforming the relation between $E_F$ and $B$.} ~~ The proposed relation $\eqref{EBprop}$ was an over simplification
of the physics, and was simply taken as a definition of $E^c_n$. Clearly the relation $E^c_n = 1/B^c_n$ can be deformed,
which again does not spoil the quantization on the plateaux but modifies $E^c_n$.
\bigskip
\noindent $\bullet$ ~~ {\bf Modeling the effect of finite temperature.} ~~
At zero temperature ${\bf T}$ the jumps at the transitions in $\rho_{xy}$ are known to be infinitely sharp, i.e. are close to step functions.
At finite temperature these sharp transitions are broadened smoothly and have a finite width. It is known experimentally that the
jumps are still centered around the zero temperature $B^c_n$ but deformed in a smooth way that is symmetric about $B^c_n$.
This behavior can be incorporated in a relatively simple way that we now describe. In finding this deformation we were motivated by
a deformation of an integral representation of the zeta function that closely resembles adding a chemical potential to the Fermi-Dirac distribution. Namely:
\begin{equation}
\label{FermiPoly}
- \Gamma (s)\, {\rm Li}_s (-e^{-\mu}) = \int_0^\infty d\varepsilon \, \varepsilon^{s-1} \inv{e^{\varepsilon + \mu} +1 }, ~~~ ~~~~\Re (s) > 0,
\end{equation}
where ${\rm Li}_s (z)$ is the polylogarithm:
\begin{equation}
\label{LiDef}
{\rm Li}_s (z) = \sum_{n=1}^\infty \frac{ z^n }{n^s}
\end{equation}
(analytically continued).
In the above formula $\varepsilon^{s-2}$ can perhaps be viewed as a kind of density of states.
The above formula applied to a free gas of fermions would identify $\mu$ as minus the chemical potential divided by the temperature,
however this does not necessarily correspond to the physical situation here.
It does however suggest
to replace $\zeta (s)$ in \eqref{thetaDef}
by the polylogarithm
\begin{equation}
\label{thetaPoly}
\theta_\mu (\sigma, t) = \Im \log \Gamma (s/2) - t \, \log \sqrt{\pi }+ {\rm arg} \, {\rm Li}_{s} (e^{-\mu} ).
\end{equation}
($s=\sigma+it$).
Note that
${\rm Li}_s (1) =\zeta (s)$.
Let us thus consider the deformation:
\begin{equation}
\label{rhoxyPoly}
\rho_{xy} (B,\mu) = \frac{\pi}{\theta_\mu (\tfrac{1}{2}, 1/B) + 2 \pi } .
\end{equation}
The resulting resistivity closely captures the broadening of the transitions found in the experimental data, as seen in Figure \ref{MuPlotKey}.
\begin{figure}[t]
\centering\includegraphics[width=0.9\textwidth]{MuPlotKey.pdf}
\caption{The conductivity $1/\rho_{xy}$ in \eqref{rhoxyPoly} with $\mu = 0.01, 0.05, 0.10, 0.15$.}
\label{MuPlotKey}
\end{figure}
It is then interesting to see what \eqref{rhoxyPoly} implies for the de-localization exponent $\nu$.
At the transition the correlation length diverges $\xi_c \sim |x-x_c|^{-\nu} $ where $x$ could be the magnetic field for instance.
The broadening of the transition at finite temperature depends on $\nu$. At zero temperature ${\bf T}$ the transition is sharp, thus
$d\rho_{xy} /dB$ diverges. It is known from the physics that (see for instance \cite{RIMS}):
\begin{equation}
\label{exponentT}
\frac{\partial \rho_{xy}}{\partial B} \Big\vert_{B=B^c_n} \sim {\bf T}^{-\kappa}
\end{equation}
where
$\kappa = 1/(\nu \, z)$. Here $z$ is the dynamical exponent that relates temperature and phase coherence length
$\ell_\Phi \sim T^{-1/z}$. For relativistic systems $z = 1$ and it is known that for the IQHE $z \approx 1$.
From the formula \eqref{rhoxyPoly} one sees that the sharpness of the transition is controlled by $\mu$, where the derivative
in \eqref{exponentT} is infinite when $\mu =0$. At the $n$-th transition around $\mu =0$, from the formula \eqref{rhoxyPoly} the simple exponent $\kappa =1$ is obtained:
\begin{equation}
\label{exponent}
\frac{\partial \rho_{xy}}{\partial B} \Big\vert_{B=B^c_n} = C_n \, \mu^{-\kappa}, ~~~~~\kappa =1 .
\end{equation}
The exponent $\kappa$ is the same for all $n$ but $C_n$ varies, for instance
$C_1 = 17.46, C_2 =11.59$.
Experimentally $\nu \approx 2.38$ whereas relatively recent analysis of the Chalker-Coddington network model gives $\nu = 2.59$
\cite{RIMS}.
Based on the formula \eqref{rhoxyPoly} we can obtain non-trivial $\kappa \neq 1$ by simply replacing
$\mu$ by $\mu^\kappa$.
\bigskip
\noindent $\bullet$ ~~ {\bf A deformation of the actual Riemann zeros.} ~~
There is another interesting deformation which is rather different than the above which involves deforming the $\tfrac{1}{2}$ in $\theta(\tfrac{1}{2}, 1/B)$ in \eqref{rhoxyformula}, as we now explain.
From $\overline{\chi (s)} = \chi(\overline{s})$ one has
$\theta (\sigma, -t) = - \theta (\sigma, t)$~ ${\rm mod} ~ 2 \pi$.
Combined with the functional equation \eqref{thetaFunc}, one has
\begin{equation}
\label{thetasumzero}
\theta(\sigma, t) + \theta(1-\sigma, t) = 0, ~~~~~{\rm mod} ~ 2 \pi .
\end{equation}
Let us then define
\begin{equation}
\label{thetasum}
\theta_S (\sigma, t) \equiv \tfrac{1}{2} \( \theta (\sigma, t) + \theta (1-\sigma, t) \).
\end{equation}
We can thus define what is necessarily an integer $\mathfrak{n} (\sigma, t)$ for all $\sigma, t$:
\begin{equation}
\label{ncal}
\mathfrak{n} (\sigma, t) = \theta_S(\sigma, t)/\pi +1.
\end{equation}
Let us then deform $\rho_{xy}$ as follows:
\begin{equation}
\label{rhoxyDeformed}
\rho_{xy} (B, \sigma) = \frac{\pi}{\theta_S (\sigma, 1/B) + 2 \pi}.
\end{equation}
When $\sigma=\tfrac{1}{2}$, ~$\mathfrak{n} (\tfrac{1}{2}, T)$ equals the number of zeros along the critical line $N(T)$ in eq.
\eqref{NofT} (assuming RH).
We have observed an interesting mathematical property:
$\mathfrak{n} (\sigma, T)$ is also equal to $N(T)$ for continuous $\sigma \neq \tfrac{1}{2}$ but with small deformations of the transition values $t_n
\to \widehat{t}_n$ that depend on $\sigma$ and $n$. The deformed $\widehat{t}_n$ are clearly no longer zeros of $\zeta$. One explanation for this property is that small deformations from $\sigma = \tfrac{1}{2}$
should not change $N(t)$ as long as one is on a plateaux and not too close to the transition, however we have no proof of this.
More precisely $\mathfrak{n} (\sigma, T) = N(T)$ for $T$ deep inside the plateaux away from the transitions. We have verified this for $n$ up to $1000$.
In other words this deformation of $\sigma$ from $\tfrac{1}{2}$ does not change the topological number $n$ on the plateaux, however
the critical values $E^c_n$ are slightly deformed from $t_n$ in a non-trivial manner. This is only true for $\sigma$ not very large, otherwise the counting is affected by the poles
of $\chi (s)$ at the poles of $\Gamma (s/2)$. Thus in such a deformation one should limit $ -1 < \sigma < 2 $, which includes values outside the critical strip.
We show this numerically in Figure \ref{sigmaDeformation} around the first zero $t_1 = 14.1347..$ for the extreme deformation $\sigma =2$.
One sees that $t_1$ is deformed to approximately $\widehat{t}_1 = 14.42$.
It is somewhat remarkable that the function $\theta_S (\sigma, t)$ knows about $N(T)$ on the plateaux even though it can be computed from $\zeta$ for values completely {\it outside} the critical strip $\sigma >1$.
This perhaps has some interesting implications in analytic number theory.
\begin{figure}[t]
\centering\includegraphics[width=.5\textwidth]{sigmaDeformation.pdf}
\caption{$N(t) = \mathfrak{n} (\sigma = \tfrac{1}{2}, t)$ (blue line) verses $\mathfrak{n} (\sigma = 2, t)$ (yellow line) as a function of $t$ around the first zero $t_1=14.1347..$. For $\mathfrak{n} (2,t)$ one sees that the plateaux values have not changed, i.e. are still $0$ or $1$, however the transition is deformed away from the actual Riemann zero $t_1 = 14.13..$ to $14.42..$.}
\label{sigmaDeformation}
\end{figure}
\bigskip
\noindent $\bullet$ ~~ {\bf Deformations based on other $L$-functions.} ~
On the more exotic side, in analytic number theory
there are an infinite number of known $L$-functions that are expected to satisfy the so-called Grand Riemann Hypothesis, in particular those based on Dirichlet characters or on modular forms \cite{Apostol}. Replacing $\theta$ in \eqref{rhoxyformula} with the argument of the completion of such an $L$-function analogous to \eqref{chidef}, which is known to also involve the gamma function \cite{Apostol},
one still has a robust quantization for $\rho_{xy}$, however the $t_n$ and thus the $B^c_n$ and $E^c_n$ are different in a non-smooth way.
\bigskip
\section{Closing remarks}
We have proposed a phenomenological formula for the transverse resistivity for the IQHE built from the gamma and zeta functions
which appear to capture the main physical properties at least qualitatively. The physics is very speculative: we emphasize once again that we have not performed any computation of the resistivity in any specific quantum many-body problem whatsoever, thus the main open question is whether a physical model exists that has a resistivity
corresponding to our proposed formula. If we simply assume the formula we proposed for $\rho_{xy}$, then the non-trivial Riemann zeros play an essential role, and this perhaps offers a new perspective on the Riemann Hypothesis which we have partially explored.
For instance, if the RH were false, then not all integers $n$ in the quantization \eqref{rhoxy} would be physically realized.
All of the pure mathematics we have used is well-known, except for the discussion surrounding \eqref{rhoxyDeformed}.
A common link between the IQHE and the Riemann zeros perhaps comes from random matrix theory, since the latter has been applied to both the Riemann zeros and to disordered systems. This is an appealing connection, to be contrasted to the hamiltonians proposed toward a realization of
the Hilbert-P\'olya idea. Proposals such as $H= xp$ and variations are not random hamiltonians; instead the randomness of the zeros is attributed to the chaotic behavior of such hamiltonians \cite{BerryK}, which is very different than a particle moving in a random landscape, such as in the IQHE.
In fact, relatively recently, random matrix theory was applied to a study of the extreme values of the zeta function on the critical line
by making an analogy with the so-called freezing transition in disordered landscapes \cite{Fyodorov1,Fyodorov2},
and such a freezing transition is expected to play a role in the IQHE in order to understand its multi-fractal properties.
\section{Acknowledgements}
We wish to thank Giuseppe Mussardo and Germ\`an Sierra for discussions.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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Putin invites public ideas on voting transparency
Russian Prime Minister Vladimir Putin (RIA Novosti / Yana Lapikova) © RIA Novosti
PM Vladimir Putin has called on Popular Front movement activists to gather public and non-governmental organizations' ideas on how to provide a maximally legitimate and transparent presidential poll.
Putin underlined that he, as one of presidential candidates, does not need "any ballot rigging" during the March 4 vote. "I'm interested in absolutely transparent elections. I want it to be clear to everyone. I want to rely on people's will, their trust, since if it doesn't exist, there is no point in working," he said. Earlier this month, in response to mass protests against alleged fraud during the December 4 parliamentary vote, Putin suggested equipping all the polling stations in Russia with round-the-clock webcams. On Tuesday, during the session of the Russian Popular Front's coordinating council, Putin came back to the topic, saying that it is important exactly how this idea would be put to life. Putin stressed that all the four parties that made it to the parliament should take part in the presidential campaign process. Their representatives should be present at polling station, have an opportunity to control the process, while webcams must work night and day and control both the places where ballots are cast and counted. The leader of the Popular Front, Putin asked for opinion of participants of the meeting on what else could be done to make sure "that there would be no doubts that the elections are legitimate, impartial and transparent." "Absolutely, we should stay within the frameworks of the law," he stressed, as cited by Itar-Tass. The prime minister stressed that no "amateurish performances" are acceptable. Addressing the movement activists, he suggested that they appeal to people, public organizations and listen to their proposals on the matter.Vladimir Putin also suggested opening an internet debate on improving election transparency."Indeed, I believe we should open a discussion on the internet, listen to people, to their constructive proposals, and summarize them. And if you see that there are ideas that would really lead to increasing the transparency of the [voting] process, we should certainly use them," he said.In addition, Putin – who also chairs the United Russia party that won the recent vote – expressed his readiness to discuss the issue with the head of the Central Election Commission, Vladimir Churov.As for alleged violations during the recent State Duma elections, the only way to deal with them is through the courts. Putin stressed than any talks about reconsidering the results are useless now that the State Duma vote has been run, the parties have started their work in the lower house, and a speaker was elected. The PM accused the critics of the power who doubt the fairness of the election results of having neither a common program nor a clear goal. "What's the problem here? [The opposition] have no common program – there are many programs, but no united one – no clear and understandable ways of achieving goals, which are also unclear, and there are no people who are capable of doing something concrete," he said, cites Interfax. Putin observed that there are political forces in Russia – as in any other country – for whom a "Brownian movement" is more important than the prospect of development. He stressed though that they have their right to exist and should be treated with respect.
Trends:Election 2012
Putin's campaign team to be modeled on Popular Front
Politically-active youth a good legacy of 'Putin's regime' - PM
Putin eyes total anti-fraud webcam surveillance of polling stations
Medvedev calls for major reform of Russia's political system
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Kudrin's 2 cents: Ex finance minister urges opposition-government dialogue
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\section{Framework}
\label{sec:framework}
\subsection{The model}
Let us consider the non linear regression model of the form
\[
Y_{n} = f \left( X_{n} , \theta \right) + \epsilon_{n}
\]
where $( X_n, Y_n,\epsilon_n)_{n\geq 1}$ is a sequence of independent and identically distributed random vectors in $\mathbb{R}^{p} \times \mathbb{R} \times \mathbb{R}$.
Furthermore, for all $n$, $\epsilon_n$ is independent from $X_n$
and is a zero-mean random variable.
In addition, the function $f$ is assumed to be almost surely twice differentiable with respect to the second variable.
Under certain assumptions, $\theta$ is a local minimizer of the functional $G: \mathbb{R}^{q} \longrightarrow \mathbb{R}_{+}$ defined for all $h \in \mathbb{R}^{q}$ by
\[
G(h) = \frac{1}{2}\mathbb{E}\left[ \left( Y - f \left( X,h \right) \right)^{2} \right] =: \frac{1}{2} \mathbb{E}\left[ g(X,Y,h) \right] ,
\]
where $(X, Y, \epsilon)$ has the same distribution as $(X_1, Y_1, \epsilon_1)$.
Suppose from now that the following assumptions are fulfilled:
\begin{itemize}
\item[\textbf{(H1a)}] There is a positive constant $C$ such that for all $h \in \mathbb{R}^{q}$,
\[
\mathbb{E}\left[ \left\| \nabla_h g\left( X,Y,h \right) \right\|^{2}\right] \leq C,
\]
\item[\textbf{(H1b)}] There is a positive constant $C''$ such that for all $h \in \mathbb{R}^{q}$,
\[
\mathbb{E}\left[ \left\| \nabla_{h} f \left( X, h \right) \right\|^{4} \right] \leq C''
\]
\item[\textbf{(H1c)}] The matrix $L(h)$ defined for all $h \in \mathbb{R}^{q}$ by
\[
L(h) = \mathbb{E}\left[ \nabla_{h}f (X,h)\nabla_{h}f(X,h)^{T} \right]
\]
is positive at $\theta$.
\end{itemize}
Assumption \textbf{(H1a)} ensures ifrst that the functional $G$ is Frechet differentiable for all $h \in \mathbb{R}^{q}$. Moreover, since $\epsilon$ is independent from $X$ and zero-mean,
\[
\nabla G (h) = \mathbb{E} \left[ \left( f(X,h) - f(X,\theta) \right) \nabla_{h} f \left( X,h \right) \right] .
\]
Then, $\nabla G(\theta) = 0$.
Assumption \textbf{(H1b)} will be crucial to control the possible divergence of estimates of $L(\theta)$ as well as to give their rate of convergence. Finally, remark that thanks to assumption \textbf{(H1c)}, $L(\theta)$ is invertible.
\subsection{Construction of the Stochastic Gauss-Newton algorithm}
In order to estimate $\theta$, we propose in this work a new approach.
Instead of using straight a Stochastic Newton algorithm based on the estimate of the Hessian of the functionnal $G$, we will substitute this estimate by an estimate of $L(\theta)$, imitating thereby the Gauss-Newton algorithm. This leads to an algorithm of the form
\begin{equation}
\label{SGNalgo}
\theta_{n+1} =\theta_{n} + \frac{1}{n+1}L_n^{-1}\left(Y_{n+1} - f\left( X_{n+1},\theta_{n}\right)\right)\nabla_{h}f\left( X_{n+1} , \theta_{n} \right),
\end{equation}
where
\[L_{n}:=\frac{1}{n}\sum_{i=1}^{n} \nabla_{h}f \left( X_{i} , \theta_{i-1} \right) \nabla_{h}f \left( X_{i} , \theta_{i-1} \right)^{T} \]
is a natural recursive estimate of $L(\theta)$. Remark that supposing the functional $G$ is twice differentiable leads to
\[
\nabla^{2}G(h) = \mathbb{E}\left[ \nabla_{h} f \left( X,h \right) \nabla_{h} f\left( X,h \right)^{T} \right] - \mathbb{E}\left[ \left( f(X,\theta) - f(X,h) \right) \nabla_{h}^{2}f(X,h) \right],
\]
and in particular, $ H = \nabla^{2}G(\theta) =L(\theta)$. Then, $L_{n}$ is also an estimate of $H$. The proposed algorithm can so be considered as a Stochastic Newton algorithm, but does not require an explicit formula for the Hessian of $G$. Furthermore, the interest of considering $L_{n}$ as an estimate of $H$ is that we can update recursively the inverse of $L_{n}$ thanks to the Riccati's formula. To obtain the convergence of such an algorithm, it should be possible to state the following assumption:
\begin{itemize}
\item[\textbf{(H*)}] There is a positive constant $c$ such that for all $h \in \mathbb{R}^{q}$,
\[
\lambda_{\min} \left( L (h) \right) \geq c.
\]
\end{itemize}
Nevertheless, this assumption consequently limits the family of functions $f$ we can consider.
\subsection{The algorithms}
In order to free ourselves from the restrictive previous assumption \textbf{(H*)},
we propose to estimate $\theta$ with the following Gauss-Newton algorithm.
\begin{defi}[Stochastic Gauss-Newton algorithm]
Let $(Z_n)_{n \geq 1}$ be a sequence of random vectors, independent and for all $n\geq 1$, $Z_n \sim \mathcal{N}(0,I_q)$.
The Gauss-Newton algorithm is defined recursively for all $n \geq 0$ by
\begin{align}
\notag & \widetilde{\Phi}_{n+1} = \nabla_{h} f \left( X_{n+1},\widetilde{\theta}_{n} \right) \\
\label{defsgn}& \widetilde{\theta}_{n+1} = \widetilde{\theta}_{n} + \widetilde{H}_{n}^{-1}\widetilde{\Phi}_{n+1} \left( Y_{n+1} - f \left( X_{n+1},\widetilde{\theta}_{n} \right)\right) \\
\notag & \widetilde{H}_{n+ \frac{1}{2}}^{-1} = \widetilde{H}_{n}^{-1} - \left( 1+ \frac{c_{\widetilde{\beta}}}{(n+1)^{\widetilde{\beta}}}Z_{n+1}^{T}\widetilde{H}_{n}^{-1}Z_{n+1} \right)^{-1} \frac{c_{\widetilde{\beta}}}{(n+1)^{\widetilde{\beta}}} \widetilde{H}_{n}^{-1} Z_{n+1}Z_{n+1}^{T}\widetilde{H}_{n}^{-1} \\
\notag & \widetilde{H}_{n+1}^{-1} = \widetilde{H}_{n+\frac{1}{2}}^{-1} - \left( 1+ \widetilde{\Phi}_{n+1}^{T} \widetilde{H}_{n+ \frac{1}{2}}^{-1} \hat{\Phi}_{n+1} \right)^{-1} \widetilde{H}_{n+ \frac{1}{2}}^{-1} \widetilde{\Phi}_{n+1}\widetilde{\Phi}_{n+1}^{T} \widetilde{H}_{n+ \frac{1}{2}}^{-1} ,
\end{align}
with $\widetilde{\theta}_{0}$ bounded, $\widetilde{H}_{0}^{-1}$ symmetric and positive, $c_{\widetilde{\beta}} \geq 0$ and $\widetilde{\beta} \in (0 , 1/2)$.
\end{defi}
Note that compared with the algorithm (\ref{SGNalgo}),
matrix $(n+1)L_n$ has been replaced by matrix $\widetilde{H}_n$ defined by:
\[
\widetilde{H}_n = \widetilde{H}_0 + \sum_{i=1}^{n} \widetilde{\Phi}_i\widetilde{\Phi}_i^T
+ \sum_{i=1}^{n}\frac{c_{\widetilde{\beta}}}{i^{\widetilde{\beta}}}Z_iZ_i^T.
\]
Matrix $\widetilde{H}_n^{-1}$ is iteratively computed thanks to
Riccati's inversion formula (see \cite[p.96]{Duf97}) which is applied twice: first recursively inverse matrix $\widetilde{H}_{n+\frac{1}{2}} = \widetilde{H}_{n} +\frac{c_{\widetilde{\beta}}}{(n+1)^{\widetilde{\beta}}}Z_{n+1}Z_{n+1}^T$,
then matrix $\widetilde{H}_{n+1} = \widetilde{H}_{n+\frac{1}{2}} + \widetilde{\Phi}_{n+1} \widetilde{\Phi}_{n+1}^T$.
\vspace{1ex}
In fact, introducing this additional term enables to ensure, taking $c_{\beta} > 0$ that (see the proof of Theorem~\ref{consistency})
\[
\lambda_{\max} \left( \widetilde{H}_{n}^{-1} \right) = \mathcal{O}\left( n^{1-\widetilde{\beta}} \right) \quad \mbox{a.s.}
\]
Therefore, it enables to control the possible divergence of the estimates of the inverse of the Hessian and to obtain convergence results without assuming \textbf{(H*)}.
Anyway, if assumption \textbf{(H*)} is verified, one can take $c_{\widetilde{\beta}} = 0$ and Theorem \ref{theothetatilde} remains true. Remark that considering the Gauss-Newton algorithm amounts to take a step sequence of the form $\frac{1}{n}$. Nevertheless, in the case of stochastic gradient descents, it is well known in practice that this can lead to non sufficient results with a bad initialization. In order to overcome this problem, we propose an Averaged Stochastic Gauss-Newton algorithm, which consists in modifying equation \eqref{defsgn} by introducing a term $n^{1-\alpha}$ (with $\alpha \in (1/2,1)$), leading step sequence of the form $\frac{1}{n^{\alpha}}$. Finally, in order to ensure the asymptotic efficiency, we add an averaging step.
\begin{defi}[Averaged Stochastic Gauss-Newton algorithm]
The Averaged Stochastic Gauss Newton algorithm is recursively defined for all $n \geq 0$ by
\begin{align}
\notag \overline{\Phi}_{n+1} & = \nabla_{h} f \left( X_{n+1} , \overline{\theta}_{n} \right) \\
\label{defsgnalpha}\theta_{n+1} & = \theta_{n} + \gamma_{n+1}\overline{S}_{n}^{-1}\left( Y_{n+1} - f \left( X_{n+1},\theta_{n} \right) \right)\nabla_{h} f \left( X_{n+1} , \theta_{n} \right) \\
\label{asgn}\overline{\theta}_{n+1} & = \frac{n+1}{n+2}\overline{\theta}_{n} + \frac{1}{n+2}\theta_{n+1} \\
\notag S_{n+\frac{1}{2}}^{-1} & = S_{n}^{-1} - \left( 1+ \frac{c_{\beta}}{(n+1)^{\beta}} Z_{n+1}^{T}S_{n}^{-1}Z_{n+1} \right)^{-1} \frac{c_{\beta}}{(n+1)^{\beta}} S_{n}^{-1}Z_{n+1}Z_{n+1}^{T}S_{n}^{-1} \\
\notag S_{n+1}^{-1} & = S_{n}^{-1} - \left( 1+ \overline{\Phi}_{n+1}^{T}S_{n}^{-1}\overline{\Phi}_{n+1} \right)^{-1} S_{n}^{-1}\overline{\Phi}_{n+1}\overline{\Phi}_{n+1}^{T}S_{n}^{-1} .
\end{align}
where $\overline{\theta}_{0}=\theta_{0}$ is bounded, $S_{0}$ is symmetric and positive, $\gamma_{n} = c_{\alpha}n^{-\alpha}$ with $c_{\alpha}> 0,c_{\beta} \geq 0$, $\alpha \in (1/2,1)$, $\beta \in ( 0 , \alpha - 1/2)$ and $\overline{S}_{n}^{-1} = (n+1)S_{n}^{-1}$.
\end{defi}
Let us note that despite the modification of the algorithm, Riccati's formula always hold. Finally, remark that if assumption \textbf{(H*)} is satisfied, one can take $c_{\beta}=0$ and Theorem~\ref{consistency} in Section~\ref{sectiontheo} remains true.
\subsection{Additional assumptions}
We now suppose that these additional assumptions are fulfilled:
\begin{itemize}
\item[\textbf{(H2)}] The functional $G$ is twice Frechet differentiable in $\mathbb{R}^{q}$ and
there is a positive constant $C'$ such that for all $h\in \mathbb{R}^{q}$,
\[
\left\| \nabla^{2}G(h) \right\| \leq C' .
\]
\end{itemize}
Note that this is an usual assumption in stochastic convex optimization (see for instance \citep{KY03}), and especially for studying the convergence of stochastic algorithms \citep{bach2014adaptivity,godichon2016,gadat2017optimal}.
\begin{itemize}
\item[\textbf{(H3)}] The function $L$ is continuous at $\theta$.
\end{itemize}
Assumption \textbf{(H3)} is used for the consistency of the estimates of $L(\theta)$, which enables to give the almost sure rates of convergence of stochastic Gauss-Newton estimates and their averaged version.
Let us now make some additional assumptions on the Hessian of the function we would like to minimize:
\begin{itemize}
\item[\textbf{(H4a)}] The functional $h \longmapsto \nabla^{2}G(h)$ is continuous on a neighborhood of $\theta$.
\item[\textbf{(H4b)}] The functional $h \longmapsto \nabla^{2}G(h)$ is $C_{G}$-Lipschitz on a neighborhood of $\theta$.
\end{itemize}
Assumption \textbf{(H4a)} is useful for establishing the rate of convergence of stochastic Gauss-Newton algorithms given by \eqref{defsgn} and \eqref{defsgnalpha} while assumption \textbf{(H4b)} enables to give the rate of convergence of the averaged estimates. Clearly \textbf{(H4b)} implies \textbf{(H4a)}. Note that as in the case of assumption \textbf{(H2)}, these last ones are crucial to obtain almost sure rates of convergence of stochastic gradient estimates (see for instance \citep{pelletier1998almost,godichon2016}).
\section{Introduction}
We consider in this paper nonlinear regression model of the form
\begin{equation}
\label{model}Y_n = f(X_n,\theta) + \varepsilon_n, \ \ n\in\mathbb{N},
\end{equation}
where the observations $(X_n,Y_n)_n$ are independent random vectors in $\mathbb{R}^p\times \mathbb{R}$, $(\varepsilon_n)_n$ are independent, identically distributed zero-mean non observable random variables. Moreover, $f: \mathbb{R}^p\times \mathbb{R}^q \longrightarrow \mathbb{R}$
and $\theta \in \mathbb{R}^q$ is the unknown
parameter to estimate.
\vspace{1ex}
Nonlinear regression models are a standard tool for modeling real phenomena
with a complex dynamic.
It has a wide range of applications including maching learning (\cite{bach2014adaptivity}), ecology (\cite{komori2016asymmetric}), econometry (\cite{varian2014big}), pharmacokinetics (\cite{Bates88}), epidemiology (\cite{suarez2017}) or biology (\cite{Giurcuaneanu05}).
Most of the time, the parameter $\theta$ is estimated using
the least squares method, thus it is estimated by
\[ \widehat\theta_n = \arg\min_{h \in \mathbb{R}^q} \sum_{j=1}^n (Y_j - f(X_j, h))^2 \]
Many authors have studied the asymptotic behavior of the least squares estimator,
under various assumptions with different methods.
For example, \cite{Jennrich69} consider the case when $\theta$ belongs to a compact set,
$f$ is a continuous function with a unique extremum.
\cite{Wu81} consider similar local assumptions.
\cite{lai94, Skouras, Geer90, Geer96, Yao00} generalized the consistency results.
Under a stronger assumption about the errors $\varepsilon$,
that is, considering that the errors are uniformly subgaussian,
\cite{Geer90} obtained sharper stochastic bounds using empirical process methods. Under second moment assumptions on the errors and regularity assumptions (lipschitz conditions) on $f$, \cite{Pollard06} established weak consistency and a central
limit theorem.
\cite{Yang} consider a compact set for $\theta$,
under strong regularity assumptions and the algorithm allows to reach a stationary point without certainty that it is the one we are looking for.
They built hypothesis tests and confidence intervals.
Finally, let also mention \cite{Yao00}
which considers the case of stable nonlinear autoregressive models
and establishes the strong consistency of the least squares estimator.
\vspace{1ex}
However, in practice, the calculation of the least square estimator is not explicit in most cases and therefore requires the implementation of a deterministic approximation algorithm. The second order Gauss-Newton algorithm is generally used (or sometimes Gauss-Marquard algorithm to avoid inversion problems
(see for example \cite{Bates88}).
These algorithms are therefore not adapted to the case where the data are acquired sequentially and at high frequencies.
In such a situation, stochastic algorithms
offer an interesting alternative.
One example is the stochastic gradient algorithm,
defined by
\begin{equation}
\theta_n = \theta_{n-1} - \gamma_n \nabla_\theta f(X_n, \theta_{n-1}) \pa{Y_n - f(X_n, \theta_{n-1})},
\end{equation}
where $(\gamma_n)$ is a sequence of positive real numbers decreasing towards 0. Thanks to its recursive nature,
this algorithm does not require to store all the data and can be updated automatically when the data sequentially arrive.
It is thus adapted to very large datasets of data arriving at high speed.
We refer to \cite{robbins1951} and to its averaged version \cite{PolyakJud92}
and \cite{ruppert1988efficient}.
However, even if it is often used in practice as in the case of neural networks,
the use of stochastic gradient algorithms can lead to non satistying results. Indeed, for such models, it amounts to take the same step sequence for each coordinates. Nevertheless, as explained in \cite{BGBP2019}, if the Hessian of the function we would like to minimize has eigenvalues at different scales,
this kind of "uniform" step sequences is not adapted.
\vspace{1ex}
In this paper, we propose an alternative strategy to stochastic gradient algorithms,
in the spirit of the Gauss-Newton algorithm.
It is defined by :
\begin{eqnarray}
\phi_{n} & = & \nabla_\theta f(X_{n}, \theta_n)
\label{GNun} \\
S_{n}^{-1} &= & S_{n-1}^{-1} - (1 + \phi_{n}^T S_n^{-1} \phi_{n})^{-1}
S_{n-1}^{-1} \phi_{n} \phi_{n}^T S_{n-1}^{-1}
\label{GNdeux} \\
\theta_{n} &= &\theta_{n-1} + S_{n}^{-1}\phi_{n}\pa{Y_{n} -f(X_{n}, \theta_{n-1})}
\label{GNtrois}
\end{eqnarray}
where the initial value $\theta_0$ can be arbitrarily chosen and $S_0$ is a positive definite deterministic matrix,
typically $S_0 = I_q$ where $I_q$ denotes the identity matrix of order $q$.
Remark that thanks to Riccati's formula (see \cite[p. 96]{Duf97}, also called Sherman Morrison's formula (\cite{Sherman50}), $S_n^{-1}$ is the inverse of the matrix $S_{n}$ defined by
\[S_n = S_0 + \sum_{j=1}^{n}\phi_j \phi_j^T.\]
When the function $f$ is linear of the form $f(x,\theta) = \theta^T x$,
algorithm (\ref{GNun})-(\ref{GNtrois}) rewrites as the standard recursive least-squares estimators
(see \cite{Duf97}) defined by:
\begin{eqnarray*}
S_n^{-1} &= & S_{n-1}^{-1} - (1 + X_n^T S_{n-1}^{-1} X_n)^{-1}
S_{n-1}^{-1} X_nX_n^T S_{n-1}^{-1} \\
\theta_n &= &\theta_{n-1} + S_{n}^{-1}X_n\pa{Y_n - \theta_{n-1}^T X_n}
\end{eqnarray*}
This algorithm can be considered as a Newton stochastic algorithm since the matrix $n^{-1} S_n$ is an estimate of the Hessian matrix of the least squares criterion.
\vspace{1ex}
To the best of our knowledge and apart from the least squares estimate mentioned above,
second order stochastic algorithms are hardly ever used and studied since they often require
the inversion of a matrix at each step, which can be very expensive in term of time calculation.
To overcome this problem some authors (see for instance \cite{mokhtari2014res,lucchi2015variance,byrd2016stochastic})
use the BFGS (for \emph{Broyden-Fletcher-Goldfarb-Shanno}) algorithm
which is based on the recursive estimation of a matrix
whose behavior is closed to the one of the inverse of the Hessian matrix.
Nevertheless, this last estimate need a regularization of the objective function,
leading to unsatisfactory estimation of the unknown parameter.
In a recent paper dedicated to estimation of parameters in logistic regression models \citep{BGBP2019},
the authors propose a truncated Stochastic Newton algorithm. This truncation opens the way for online stochastic Newton algorithm without necessity to penalize the objective function.
In the same spirit of this work, and to relax assumption on the function $f$,
we consider in fact a modified version of the
stochastic Gauss-Newton algorithm defined by \eqref{GNtrois},
that enables us to obtain the asymptotic efficiency of the estimates
in a larger area of assumptions.
In addition, we introduce the following new \emph{Averaged Stochastic Gauss-Newton} algorithm (ASN for short)
defined by
\begin{eqnarray}
\phi_n & = & \nabla_h f(X_n, \overline{\theta}_{n-1})
\label{AGNun} \\
S_n^{-1} &= & S_{n-1}^{-1} - (1 + \phi_n^T S_{n-1}^{-1} \phi_n)^{-1}
S_{n-1}^{-1} \phi_n \phi_n^T S_{n-1}^{-1}
\label{AGNdeux} \\
\theta_n &= &\theta_{n-1} + n^\beta S_n^{-1}\phi_n\pa{Y_n -f(X_n, \theta_{n-1})}
\label{AGNtrois} \\
\overline{\theta}_n &=& \overline{\theta}_{n-1}
\label{AGNquatre} + \dfrac{1}{n}\,\pa{\theta_n - \overline{\theta}_{n-1}}
\end{eqnarray}
where $\beta\in (0, 1/2)$, $\overline{\theta}_0 = 0$.
The introduction of the term $n^\beta$ before the term $S_n^{-1}$ in (\ref{AGNtrois}) allows the algorithm to move quickly which enables to reduce the sensibility to a bad initialization.
The averaging step allows to maintain an optimal asymptotic behavior.
Indeed, under assumptions, we first give the rate of convergence of the estimates, before proving their asymptotic efficiency.
\vspace{1ex}
The paper is organized as follows.
Framework and algorithms are introduced in Section~\ref{sec:framework}.
In Section~\ref{sectiontheo}, we give the almost sure rates of convergence of the estimates and establish their asymptotic normality. A simulation study illustrating the interest of averaging is presented in Section~\ref{sectionsimu}. Proofs are postponed in Section~\ref{sectionproof} while some general results used in the proofs on almost sure rates of convergence for martingales are given in Section~\ref{sectionmartingales}.
\section{Useful results on martingales}\label{sectionmartingales}
\subsection{A useful theorem for stochastic algorithms with step sequence $(n^{-\alpha})_n$}
\begin{theo}\label{theomartbeta}
Let $H$ be a separable Hilbert space and let us consider
\[
M_{n+1} = \sum_{k=1}^{n} \beta_{n,k} \gamma_{k} R_{k} \xi_{k+1},
\]
where
\begin{itemize}
\item $\left( \xi_{n} \right)$ is a $H$-valued martingale differences sequence adapted to a filtration $\left( \mathcal{F}_{n} \right)$ such that \begin{align}
\notag & \mathbb{E}\left[ \left\| \xi_{n+1} \right\|^{2} |\mathcal{F}_{n} \right] \leq C + R_{2,n} \quad a.s, \\
\label{hypmart} & \sum_{n\geq 1}\gamma_{n}\mathbb{E}\left[ \left\| \xi_{n+1} \right\|^{2}\mathbb{1}{\left\| \xi_{n+1} \right\|^{2} \geq \gamma_{n}^{-1}(\ln n)^{-1}} |\mathcal{F}_{n} \right] < + \infty \quad a.s,
\end{align}
where $C\geq 0$ and $(R_{2,n})_n$ converges almost surely to $0$;
\item $\gamma_{n}=cn^{-\alpha}$ with $c> 0$ and $\alpha \in (1/2,1)$;
\item $(R_{n})$ is a sequence of operators on $H$ such that, for a deterministic sequence $\left( v_{n} \right)$,
\[
\left\| R_{n} \right\|_{op} = o \left( v_{n} \right) \quad a.s \quad \quad \text{and} \quad \quad v_{n} = \frac{(\ln n)^{a}}{n^{b}} .
\]
with $a,b \geq 0$;
\item For all $n \geq 1$ and $1 \leq k \leq n$,
\[
\beta_{n,k} = \prod_{j=k+1}^{n} \left( I_{H} - \gamma_{k} \Gamma \right)\quad \text{and} \quad \beta_{n,n} = I_{H},
\]
where $\Gamma $ is a symmetric operator on $H$ such that $0 < \lambda_{\min} (\Gamma ) \leq \lambda_{\max} (\Gamma) < + \infty $.
\end{itemize}
Then,
\[
\left\| M_{n+1} \right\|^{2} = O \left( \gamma_{n}v_{n}^{2}\ln n \right) \quad a.s.
\]
\end{theo}
\begin{rmq}
Note equation \eqref{hypmart} holds since there are $\eta > \frac{1}{\alpha} -1$ and a positive constant $C_{2}$ such that
\[
\mathbb{E}\left[ \left\| \xi_{n+1} \right\|^{2+2\eta} |\mathcal{F}_{n} \right] \leq C_{2} + R_{\eta,n}
\]
with $R_{\eta,n}$ converging to $0$.
\end{rmq}
\begin{rmq}
Previous theorem remains true considering a sequence $(R_{n})$ satisfying that there are a positive constant $C_{R}$ and a rank $n_{R}$ such that for all $n \geq n_{R}$, $\left\| R_{n} \right\|_{op} \leq C_{R}v_{n}$.
\end{rmq}
\begin{proof}
Let us now consider the events
\begin{align*}
& A_{n} = \left\lbrace R_{n} > v_{n} \quad \text{or} \quad R_{2,n}> C \right\rbrace \\
& B_{n+1} = \left\lbrace R_{n} \leq v_{n}, R_{2,n} \leq C, \left\| \xi_{n+1} \right\|\leq \delta_{n} \right\rbrace \\
& C_{n+1} = \left\lbrace R_{n} \leq v_{n}, R_{2,n} \leq C, \left\| \xi_{n+1} \right\| > \delta_{n} \right\rbrace
\end{align*}
with $\delta_{n} = \gamma_{n}^{-1/2}(\ln n)^{-1/2}$. One can remark that $A_{n}^{c} = B_{n+1} \sqcup C_{n+1}$. Then, one can write $M_{n+1}$ as
\begin{align*}
M_{n+1} & = \sum_{k=1}^{n} \beta_{n,k} \gamma_{k} R_{k} \xi_{k+1}\mathbb{1}{A_{k}} + \sum_{k=1}^{n} \beta_{n,k} \gamma_{k} R_{k} \xi_{k+1}\mathbb{1}{A_{k}^{c}} \\
& = \sum_{k=1}^{n} \beta_{n,k} \gamma_{k} R_{k} \xi_{k+1}\mathbb{1}{A_{k}} + \sum_{k=1}^{n} \beta_{n,k} \gamma_{k} R_{k} \left( \xi_{k+1}\mathbb{1}{B_{k+1}} - \mathbb{E}\left[ \xi_{k+1} \mathbb{1}{B_{k+1}} |\mathcal{F}_{k} \right] \right) \\
& + \sum_{k=1}^{n} \beta_{n,k} \gamma_{k} R_{k} \left( \xi_{k+1}\mathbb{1}{C_{k+1}} - \mathbb{E}\left[ \xi_{k+1} \mathbb{1}{C_{k+1}} |\mathcal{F}_{k} \right] \right).
\end{align*}
Let us now give the rates of convergence of these three terms.
\bigskip
\noindent\textbf{Bounding $ M_{1,n+1} := \sum_{k=1}^{n} \beta_{n,k} \gamma_{k} R_{k} \xi_{k+1}\mathbb{1}{A_{k}} $. }
Remark that there is a rank $n_{0}$ such that for all $n \geq n_{0}$, $\left\| I_{H} - \gamma_{n} \Gamma \right\|_{op} \leq \left( 1- \lambda_{\min} \gamma_{n} \right) $. Furthermore, $M_{1,n+1} = \left( I_{H} - \gamma_{n} \Gamma \right) M_{1,n} + \gamma_{n} R_{n} \xi_{n+1} \mathbb{1}{A_{n}}$. Then, for all $n \geq n_{0}$,
\[
\mathbb{E}\left[ \left\| M_{1,n+1} \right\|^{2} |\mathcal{F}_{n} \right] \leq \left( 1- \lambda_{\min}\gamma_{n} \right)^{2} \left\| M_{1,n} \right\|^{2} + \gamma_{n}^{2} \left\| R_{n} \right\|_{op}^{2} \left( C + R_{2,n} \right) \mathbb{1}{A_{n}} .
\]
Considering $V_{n+1} = \prod_{k=1}^{n} \left( 1 + \lambda_{\min} \gamma_{k} \right)^{2} \left\| M_{1,n+1} \right\|^{2}$, it comes
\[
\mathbb{E}\left[ V_{n+1} |\mathcal{F}_{n} \right] \leq \left( 1 - \lambda_{\min}^{2} \gamma_{n}^{2} \right)^{2} V_{n} + \prod_{k=1}^{n} \left( 1 + \lambda_{\min} \gamma_{k} \right)^{2}\gamma_{n}^{2} \left\| R_{n} \right\|_{op}^{2} \left( C + R_{2,n} \right) \mathbb{1}{A_{n}}
\]
Moreover, $\mathbb{1}{A_{n}}$ converges almost surely to $0$ so that
\[
\sum_{n\geq 1} \prod_{k=1}^{n} \left( 1 + \lambda_{\min} \gamma_{k} \right)^{2}\gamma_{n}^{2} \left\| R_{n} \right\|_{op}^{2} \left( C + R_{2,n} \right) \mathbb{1}{A_{n}} < + \infty \quad a.s
\]
and applying Robbins-Siegmund Theorem, $V_{n}$ converges almost surely to a finite random variable, i.e
\[
\left\| M_{1,n+1} \right\|^{2} = \mathcal{O} \left( \prod_{k=1}^{n} \left( 1 + \lambda_{\min} \gamma_{k} \right)^{-2} \right) \quad a.s
\]
and converges exponentially fast.
\bigskip
\noindent\textbf{Bounding $M_{2,n+1} := \sum_{k=1}^{n} \beta_{n,k} \gamma_{k} R_{k} \left( \xi_{k+1}\mathbb{1}{B_{k+1}} - \mathbb{E}\left[ \xi_{k+1} \mathbb{1}{B_{k+1}} |\mathcal{F}_{k} \right] \right)$. }
Let us denote $\Xi_{k+1} = R_{k} \left( \xi_{k+1}\mathbb{1}{B_{k+1}} - \mathbb{E}\left[ \xi_{k+1} \mathbb{1}{B_{k+1}} |\mathcal{F}_{k} \right] \right)$. Remark that $\left( \Xi_{n} \right)$ is a sequence of martingale differences adapted to the filtration $\left( \mathcal{F}_{n} \right)$. As in \cite{Pinelis} (proofs of Theorems~3.1 and 3.2), let $\lambda > 0$ and consider for all $t \in [ 0, 1]$ and $j \leq n$,
\[
\varphi(t) = \mathbb{E}\left[ \cosh \left( \lambda \left\| \sum_{k=1}^{j-1} \beta_{n,k}\gamma_{k} \Xi_{k+1} + t \beta_{n,j} \gamma_{j}\Xi_{j+1} \right\| \right) \left|\mathcal{F}_{j}\right. \right].
\]
One can check that $\varphi '(0) = 0$ and (see Pinellis for more details)
\[
\varphi '' (t) \leq \lambda^{2} \mathbb{E}\left[ \left\| \beta_{n,j} \gamma_{j}\Xi_{j+1} \right\|^{2}e^{ \lambda t \left\| \beta_{n,j} \gamma_{j}\Xi_{j+1} \right\|} \cosh \left( \lambda \left\| \sum_{k=1}^{j-1} \beta_{n,k}\gamma_{k} \Xi_{k+1} \right\| \right) |\mathcal{F}_{j} \right]
\]
Then,
\begin{align*}
\mathbb{E}\left[ \cosh \left( \lambda \left\| \sum_{k=1}^{j} \beta_{n,k}\gamma_{k} \Xi_{k+1} \right\| \right) | \mathcal{F}_{j} \right] = \varphi (1) & = \varphi (0) + \int_{0}^{1} (1-t) \varphi ''(t) dt \\
& \leq \left( 1+ e_{j,n } \right)\cosh \left( \lambda \left\| \sum_{k=1}^{j-1} \beta_{n,k}\gamma_{k} \Xi_{k+1} \right\| \right)
\end{align*}
with $e_{j,n} = \mathbb{E}\left[ e^{\lambda \left\| \beta_{n,j} \gamma_{j}\Xi_{j+1} \right\|} -1 - \lambda\left\| \beta_{n,j} \gamma_{j}\Xi_{j+1} \right\| |\mathcal{F}_{j} \right]$, which is well defined since $\Xi_{j+1}$ is a.s. finite. Moreover, considering
\[
G_{n+1} = \frac{\cosh \left( \lambda \left\| \sum_{k=1}^{n} \beta_{n,k}\gamma_{k} \Xi_{k+1} \right\| \right)}{\prod_{j=1}^{n} \left( 1 + e_{j,n} \right)} \quad \quad \text{and} \quad \quad G_{0} = 1
\]
and since $\mathbb{E}\left[ G_{n+1} |\mathcal{F}_{n} \right] =G_{n}$, it comes $\mathbb{E}\left[ G_{n+1} \right] = 1 $. For all $r > 0$,
\begin{align*}
\mathbb{P}\left[ \left\| M_{2,n+1} \right\| \geq r \right] & = \mathbb{P}\left[ G_{n+1} \geq \frac{\cosh (\lambda r )}{\prod_{j=1}^{n}\left( 1+ e_{j,n} \right)} \right] \leq \mathbb{P}\left[ 2G_{n+1} \geq \frac{e^{\lambda r }}{\prod_{j=1}^{n} \left( 1+ e_{jn} \right)} \right].
\end{align*}
Furthermore, let $\epsilon_{j+1} = \xi_{j+1}\mathbb{1}{B_{j}} - \mathbb{E}\left[\xi_{j+1} \mathbb{1}{B_{j}} | \mathcal{F}_{j} \right]$ and remark that $\mathbb{E}\left[ \left\| \epsilon_{j+1} \right\|^{2} |\mathcal{F}_{j} \right] \leq 2C$. Then, recalling that $\delta_{n} = \gamma_{n}^{-1/2}(\ln n)^{-1/2}$, and since for all $k \geq 2$,
\[
\mathbb{E}\left[ \left\| \epsilon_{j+1}\right\|^{k} |\mathcal{F}_{j} \right] \leq 2^{k-2}\delta_{j}^{k-2} \mathbb{E}\left[ \left\| \xi_{j+1} \right\|^{2} \mathbb{1}{B_{j}} |\mathcal{F}_{j} \right] \leq 2^{k-1}C\delta_{j}^{k-2} ,
\]
\begin{align*}
e_{j,n} = \sum_{k=2}^{\infty} \lambda^{k} \left\| \beta_{n,j}\right\|_{op}^{k} \gamma_{j}^{k} \mathbb{E}\left[ \left\| \Xi_{j+1} \right\|^{k} |\mathcal{F}_{j} \right]
& \leq \sum_{k=2}^{\infty} \lambda^{k} \left\| \beta_{n,j}\right\|_{op}^{k} \gamma_{j}^{k} v_{j}^{k} \mathbb{E}\left[ \left\| \epsilon_{j+1} \right\|^{k} |\mathcal{F}_{k} \right] \\
& \leq \sum_{k=2}^{\infty} \lambda^{k} \left\| \beta_{n,j}\right\|_{op}^{k} \gamma_{j}^{k} v_{j}^{k} 2^{k-1}C\delta_{j}^{k-2} \\
& \leq 2C\lambda^{2} \left\| \beta_{n,j} \right\|_{op}^{2} \gamma_{j}^{2}v_{j}^{2} \sum_{k=2}^{\infty} (2\lambda)^{k-2} \left\| \beta_{n,j}\right\|_{op}^{k-2}\gamma_{j}^{\frac{k-2}{2}} v_{j}^{k-2}\ln j^{-\frac{k-2}{2}} \\
& = 2C\lambda^{2} \left\| \beta_{n,j} \right\|_{op}^{2} \gamma_{j}^{2}v_{j}^{2} \exp \left( 2 \lambda \left\| \beta_{n,j}\right\|_{op}\sqrt{\gamma_{j}} v_{j} \right)
\end{align*}
Then,
\[
\mathbb{P}\left[ \left\| M_{2,n+1} \right\| \geq r \right] \leq \mathbb{P}\left[ 2G_{n+1} \geq \frac{e^{\lambda r}}{\prod_{j=1}^{n}\left( 1+ 2C\lambda^{2} \left\| \beta_{n,j} \right\|_{op}^{2} \gamma_{j}^{2} v_{j}^{2}\exp \left( 2 \lambda \left\| \beta_{n,j}\right\|_{op} v_{j}\sqrt{\gamma_{j}\ln j} \right) \right) } \right]
\]
Applying Markov's inequality,
\[
\mathbb{P}\left[ \left\| M_{2,n+1} \right\| \geq r \right] \leq 2 \exp \left( - \lambda r + 2C\lambda^{2} \sum_{j=1}^{n} \left\| \beta_{n,j} \right\|_{op}^{2} \gamma_{j}^{2}v_{j}^{2} \exp \left( 2 \lambda \left\| \beta_{n,j}\right\|_{op}v_{j}\sqrt{\gamma_{j}\ln j} \right) \right) .
\]
Take $\lambda = \gamma_{n}^{-1/2}v_{n}^{-1}\sqrt{\ln n}$. Let $C_{0} = \left\| \beta_{n_{0},0} \right\|_{op}$ and remark that for $n \geq 2n_{0}$ (i.e such that $\gamma_{n/2} \lambda_{\max}(\Gamma) \leq 1$), and for all $j \leq n/2$,
\[
\left\| \beta_{n,j} \right\|_{op} \leq C_{0}\exp \left( - c\lambda_{\min}(n/2)^{1-\alpha} \right),
\]
so that for all $j \leq n/2$,
\[
\lambda \left\|\beta_{n,j} \right\|_{op} \gamma_{j}v_{j} \leq C_{0}\exp \left( - \lambda_{\min}(n/2)^{1-\alpha} \right)\sqrt{n^{2b+\alpha}\ln n} \limite{n\to + \infty}{a.s} 0 .
\]
Furthermore, for all $n \geq 2n_{0}$, and for all $j \geq n/2$,
\[
\lambda \left\|\beta_{n,j} \right\|_{op} \frac{\sqrt{\gamma_{j}}v_{j}}{\sqrt{\ln j}} \leq C_{0} 2^{2b+\alpha+1}.
\]
Then, there is a positive constant $C''$ such that for all $n \geq 1$ and $j \leq n$,
\[
\exp \left( \lambda \left\|\beta_{n,j} \right\|_{op} \sqrt{\gamma_{j}}v_{j} \right) \leq C''
\]
Finally, one can easily check that (see Lemma E.2 in \cite{CG2015})
\[
\sum_{j=1}^{n} \left\| \beta_{n,j}\right\|_{op}^{2} \gamma_{j}^{2} \frac{(\ln j)^{2a}}{j^{2b}} =\mathcal{O} \left( \frac{(\ln n)^{2a}}{n^{2b+\alpha}} \right) .
\]
There is a positive constant $C'''$ such that
\[
\mathbb{P}\left[ \left\| M_{2,n+1} \right\| \geq r \right] \leq \exp \left( - r v_{n}^{-1}\gamma_{n}^{-1/2}\sqrt{\ln n} + C''' \ln n \right)
\]
Then , taking $r = \left( 2+C''' \right) v_{n} \sqrt{\gamma_{n}\ln n}$, it comes
\[
\mathbb{P}\left[ \left\| M_{2,n+1} \right\| \geq \left( 2+C''' \right) v_{n} \sqrt{\gamma_{n}\ln n} \right] \leq \exp \left( - 2 \ln n \right) = \frac{1}{n^{2}}
\]
and applying Borell Cantelli's lemma,
\[
\left\| M_{2,n+1} \right\| = \mathcal{O} \left( v_{n}\sqrt{\gamma_{n}\ln n} \right) \quad a.s.
\]
\noindent\textbf{Bounding $M_{3,n+1} := \sum_{k=1}^{n} \beta_{n,k} \gamma_{k} R_{n} \left( \xi_{k+1}\mathbb{1}{C_{k+1}} - \mathbb{E}\left[ \xi_{k+1} \mathbb{1}{C_{k+1}} |\mathcal{F}_{k} \right] \right)$. } Let us denote $\epsilon_{k+1} = \xi_{k+1}\mathbb{1}{C_{k+1}} - \mathbb{E}\left[ \xi_{k+1} \mathbb{1}{C_{k+1}} |\mathcal{F}_{k} \right]$ and remark that for $n \geq n_{0} $,
\begin{align*}
\mathbb{E}\left[ \left\| M_{3,n+1} \right\|^{2} |\mathcal{F}_{n} \right] & \leq \left( 1- \lambda_{\min} \gamma_{n} \right) \left\| M_{3,n} \right\|^{2} + \gamma_{n}^{2} v_{n}^{2} \mathbb{E}\left[ \left\| \epsilon_{n+1} \right\|^{2} |\mathcal{F}_{n} \right] \\
& \leq \left( 1- \lambda_{\min} \gamma_{n} \right) \left\| M_{3,n} \right\|^{2} + \gamma_{n}^{2}v_{n}^{2} \mathbb{E}\left[ \left\| \xi_{n+1} \right\|^{2} \mathbb{1}{\left\| \xi_{n+1} \right\|^{2} \geq \gamma_{n}^{-1}} |\mathcal{F}_{n} \right]
\end{align*}
Let $V_{n}' = \frac{1}{\gamma_{n}v_{n}^{2}} \left\| M_{3,n} \right\|^{2}$. There are a rank $n_{1}$ and a positive constant $c$ such that for all $n \geq n_{1}$
\[
\mathbb{E}\left[ V_{n+1} |\mathcal{F}_{n} \right] \leq \left( 1- c\gamma_{n} \right) V_{n} + \mathcal{O} \left( \gamma_{n}\mathbb{E}\left[ \left\| \xi_{n+1} \right\|^{2} \mathbb{1}{\left\| \xi_{n+1} \right\|^{2} \geq \gamma_{n}^{-1}} |\mathcal{F}_{n} \right] \right) \quad a.s.
\]
Applying Robbins-Siegmund Theorem as well as equation \eqref{hypmart}, it comes
\[
\left\| M_{3,n+1} \right\|^{2} = \mathcal{O} \left( \gamma_{n}v_{n}^{2} \right) \quad a.s.
\]
\end{proof}
\subsection{A useful theorem for averaged stochastic algorithms}
\begin{theo}\label{theomartmoy}
Let $H$ be a separable Hilbert space and let
\[
M_{n} = \frac{1}{n}\sum_{k=1}^{n} R_{k} \xi_{k+1},
\]
where
\begin{itemize}
\item $\left( \xi_{n} \right)$ is a $H$-valued martingale differences sequence adapted to a filtration $\left( \mathcal{F}_{n} \right)$ verifying
\[
\mathbb{E}\left[ \left\| \xi_{n+1} \right\|^{2} |\mathcal{F}_{n} \right] \leq C + R_{2,n}
\]
where $(R_{2,n})_n$ converges almost surely to $0$.
\item $(R_{n})$ is a sequence of operators on $H$ such that for a deterministic sequence $\left( v_{n} \right)$,
\[
\left\| R_{n} \right\|_{op} = \mathcal{O} \left( v_{n} \right)\quad a.s \quad \text{and} \quad \exists c \leq 1,(a_{n}), \quad \frac{v_{n}}{v_{n+1}} = 1 + \frac{c}{n} + \frac{a_{n}}{n} + o \left( \frac{a_{n}}{n} \right),
\]
with $(a_{n})$ converging to $0$.
\end{itemize}
Then, for all $\delta > 0$,
\begin{itemize}
\item If $\sum_{n\geq 1} v_{n}^{2} < + \infty \quad a.s$,
\[
\left\| M_{n}^{2} \right\|^{2} = \mathcal{O} \left( \frac{1}{n^{2}} \right) \quad a.s.
\]
\item If $c < 1/2$,
\[
\left\| M_{n} \right\|^{2} = o \left( n^{-1}v_{n}^{-2}(\ln n)^{1+\delta} \right) \quad a.s.
\]
\item If $\sum_{n\geq 1}\frac{a_{n}}{n} < + \infty$ and if $1/2 \leq c \leq 1$,
\[
\left\| M_{n} \right\|^{2}= o \left( n^{2c-2}v_{n}^{-2}(\ln n)^{1+\delta} \right) \quad a.s
\]
\item If $\sum_{n\geq 1}\frac{a_{n}}{n} = + \infty$ and if $1/2 \leq c < 1$, for all $a<2-2c$
\[
\left\| M_{n} \right\|^{2} = o \left( n^{-a}v_{n}^{-2} \right) \quad a.s.
\]
\end{itemize}
\end{theo}
\begin{proof}
If $\sum_{n\geq 1} v_{n}^{2} < + \infty$, let us consider $W_{n} = n^{2} \left\| M_{n}\right\|^{2}$. We have
\[
\mathbb{E}\left[ W_{n+1} |\mathcal{F}_{n} \right] \leq W_{n} + \left\| R_{n} \right\|_{op} \mathbb{E}\left[ \left\| \xi_{n+1} \right\|^{2} |\mathcal{F}_{n} \right] .
\]
Then,
\[
\mathbb{E}\left[ W_{n+1} |\mathcal{F}_{n} \right] \leq W_{n} + \mathcal{O} \left( v_{n+1}^{2} \right) \quad a.s
\]
and applying Robbins-Siegmund Theorem,
\[
\left\| M_{n} \right\|^{2} = \mathcal{O} \left( \frac{1}{n^{2}} \right) .
\]
Let us consider $a \leq 1$ and $V_{n+1,a} = \frac{(n+1)^{a}}{v_{n+1}^{2}(\ln (n+1))^{1+\delta}} \left\| M_{n+1} \right\|^{2}$. Then,
\begin{align*}
\mathbb{E}\left[ V_{n+1,a} |\mathcal{F}_{n} \right] & = \frac{(n+1)^{a}}{(\ln (n+1))^{1+\delta}} \left( \frac{n}{n+1} \right)^{2}\frac{v_{n}^{2}}{v_{n+1}^{2}}\left\| M_{n} \right\|^{2} + \frac{(n+1)^{a}}{(\ln (n+1))^{1+\delta}}\frac{1}{(n+1)^{2}} \frac{\left\| R_{n} \right\|_{op}}{v_{n+1}^{2}} \mathbb{E}\left[ \left\| \xi_{n+1} \right\|^{2} |\mathcal{F}_{n} \right] \\
& \leq \left( \frac{n}{n+1}\right)^{2-a}\frac{v_{n+1}^{2}}{v_{n}^{2}} V_{n} + \mathcal{O} \left( \frac{1}{n^{2-a}(\ln n)^{1+\delta}} \right) \quad a.s \\
& = \left( 1- (2-a -2c) \frac{1}{n} + \frac{a_{n}}{n} + \mathcal{O} \left( \frac{1}{n^{2}} \right) \right) V_{n} + \mathcal{O} \left( \frac{1}{n^{2-a}(\ln n)^{1+\delta}} \right) \quad a.s
\end{align*}
Applying Robbins-Siegmund theorem,
\begin{itemize}
\item If $c < 1/2$, one can take $a= 1$ and
\[
\left\| M_{n} \right\|^{2} = o \left( n^{-1}v_{n}^{2}(\ln n)^{1+\delta} \right) \quad a.s.
\]
\item If $\sum_{n\geq 1}\frac{a_{n}}{n} < + \infty$ and if $1/2 \leq c \leq 1$, one can take $a=2-2c$ and
\[
\left\| M_{n} \right\|^{2}= o \left( n^{2c-2}v_{n}^{2}(\ln n)^{1+\delta} \right) \quad a.s
\]
\item If $\sum_{n\geq 1}\frac{a_{n}}{n} = + \infty$ and if $1/2 \leq c < 1$, for all $a<2-2c$
\[
\left\| M_{n} \right\|^{2} = o \left( n^{-a}v_{n}^{2}(\ln n)^{1+\delta} \right) \quad a.s.
\]
\end{itemize}
\end{proof}
\section{Proofs}\label{sectionproof}
\subsection{Proofs of Theorem \ref{consistency} and Corollary \ref{corconvsn}}
\begin{lem}\label{superlem}
Assuming \textbf{(H1)} and \textbf{(H2)} and taking $c_{\beta}> 0$, it comes
\[
\lambda_{\max} \left( S_{n}^{-1} \right) = \mathcal{O} \left( n^{\beta-1} \right) \quad a.s \quad \text{and} \quad \lambda_{\max} \left( S_{n} \right) =\mathcal{O}(n)\quad a.s.
\]
\end{lem}
\begin{proof}[Proof of Lemma \ref{superlem}]
First, note that
\[
\lambda_{\min}\left( S_{n} \right) \geq \lambda_{\min} \left(\sum_{i=1}^{n} \frac{c_{\beta}}{i^{\beta}} Z_i Z_i^{T} \right),
\]
and one can check that
\begin{equation}
\label{vitzi}
\frac{1}{\sum_{i=1}^{n}\frac{c_{\beta}}{i^{\beta}}} \sum_{i=1}^{n} \frac{c_{\beta}}{i^{\beta}}Z_{i}Z_{i}^{T} \xrightarrow[n\to + \infty]{a.s} I_{q} .
\end{equation}
Since
\[\sum_{i=1}^{n} \frac{c_{\beta}}{i^{\beta}} \sim \frac{c_{\beta}}{1-\beta}n^{1-\beta},\] it comes
\[
\lambda_{\max} \left( S_{n}^{-1} \right) = \mathcal{O} \left( n^{\beta -1 } \right) \quad a.s.
\]
Let us now give a bound of $\lambda_{\max}\left( S_{n} \right)$. First, remark that $S_{n}$ can be written as
\begin{equation}
\label{decsn} S_{n} = S_{0} + \sum_{i=1}^{n} \mathbb{E}\left[ \overline{\Phi}_{i}\overline{\Phi}_{i}^{T} |\mathcal{F}_{i-1} \right] + \sum_{i=1} \Xi_{i} + \sum_{i=1}^{n} \frac{c_{\beta}}{i^{\beta}}Z_{i}Z_{i}^{T},
\end{equation}
where $\Xi_{i} := \overline{\Phi}_{i}\overline{\Phi}_{i}^{T} - \mathbb{E}\left[ \overline{\Phi}_{i}\overline{\Phi}_{i}^{T} |\mathcal{F}_{i-1} \right]$ and $\left( \mathcal{F}_{i} \right)$ is the $\sigma$-algebra generated by the sample, i.e $\mathcal{F}_{i} := \sigma \left( \left( X_{1}, Y_{1} \right) , \ldots ,\left( X_{i} , Y_{i} \right) \right)$. Thanks to assumption \textbf{(H1b)}, $\mathbb{E}\left[ \left\| \overline{\Phi}_{i}\overline{\Phi}_{i}^{T} \right\|_{F}^{2} |\mathcal{F}_{i-1} \right] \leq C''$, and applying Theorem~\ref{theomartmoy}, it comes for all positive constant $\delta > 0$,
\begin{equation}\label{vitXi}
\left\| \sum_{i=1}^{n} \Xi_{i} \right\|_{F}^{2} = o \left( n (\ln n)^{1+\delta} \right) \quad a.s,
\end{equation}
where $\left\| . \right\|_{F}$ is the Frobenius norm. Then,
\[
\left\| S_{n} \right\|_{F} = \mathcal{O} \left( \max \left( \left\| S_{0} \right\|_{F}, C''n , \sqrt{n (\ln n)^{1+\delta}} , n^{1-\beta} \right)\right) \quad a.s,
\]
which concludes the proof.
\end{proof}
\begin{proof}[Proof of Theorem \ref{consistency}]
With the help of a Taylor's decomposition, it comes
\[
G \left( \theta_{n+1} \right) = G \left( \theta_{n} \right) + \nabla G \left( \theta_{n} \right)^{T}\left( \theta_{n+1} - \theta_{n} \right) + \frac{1}{2}\left( \theta_{n+1} - \theta_{n} \right)^{T} \int_{0}^{1} \nabla^{2} G \left( \theta_{n+1} + t \left( \theta_{n+1} - \theta_{n} \right) \right) dt \left( \theta_{n+1} - \theta_{n} \right) .
\]
Then, assumption \textbf{(H2)} yields
\[
G \left( \theta_{n+1} \right) \leq G \left( \theta_{n} \right) + \nabla G \left( \theta_{n} \right)^{T}\left( \theta_{n+1} - \theta_{n} \right) + \frac{C'}{2}\left\| \theta_{n+1} - \theta_{n} \right\|^{2}.
\]
Replacing $\theta_{n+1}$,
\begin{align*}
G & \left( \theta_{n+1} \right)\leq G \left( \theta_{n} \right) - \gamma_{n+1}\nabla G \left( \theta_{n} \right)^{T}\overline{S}_{n}^{-1}\nabla_{h} g \left( X_{n+1} , Y_{n+1} , \theta_{n} \right) + \frac{C'}{2}\gamma_{n+1}^{2} \left\| \overline{S}_{n}^{-1} \nabla_{h} g \left( X_{n+1} , Y_{n+1} ,\theta_{n} \right) \right\|^{2} \\
& \leq G \left( \theta_{n} \right) - \gamma_{n+1} \nabla G \left( \theta_{n} \right)^{T} \overline{S}_{n}^{-1} \nabla_{h} g \left( X_{n+1} , Y_{n+1} , \theta_{n} \right) + \frac{C'}{2}\gamma_{n+1}^{2} \left( \lambda_{\max} \left( \overline{S}_{n}^{-1} \right) \right)^{2} \left\| \nabla_{h} g \left( X_{n+1} , Y_{n+1} ,\theta_{n} \right) \right\|^{2}.
\end{align*}
Assumption \textbf{(H1a)} leads to
\begin{align*}
\mathbb{E}\left[ G \left( \theta_{n+1} \right) |\mathcal{F}_{n} \right] & \leq G \left( \theta_{n} \right) - \gamma_{n+1} \nabla G \left( \theta_{n} \right)^{T} \overline{S}_{n}^{-1} \nabla G \left( \theta_{n} \right) + \frac{CC'}{2}\gamma_{n+1}^{2} \left( \lambda_{\max} \left( \overline{S}_{n}^{-1} \right) \right)^{2} \\
& \leq G \left( \theta_{n} \right) - \gamma_{n+1}\lambda_{\min} \left( \overline{S}_{n}^{-1} \right) \left\| \nabla G \left( \theta_{n} \right) \right\|^{2} + \frac{CC'}{2}\gamma_{n+1}^{2}\left( \lambda_{\max} \left( \overline{S}_{n}^{-1} \right) \right)^{2}.
\end{align*}
Thanks to Lemma \ref{superlem}, and since $\beta < \alpha - 1/2$,
\[
\sum_{n\geq 1} \gamma_{n+1}^{2}\left( \lambda_{\max} \left (\overline{S}_{n}^{-1} \right) \right)^{2} < + \infty \quad a.s,
\]
so that, applying Robbins-Siegmund Theorem (see \cite{Duf97} for instance), $G \left( \theta_{n} \right)$ converges almost surely to a finite random variable and
\[
\sum_{n\geq 1} \gamma_{n+1} \lambda_{\min} \left( \overline{S}_{n}^{-1} \right)\left\| \nabla G \left( \theta_{n} \right) \right\|^{2} = \sum_{n\geq 1 } \gamma_{n+1} \lambda_{\max} \left( \overline{S}_{n} \right)^{-1} \left\| \nabla G \left( \theta_{n} \right) \right\|^{2} < + \infty \quad a.s.
\]
Lemma~\ref{superlem} implies $\sum_{n\geq 1} \gamma_{n+1} \lambda_{\max} \left( \overline{S}_{n}\right)^{-1} = + \infty$ almost surely, so that there is alsmot surely a subsequence $\theta_{\varphi_{n}}$ such that $\left\| \nabla G \left( \theta_{\varphi_{n}} \right) \right\|^{2} $ converges to $0$.
\end{proof}
\begin{proof}[Proof of Corollary \ref{corconvsn}] Let us give the convergence of each term in decomposition (\ref{decsn}). Since $\beta > 0$ and applying (\ref{vitXi}), it comes
\[
\frac{1}{n}\left\| \sum_{i=1}^{n}\Xi_{i} \right\|_{F} \xrightarrow[n\to + \infty]{a.s} 0 \quad a.s \quad \text{and} \quad \frac{1}{n}\left\| \sum_{i=1}^{n} \frac{c_{\beta}}{i^{\beta}}Z_{i}Z_{i}^{T} \right\|_{F} \xrightarrow[n\to + \infty]{a.s} 0 \quad a.s.
\]
Finally, since $\overline{\theta}_{n}$ converges almost surely to $\theta$, assumption \textbf{(H3)} together with Toeplitz lemma yield
\[
\frac{1}{n}\sum_{i=1}^{n} \mathbb{E}\left[ \overline{\Phi}_{i}\overline{\Phi}_{i}^{T} |\mathcal{F}_{i-1} \right] \xrightarrow[n\to + \infty]{a.s} \mathbb{E}\left[ \nabla_{h}f \left( X, \theta \right) \nabla_{h} f\left( X , \theta \right)^{T} \right] = L(\theta).
\]
\end{proof}
\subsection{Proof of Theorem \ref{ratetheta}}
First, $\theta_{n+1}$ can be written as
\begin{equation}
\label{decxi} \theta_{n+1} - \theta = \theta_{n} - \theta -\gamma_{n+1}\overline{S}_{n}^{-1} \nabla G \left( \theta_{n} \right) + \gamma_{n+1}\overline{S}_{n}^{-1}\xi_{n+1},
\end{equation}
with $\xi_{n+1} :=\nabla G\left( \theta_{n} \right) - \nabla_{h} g \left( X_{n+1} , Y_{n+1} , \theta_{n} \right)$. Remark that $\left( \xi_{n} \right)$ is a sequence of martingale differences adapted to the filtration $\left( \mathcal{F}_{n} \right)$. Moreover, linearizing the gradient and noting $H = \nabla^{2}G(\theta)$, it comes
\begin{align}
\label{decareutiliser} \theta_{n+1} - \theta & = \theta_{n} - \theta - \gamma_{n+1}\overline{S}_{n}^{-1} H \left( \theta_{n} - \theta \right) + \gamma_{n+1}\overline{S}_{n}^{-1}\xi_{n+1} - \gamma_{n+1}\overline{S}_{n}^{-1}\delta_{n} \\
\notag & = \left( 1-\gamma_{n+1} \right)\left( \theta_{n} - \theta \right) + \gamma_{n+1}\left( H^{-1} -\overline{S}_{n}^{-1} \right) H \left( \theta_{n} - \theta \right)\\
\label{decdelta} & + \gamma_{n+1}\overline{S}_{n}^{-1}\xi_{n+1} -\gamma_{n+1}\overline{S}_{n}^{-1}\delta_{n},
\end{align}
where $\delta_{n} = \nabla G \left( \theta_{n} \right) - H \left( \theta_{n} - \theta \right) $ is the remainder term in the Taylor's decomposition of the gradient. By induction, one can check that for all $n \geq 1$,
\begin{align}
\notag \theta_{n} - \theta & = \beta_{n,0} \left( \theta_{0} - \theta \right) + \sum_{k=0}^{n-1} \beta_{n,k+1}\gamma_{k+1} \left( H^{-1} - \overline{S}_{k}^{-1}\right) H \left( \theta_{k} - \theta \right) - \sum_{k=0}^{n-1} \beta_{n,k+1}\gamma_{k+1}\overline{S}_{k}^{-1}\delta_{k} \\
\label{decbeta} & + \sum_{k=0}^{n-1} \beta_{n,k+1} \gamma_{k+1}\overline{S}_{k}^{-1}\xi_{k+1} ,
\end{align}
with, for all $k,n \geq 0$ and $k \leq n$, \[\beta_{n,k} = \prod_{j=k+1}^{n} \left( 1-\gamma_{j} \right) \quad \mbox{and} \quad \beta_{n,n}=1.\]
Applying Theorem~\ref{theomartbeta},
\begin{equation}
\label{lembeta}\left\| \sum_{k=0}^{n-1}\beta_{n,k+1}\gamma_{k+1}\overline{S}_{k}^{-1} \xi_{k+1} \right\|^{2} = \mathcal{O} \left( \frac{\ln n}{n^{\alpha}} \right) \quad a.s.
\end{equation}
We can now prove Theorem~\ref{ratetheta}.
\begin{proof}[Proof of equation~\ref{ratethetaas}]
The aim is to give the rate of convergence of each term of decomposition (\ref{decbeta}). The rate of the martingale term is given by equation \eqref{lembeta}. Remark that there is a rank $n_{\alpha}$ such that for all $n \geq n_{\alpha}$, we have $\gamma_{n}\leq 1$, so that, for all $n \geq n_{\alpha}$,
\begin{align*}
\left\| \beta_{n,0}\left( \theta_{0} - \theta \right) \right\| & \leq \left\| \theta_{0} - \theta \right\| \prod_{i=1}^{n_{\alpha}-1} \left| 1- \gamma_{i+1} \right| \prod_{i=n_{\alpha}} \left( 1-\gamma_{i+1} \right) \\
& \leq \left\| \theta_{0} - \theta \right\| \prod_{i=1}^{n_{\alpha}-1} \left| 1- \gamma_{i+1} \right| \exp \left( -\sum_{i=n_{\alpha}}^{n}\gamma_{i+1} \right) .
\end{align*}
Since $\alpha < 1$, this term converges at an exponential rate, and more precisely
\begin{equation}\label{vitexp}
\left\| \beta_{n,0}\left( \theta_{0} - \theta \right) \right\| = \mathcal{O} \left( \exp \left( - \frac{c_{\alpha}}{1-\alpha}n^{1-\alpha} \right) \right) \quad a.s.
\end{equation}
Let us denote
\[
\Delta_{n} := \sum_{k=0}^{n-1}\beta_{n,k+1}\gamma_{k+1}\left( H^{-1} - \overline{S}_{k}^{-1} \right) H \left( \theta_{k} - \theta \right) - \sum_{k=0}^{n} \beta_{n,k+1}\gamma_{k+1} \overline{S}_{k}^{-1}\delta_{k} .
\]
The aim is so to prove that this term is negligible. First, remark that the Taylor's decomposition of the gradient yields
\[
\delta_{n} = \int_{0}^{1} \left( \nabla^{2}G \left( \theta + t \left( \theta_{n} - \theta \right) \right) - H \right) \left( \theta_{n} - \theta \right) dt ,
\]
and thanks to assumption \textbf{(H4a)}, since $\theta_{n}$ converges almost surely to $\theta$ and by dominated convergence,
\[
\left\| \delta_{n} \right\| \leq \left\| \theta_{n} - \theta \right\| \int_{0}^{1} \left\| \nabla^{2}G \left( \theta + t \left( \theta_{n} - \theta \right) \right) - H \right\|_{op} dt = o \left( \left\| \theta_{n} - \theta \right\| \right) \quad a.s
\]
In a similar way, since $\overline{S}_{n}^{-1}$ converges almost surely to $H^{-1}$,
\[
\left\| \left( H^{-1} - \overline{S}_{n}^{-1} \right) H \left( \theta_{n} - \theta \right) \right\| = o \left( \left\| \theta_{n} - \theta \right\| \right) \quad a.s.
\]
Moreover, since
\[
\Delta_{n+1} = \left( 1-\gamma_{n+1} \right) \Delta_{n} + \gamma_{n+1} \left( H^{-1} - \overline{S}_{n}^{-1} \right) H \left( \theta_{n} - \theta \right) - \gamma_{n+1}\overline{S}_{n}^{-1}\delta_{n},
\]
we have,
\begin{align*}
\left\| \Delta_{n+1} \right\| & \leq \left| 1- \gamma_{n+1} \right| \left\| \Delta_{n} \right\| + o \left( n^{-\alpha} \left\| \theta_{n} - \theta \right\| \right) \quad a.s \\
& \leq \left| 1- \gamma_{n+1} \right| \left\| \Delta_{n} \right\| + o \left( n^{-\alpha} \left\| \Delta_{n} + \sum_{k=0}^{n-1} \beta_{n,k+1} \gamma_{k+1} \overline{S}_{k}^{-1} \xi_{k+1} + \beta_{n,0}\left( \theta_{0} - \theta \right) \right\| \right) \quad a.s.
\end{align*}
Then, since $\beta_{n,0}\left( \theta_{0} - \theta \right)$ converges at an exponential rate to $0$ and thanks to equation \eqref{lembeta},
\[
\left\| \Delta_{n+1} \right\| \leq \left( 1- \gamma_{n+1} \right) \left\| \Delta_{n} \right\| + o \left( \gamma_{n+1} \sqrt{\frac{\ln n}{n^{\alpha}}} + \gamma_{n+1}\left\| \Delta_{n} \right\| \right) \quad a.s ,
\]
and applying a stabilization Lemma (see \cite{Duf97} for instance),
\[
\left\| \Delta_{n} \right\| = \mathcal{O} \left( \sqrt{\frac{\ln n}{n^{\alpha}}}\right) \quad a.s
\]
which concludes the proof.
\end{proof}
\begin{proof}[Proof of equation \eqref{tlc}]
In order to get the asymptotic normality, we will apply the Central Limit Theorem in \cite{Jak88} to the martingale term in decomposition (\ref{decbeta}) and prove that other terms of this decomposition are negligible. The rate of convergence of the first term on the right-hand side of equality (\ref{decbeta}) is given by equality (\ref{vitexp}). Moreover, applying Theorem \ref{ratetheta} and Remark \ref{rempourletrucpourri} as well as Lemma E.2 in \cite{CG2015}, one can check that for all $\delta > 0$,
\[
\left\| \sum_{k=0}^{n-1}\beta_{n,k+1}\gamma_{k+1}\left( H^{-1} - \overline{S}_{k}^{-1} \right) H \left( \theta_{k} - \theta \right) \right\|^{2} = o \left( \frac{(\ln n)^{1+\delta}}{n^{ \alpha + \beta}} \right) \quad a.s,
\]
and this term is so negligible. In the same way,
\[
\left\| \sum_{k=0}^{n-1}\beta_{n,k+1}\gamma_{k+1}\overline{S}_{k}^{-1} \delta_{k} \right\|^{2} = o \left( \frac{(\ln n)^{2+ \delta}}{n^{ 2\alpha }} \right) \quad a.s.
\]
Note that the martingale term can be written as
\[
\sum_{k=0}^{n-1} \beta_{n,k+1}\gamma_{k+1}\overline{S}_{k}^{-1}\xi_{k+1}= \sum_{k=0}^{n-1} \beta_{n,k+1} c_{\alpha}\gamma_{k+1} \left( \overline{S}_{k}^{-1} - H^{-1} \right) \xi_{k+1} + \sum_{k=0}^{n-1} \beta_{n,k+1}\gamma_{k+1} H^{-1}\xi_{k+1} .
\]
Applying Theorem \ref{theomartbeta} and Remark \ref{rempourletrucpourri},
\[
\left\| \sum_{k=0}^{n} \beta_{n+1,k+1} \gamma_{k+1} \left( \overline{S}_{k}^{-1} - H^{-1} \right) \xi_{k+1} \right\|^{2} = O \left( \frac{\ln n}{n^{\alpha + 2\beta}} \right) \quad a.s.
\]
Finally, let us now prove that the martingale term verifies assumption in \cite{Jak88}, i.e that we have
\begin{equation}
\label{cond1} \forall \nu > 0 , \quad \lim_{n\to + \infty} \mathbb{P}\left[ \sup_{0\leq k \leq n} \sqrt{\frac{n^{\alpha}}{c_{\alpha}}} \left\| \beta_{n+1,k+1} c_{\alpha}(k+1)^{-\alpha}H^{-1} \xi_{k+1} \right\| > \nu \right] = 0 .
\end{equation}
\begin{equation}
\label{cond2} \frac{n^{\alpha}}{c_{\alpha}} \sum_{k=0}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} \xi_{k+1} \xi_{k+1}^{T} H^{-1} \xrightarrow[n\to + \infty]{a.s} \frac{1}{2}\sigma^{2} H^{-1} .
\end{equation}
\medskip
\noindent\textbf{Proof of equation (\ref{cond1}):} Thanks to assumption \textbf{(H5)}, one can check that for all $n\geq 1$,
\begin{equation}
\label{majxipourri}\mathbb{E}\left[ \left\| \xi_{n+1} \right\|^{2+2\eta} |\mathcal{F}_{k} \right] \leq 2^{2+2\eta}C_{\eta}
\end{equation}
Then, applying Markov's inequality,
\begin{align*}
\mathbb{P}\left[ \sup_{0\leq k \leq n} \sqrt{\frac{n^{\alpha}}{c_{\alpha}}} \left\| \beta_{n+1,k+1} \gamma_{k+1}H^{-1} \xi_{k+1} \right\| > \nu \right] & \leq \sum_{k=0}^{n} \mathbb{P}\left[ \sqrt{\frac{n^{\alpha}}{c_{\alpha}}} \left\| \beta_{n+1,k+1} \gamma_{k+1}H^{-1} \xi_{k+1} \right\| > \nu \right] \\
& \leq \sum_{k=0}^{n} \mathbb{P}\left[ \left\| \xi_{k+1} \right\| > \frac{\sqrt{c_{\alpha}}\nu}{n^{\alpha/2}\left| \beta_{n+1,k+1}\right|\gamma_{k+1}\left\| H^{-1}\right\|_{op}} \right] \\
& \leq \frac{c_{\alpha}^{1+\eta}\left\| H^{-1} \right\|_{op}^{2+2\eta}}{\nu^{2+2\eta}} 2^{2+2\eta}C_{\eta}n^{\alpha\left( 1+ \eta \right)}\sum_{k=0}^{n}\left| \beta_{n+1,k+1} \right|^{2+2\eta} k^{-2\alpha\left( 1+ \eta \right)}.
\end{align*}
Moreover, note that there is a rank $n_{\alpha}$ such that for all $j \geq n_{\alpha}$ we have $c_{\alpha} j^{-\alpha} \leq 1$. For the sake of readibility of the proof (in other way, one can split the sum into two parts as in the proof of Lemma 3.1 in \cite{CCG2015}), we consider from now on that $n_{\alpha} =1$. Then
\begin{align*}
\left| \beta_{n+1,k+1} \right| & = \prod_{i=k+2}^{n+1} \left( 1-c_{\alpha}i^{-\alpha} \right) \leq \exp \left( - c_{\alpha}\sum_{i=k+2}^{n+1} i^{-\alpha} \right).
\end{align*}
Applying Lemma E.2 in \cite{CG2015}, it comes
\[
\sum_{k=0}^{n}\left| \beta_{n+1,k+1} \right|^{2+2\eta} k^{-2\alpha\left( 1+ \eta \right)} =\mathcal{O} \left( n^{-\alpha -2 \alpha \eta} \right) ,
\]
and so
\[
\lim_{n\to + \infty} \frac{c_{\alpha}^{ 1+ \eta}\left\| H^{-1} \right\|_{op}^{2+2\eta}}{\nu^{2 +2 \eta}} 2^{2+2\eta}C_{\eta}n^{\alpha (1+\eta)}\sum_{k=0}^{n}\left| \beta_{n+1,k+1} \right| k^{-2\alpha( 1+ \eta)} = 0 .
\]
\medskip
\noindent\textbf{Proof of equation (\ref{cond2}): } First, note that
\begin{align*}
\sum_{k=0}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} \xi_{k+1}\xi_{k+1}^{T}H^{-1}& = \sum_{k=0}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} \mathbb{E}\left[ \xi_{k+1}\xi_{k+1}^{T}|\mathcal{F}_{k} \right] H^{-1}\\ &+\sum_{k=0}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} \Xi_{k+1}H^{-1},
\end{align*}
with $\Xi_{k+1} = \xi_{k+1}\xi_{k+1}^{T} - \mathbb{E}\left[ \xi_{k+1}\xi_{k+1}^{T} |\mathcal{F}_{k} \right]$. $\left( \Xi_{k} \right)$ is a sequence of martingale differences adapted to the filtration $\left( \mathcal{F}_{k} \right)$. Applying Theorem~\ref{theomartbeta}, it comes
\[
\left\| \sum_{k=0}^{n}\beta_{n+1,k+1}^{2}\gamma_{k+1}^{2}H^{-1} \Xi_{k+1} H^{-1} \right\|^{2} = O \left( \frac{\ln n}{n^{3\alpha}}\right) \quad a.s.
\]
Moreover, note that
\begin{align*}
\sum_{k=0}^{n} & \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} \mathbb{E}\left[ \xi_{k+1}\xi_{k+1}^{T}|\mathcal{F}_{k} \right] H^{-1} = -\sum_{k=0}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} \nabla G\left(\theta_{k} \right) \nabla G\left( \theta_{k} \right)^{T} H^{-1} \\
& + \sum_{k=0}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} \mathbb{E}\left[ \nabla_{h} g \left( X_{k+1},Y_{k+1} , \theta_{k} \right) \nabla_{h} g \left( X_{k+1} , Y_{k+1} , \theta_{k}\right)^{T}|\mathcal{F}_{k} \right] H^{-1}.
\end{align*}
Applying Theorem \ref{ratetheta}, equality (\ref{vitexp}) and Lemma E.2 in \cite{CG2015}, since the gradient of $G$ is Lipschitz, one can check that for all $\delta > 0$,
\[
\left\| \sum_{k=0}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} \nabla G\left(\theta_{k} \right) \nabla G\left( \theta_{k} \right)^{T} H^{-1} \right\|_{F}^{2} = o \left( \frac{(\ln n)^{1+\delta}}{n^{2\alpha}} \right) \quad a.s.
\]
Moreover, noting
\[
R_{k}=\mathbb{E}\left[ \nabla_{h} g \left( X_{k+1},Y_{k+1} , \theta_{k} \right) \nabla_{h} g \left( X_{k+1} , Y_{k+1} , \theta_{k}\right)^{T}|\mathcal{F}_{k} \right] - \mathbb{E}\left[ \nabla_{h} g \left( X_{k+1},Y_{k+1} , \theta \right)\nabla_{h} g \left( X_{k+1},Y_{k+1} , \theta \right)^{T} |\mathcal{F}_{k} \right] ,
\]
\begin{align*}
& \sum_{k=0}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} \mathbb{E}\left[ \nabla_{h} g \left( X_{k+1},Y_{k+1} , \theta_{k} \right) \nabla_{h} g \left( X_{k+1} , Y_{k+1} , \theta_{k}\right)^{T}|\mathcal{F}_{k} \right] H^{-1} \\
& = \sum_{k=0}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} R_{k} H^{-1} + \sum_{k=1}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} \mathbb{E}\left[ \nabla_{h} g \left( X_{k+1},Y_{k+1} , \theta \right) \nabla_{h} g \left( X_{k+1} , Y_{k+1} , \theta\right)^{T}|\mathcal{F}_{k} \right] H^{-1}
\end{align*}
Moreover, applying Theorem \ref{ratetheta}, Lemma E.2 in \cite{CG2015}, one chan check that for all $\delta > 0$,
\[
\left\| \sum_{k=0}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} H^{-1} R_{k} H^{-1} \right\|_{F} = o \left( \frac{(\ln n)^{1+\delta}}{n^{2\alpha}} \right) \quad a.s.
\]
Furthermore, since $\mathbb{E}\left[ \nabla_{h} g \left( X_{k+1},Y_{k+1} , \theta \right) \nabla_{h} g \left( X_{k+1} , Y_{k+1} , \theta\right)^{T}|\mathcal{F}_{k} \right] = \sigma^{2}H$, applying Lemma A.1 in \cite{GB2017},
\[
\lim_{n\to \infty}\left\| H^{-1} \left( \frac{n^{\alpha}}{c_{\alpha}}\sum_{k=0}^{n} \beta_{n+1,k+1}^{2} \gamma_{k+1}^{2} \mathbb{E}\left[ \nabla_{h} g \left( X_{k+1},Y_{k+1} , \theta \right) \nabla_{h} g \left( X_{k+1} , Y_{k+1} , \theta\right)^{T}|\mathcal{F}_{k} \right] - \frac{1}{2}\sigma^{2}H \right) H^{-1} \right\|_{F} =0,
\]
which concludes the proof.
\end{proof}
\subsection{Proof of Theorem \ref{ratethetabar}}
Let us first give some decompositions of the averaged estimates. First, note that
\[
\overline{\theta}_{n} = \frac{1}{n+1}\sum_{k=0}^{n} \theta_{k}.
\]
Second, one can write decomposition (\ref{decareutiliser}) as
\begin{equation}
\label{equationcle} \theta_{n} - \theta = H^{-1} \overline{S}_{n}\frac{\left( \theta_{n} - \theta \right) - \left( \theta_{n+1} - \theta \right)}{\gamma_{n+1}} + H^{-1}\xi_{n+1} - H^{-1} \delta_{n} .
\end{equation}
Then, summing these equalities and dividing by $n+1$, it comes
\begin{equation}
\label{decmoy} \overline{\theta}_{n} - \theta = H^{-1}\frac{1}{n+1}\sum_{k=0}^{n} \overline{S}_{k}\frac{\left( \theta_{k} - \theta \right) - \left( \theta_{k+1} - \theta \right)}{\gamma_{k+1}} + H^{-1} \frac{1}{n+1} \sum_{k=0}^{n} \xi_{k+1} - H^{-1} \frac{1}{n+1}\sum_{k=0}^{n} \delta_{k} .
\end{equation}
\begin{proof}[Proof of Theorem \ref{ratethetabar}]
Let us give the rate of convergence of each term on the right-hand side of equality (\ref{decmoy}). First, in order to apply a Law of Large Numbers and a Central Limit Theorem for martingales, let us calculate
\[
\lim_{n\to \infty}\frac{1}{n+1}\sum_{k=0}^{n} \mathbb{E}\left[ \xi_{k+1}\xi_{k+1}^{T} |\mathcal{F}_{k} \right].
\]
By definition of $\left( \xi_{n} \right)$, it comes
\begin{align*}
\frac{1}{n+1}\sum_{k=0}^{n} \mathbb{E}\left[ \xi_{k+1}\xi_{k+1}^{T} |\mathcal{F}_{k} \right]& = \frac{1}{n+1}\sum_{k=0}^{n} \mathbb{E}\left[ \nabla_{h} g \left( X_{k+1} ,Y_{k+1} , \theta_{k} \right)\nabla_{h} g \left( X_{k+1} ,Y_{k+1} , \theta_{k} \right)^{T} |\mathcal{F}_{k} \right] \\
& - \frac{1}{n+1}\sum_{k=0}^{n} \nabla G\left( \theta_{k} \right) \nabla G \left( \theta_{k} \right)^{T} .
\end{align*}
By continuity and since $\theta_{k}$ converges amost surely to $\theta$, Toeplitz lemma implies
\[
\frac{1}{n+1}\sum_{k=0}^{n} \mathbb{E}\left[ \xi_{k+1}\xi_{k+1}^{T} |\mathcal{F}_{k} \right] \xrightarrow[n\to + \infty]{a.s} \mathbb{E}\left[ \nabla_{h} g \left( X,Y , \theta \right)\nabla_{h} g \left( X,Y , \theta \right)^{T} \right] .
\]
Furthermore,
\[
\mathbb{E}\left[ \nabla_{h} g \left( X,Y , \theta \right)\nabla_{h} g \left( X,Y , \theta \right)^{T} \right] = \mathbb{E}\left[ \epsilon^{2} \nabla_{h}f\left( X,Y,\theta \right) \nabla_{h}f \left( X,Y , \theta \right)^{T} \right] = \sigma^{2} H .
\]
Finally, since $\mathbb{E}\left[ \left\| \xi_{n+1} \right\|^{2+2\eta} |\mathcal{F}_{n} \right] \leq 2^{2+2\eta}C_{\eta}$, applying a Law of Large Numbers for martingales (see \cite{Duf97}),
\[
\frac{1}{(n+1)^{2}} \left\| H^{-1} \sum_{k=0}^{n} \xi_{k+1} \right\|^{2} = \mathcal{O}\left( \frac{\ln n}{n} \right) \quad a.s.
\]
Moreover, applying a Central Limit Theorem for martingales (see \cite{Duf97}),
\[
\frac{1}{\sqrt{n}}H^{-1} \sum_{k=0}^{n} \xi_{k+1} \xrightarrow[n\to + \infty]{\mathcal{L}} \mathcal{N}\left( 0 , \sigma^{2}H^{-1} \right) .
\]
Let us now prove that other terms on the right-hand side of equality (\ref{decmoy}) are negligible. Thanks to assumption \textbf{(H4b)} and since $\theta_{n}$ converges almost surely to $\theta$,
\[
\left\| \delta_{n} \right\| \leq \left\| \theta_{n} - \theta \right\| \int_{0}^{1} \left\| \nabla^{2}G \left( \theta + t \left( \theta_{n} - \theta \right) \right) - H \right\|_{op} dt = O \left( \left\| \theta_{n} - \theta \right\|^{2} \right) \quad a.s
\]
Then applying Theorem \ref{ratetheta}, for all $\delta > 0$,
\[
\frac{1}{n+1}\left\| H^{-1}\sum_{k=0}^{n} \delta_{k} \right\| \leq \frac{\left\| H^{-1} \right\|_{op}}{n+1} \sum_{k=1}^{n} \left\| \delta_{k} \right\| = o \left( \frac{(\ln n)^{1+\delta}}{n^{\alpha}} \right) \quad a.s
\]
and since $\alpha > 1/2$, this term is negligible. Finally, as in \cite{Pel00}, using an Abel's transform,
\begin{align}
\notag \frac{1}{n+1}\sum_{k=0}^{n} \overline{S}_{k}\frac{\left( \theta_{k} - \theta \right) - \left( \theta_{k+1} - \theta \right)}{c_{\alpha}(k+1)^{-\alpha}} & = - \frac{\overline{S}_{n+1}\left( \theta_{n+1} - \theta\right) }{(n+1)\gamma_{n+2}} + \frac{\overline{S}_{0}\left( \theta_{0}-\theta \right)}{(n+1)\gamma_{1}} \\
\label{termedemerde}& - \frac{1}{n+1}\sum_{k=1}^{n+1} \left( \gamma_{k}^{-1}\overline{S}_{k-1} - \gamma_{k+1}^{-1}\overline{S}_{k} \right) \left( \theta_{k} - \theta \right) .
\end{align}
Let us now give the rates of convergence of each term on the right-hand side of equality (\ref{termedemerde}). First, applying Theorem \ref{ratetheta} and since $\overline{S}_{n}$ converges almost surely to $H$,
\[
\left\| \frac{\overline{S}_{n+1}\left( \theta_{n+1} - \theta\right) }{\gamma_{n+2}(n+1)} \right\|^{2} = O \left( \frac{\ln n}{n^{2 - \alpha}} \right) \quad a.s \quad \quad \quad \text{and} \quad \quad \quad \left\| \frac{\overline{S}_{0}\left( \theta_{0}-\theta \right)}{(n+1)\gamma_{1}} \right\|^{2} = O \left( \frac{1}{n^{2}} \right) \quad a.s
\]
and these terms are negligible since $\alpha < 1$. Furthermore, since
\[
\overline{S}_{k} =\overline{S}_{k-1} - \frac{1}{k}\overline{S}_{k-1} + \frac{1}{k} \left( \overline{\Phi}_{k} \overline{\Phi}_ {k}^{T} + \frac{c_{\beta}}{k^{\beta}} Z_{k}Z_{k}^{T} \right),
\]
it comes
\begin{align*}
(*) :& =\frac{1}{n+1}\sum_{k=1}^{n+1} \left( \gamma_{k}\overline{S}_{k-1} - \gamma_{k+1}\overline{S}_{k} \right) \left( \theta_{k} - \theta \right) \\
& = \frac{1}{n+1}\sum_{k=1}^{n+1} \left( \gamma_{k}^{-1} - \gamma_{k+1}^{-1} \right) \overline{S}_{k-1} \left( \theta_{k} - \theta \right) - \frac{1}{n+1}\sum_{k=1}^{n+1}\frac{\gamma_{k+1}^{-1}}{k}\overline{S}_{k-1}\left( \theta_{k} - \theta \right) \\
& + \underbrace{\frac{1}{n+1}\sum_{k=1}^{n+1}\frac{\gamma_{k+1}^{-1}}{k } \left( \overline{\Phi}_{k} \overline{\Phi}_{k}^{T} + \frac{c_{\beta}}{k^{\beta}} Z_{k}Z_{k}^{T} \right) \left( \theta_{k} - \theta \right)}_{:=(**)} .
\end{align*}
For the first term on the right-hand side of previous equality, since $\left| \gamma_{k}^{-1} - \gamma_{k+1}^{-1} \right| \leq \alpha c_{\alpha}^{-1} k^{\alpha -1}$ and since $\overline{S}_{k-1}$ converges almost surely to $H$, applying Theorem \ref{ratetheta}, for all $\delta > 0$,
\[
\frac{1}{(n+1)^{2}}\left\| \sum_{k=1}^{n+1} \left( \gamma_{k}^{-1} - \gamma_{k+1}^{-1} \right) \overline{S}_{k-1} \left( \theta_{k} - \theta \right) \right\|^{2} = o \left( \frac{(\ln n)^{1+\delta}}{n^{2-\alpha} }\right) \quad a.s
\]
which is negligible since $\alpha < 1$. Furthermore, since $\overline{S}_{k-1}$ converges almost surely to $H$, one can check that
\[
\frac{1}{(n+1)^{2}} \left\| \sum_{k=1}^{n} \frac{\gamma_{k+1}^{-1}}{k} \overline{S}_{k-1}\left( \theta_{k} - \theta \right) \right\|^{2} = o \left( \frac{(\ln n)^{1+\delta}}{n^{2- \alpha}} \right) \quad a.s.
\]
Let us now give the rate of convergence of $(**)$. In this aim, let us consider $\delta > 0$ and introduce the events $\Omega_{k}= \left\lbrace \left\| \theta_{k} - \theta \right\| \leq \frac{(\ln k)^{1/2 + \delta}}{k^{\alpha/2 }} \right\rbrace$. Since $\delta > 0$, and thanks to Theorem \ref{ratetheta}, $\frac{\left\| \theta_{n} - \theta \right\|^{2}n^{\alpha}}{(\ln n)^{1+\delta}}$ converges almost surely to $0$, so that $\mathbf{1}_{\Omega_{k}^{C}}$ converges almost surely to $0$. Furthermore,
\begin{align*}
(**) &= \underbrace{\frac{1}{n+1}\sum_{k=1}^{n+1}\frac{\gamma_{k+1}^{-1}}{k } \left( \overline{\Phi}_{k} \overline{\Phi}_{k}^{T} + \frac{c_{\beta}}{k^{\beta}} Z_{k}Z_{k}^{T} \right) \left( \theta_{k} - \theta \right)\mathbf{1}_{\Omega_{k}}}_{:= (***)} \\&+ \frac{1}{n+1}\sum_{k=1}^{n+1}\frac{\gamma_{k+1}^{-1}}{k } \left( \overline{\Phi}_{k} \overline{\Phi}_{k}^{T} + \frac{c_{\beta}}{k^{\beta}} Z_{k}Z_{k}^{T} \right) \left( \theta_{k} - \theta \right) \mathbf{1}_{\Omega_{k}^{C}}
\end{align*}
Since $\mathbf{1}_{\Omega_{k}^{C}}$ converges almost surely to $0$,
\[
\sum_{k\geq 1}\frac{\gamma_{k+1}^{-1}}{k } \left\| \overline{\Phi}_{k} \overline{\Phi}_{k}^{T} + \frac{c_{\beta}}{k^{\beta}} Z_{k}Z_{k}^{T} \right\| \left\| \theta_{k} - \theta \right\|_{op} \mathbf{1}_{\Omega_{k}^{C}} < + \infty \quad a.s
\]
so that
\[
\frac{1}{n+1}\left\| \sum_{k=1}^{n+1}\frac{\gamma_{k+1}^{-1}}{k } \left( \overline{\Phi}_{k} \overline{\Phi}_{k}^{T} + \frac{c_{\beta}}{k^{\beta}} Z_{k}Z_{k}^{T} \right) \left( \theta_{k} - \theta \right) \mathbf{1}_{\Omega_{k}^{C}} \right\| = O \left( \frac{1}{n}\right) \quad a.s.
\]
Moreover,
\begin{align*}
(***) \leq \frac{1}{n+1}\sum_{k=1}^{n+1} \frac{\gamma_{k+1}^{-1}}{k}\left\| \overline{\Phi}_{k} \overline{\Phi}_{k}^{T} + \frac{c_{\beta}}{k^{\beta}}Z_{k}Z_{k}^{T} \right\|_{op} \frac{(\ln k)^{1/2 + \delta}}{k^{\alpha /2}} .
\end{align*}
One can consider the sequence of martigales differences $\left( \Xi_{k} \right)$ adapted to the filtration $\left( \mathcal{F}_{k} \right)$ and defined for all $k \geq 1$ by
\[
\Xi_{k} = \left\| \overline{\Phi}_{k} \overline{\Phi}_{k}^{T} + \frac{c_{\beta}}{k^{\beta}}Z_{k}Z_{k}^{T} \right\|_{op} - \mathbb{E}\left[ \left\| \overline{\Phi}_{k} \overline{\Phi}_{k}^{T} + \frac{c_{\beta}}{k^{\beta}}Z_{k}Z_{k}^{T} \right\|_{op} |\mathcal{F}_{k-1} \right] .
\]
Then,
\[
(***) \leq \frac{1}{n+1}\sum_{k=1}^{n+1} \frac{\gamma_{k+1}(\ln k)^{1/2 + \delta}}{k^{\alpha/2 +1}} \mathbb{E}\left[ \left\| \overline{\Phi}_{k} \overline{\Phi}_{k}^{T} + \frac{c_{\beta}}{k^{\beta}}Z_{k}Z_{k}^{T} \right\|_{op} |\mathcal{F}_{k-1} \right] + \frac{1}{n+1}\sum_{k=1}^{n+1} \frac{\gamma_{k+1}(\ln k)^{1/2 + \delta}}{k^{\alpha/2 +1}} \Xi_{k} .
\]
\end{proof}
Then, thanks to Assumption \textbf{(H1b)} and Toeplitz lemma,
\[
\frac{1}{n+1}\sum_{k=1}^{n+1} \frac{\gamma_{k+1}(\ln k)^{1/2 + \delta}}{k^{\alpha/2 +1}} \mathbb{E}\left[ \left\| \overline{\Phi}_{k} \overline{\Phi}_{k}^{T} + \frac{c_{\beta}}{k^{\beta}}Z_{k}Z_{k}^{T} \right\|_{op} |\mathcal{F}_{k-1} \right] = o \left( \frac{(\ln n)^{1/2 + \delta}}{n^{1- \alpha/2}} \right) \quad a.s .
\]
Furthermore, since $\alpha < 1$, with assumption \textbf{(H1b)}, Theorem~\ref{theomartmoy} leads to
\[
\left\| \frac{1}{n+1}\sum_{k=1}^{n+1} \frac{\gamma_{k+1}(\ln k)^{1/2 + \delta}}{k^{\alpha/2 +1}} \Xi_{k} \right\|^{2} = O \left( \frac{1}{n^{2}} \right) \quad a.s.
\]
\subsection{Proof of Corollary \ref{ratesn}}
\begin{proof}
The aim is to give the rate of convergence of each term of decomposition (\ref{decsn}). Note that the rate of the martingale term is given by (\ref{vitXi}), while, thanks to equation (\ref{vitzi}), we have
\[
\frac{1}{n^{2}}\left\| \sum_{k=1}^{n} \frac{c_{\beta}}{k^{\beta}} Z_{k+1}Z_{k+1}^{T} \right\|_{F}^{2} = O \left( \frac{1}{n^{2\beta}} \right) \quad a.s.
\]
Finally, since the functional $h \longmapsto \mathbb{E}\left[ \nabla_{h}f \left( X , h \right) \nabla_{h} f ( X,h )^{T} \right]$ is $C_{f}$-Lipschitz on a neighborhood of $\theta$ and since $\overline{\theta}_{n}$ converges almost surely to $\theta$, applying Theorem \ref{ratethetabar} as well as Toeplitz lemma, for all $\delta > 0$,
\begin{align*}
\frac{1}{n^{2}}\left\| \sum_{k=1}^{n} \left( \mathbb{E}\left[ \overline{\Phi}_{k+1}\overline{\Phi}_{k+1}^{T} |\mathcal{F}_{k} \right] - H \right) \right\|_{F}^{2} & = \mathcal{O} \left( \frac{C_{f}^{2}}{n^{2}} \left( \sum_{k=1}^{n} \left\| \overline{\theta}_{k} - \theta \right\| \right)^{2} \right) \quad a.s \\
& = o \left( \frac{(\ln n)^{1+\delta}}{n} \right) \quad a.s,
\end{align*}
which concludes the proof.
\begin{rmq}\label{rempourletrucpourri}
Note that to prove equality \eqref{tlc} without knowing the rate of convergence of $\overline{\theta}_{n}$, it is necessary to have a first rate of convergence of $\overline{S}_{n}$. For that purpose, we study the asymptotic behaviour of
\[
\frac{1}{n^{2}}\left\| \sum_{k=1}^{n} \left( \mathbb{E}\left[ \overline{\Phi}_{k+1}\overline{\Phi}_{k+1}^{T} |\mathcal{F}_{k} \right] - H \right) \right\|_{F}^{2}.
\]
Equality \eqref{ratethetaas} yields for all $\delta > 0$,
\[
\left\| \overline{\theta}_{n} - \theta \right\| \leq \frac{1}{n+1}\sum_{k=0}^{n} \left\| \theta_{k} - \theta \right\| = O \left( \frac{(\ln n)^{1 /2 + \delta /2}}{n^{\alpha /2}} \right) ,
\]
so that, since the functional $h \longmapsto \mathbb{E}\left[ \nabla_{h}f \left( X , h \right) \nabla_{h} f ( X,h )^{T} \right]$ is $C_{f}$-Lipschitz on a neighborhood of $\theta$,
\begin{align*}
\frac{1}{n^{2}}\left\| \sum_{k=1}^{n} \left( \mathbb{E}\left[ \overline{\Phi}_{k+1}\overline{\Phi}_{k+1}^{T} |\mathcal{F}_{k} \right] - H \right) \right\|_{F}^{2} & = \mathcal{O} \left( \frac{C_{f}^{2}}{n^{2}} \left( \sum_{k=1}^{n} \left\| \overline{\theta}_{k} - \theta \right\| \right)^{2} \right) \quad a.s \\
& = o \left( \frac{(\ln n)^{1+\delta}}{n^{\alpha}} \right) \quad a.s,
\end{align*}
and then, since $\beta < \alpha -1/2$,
\[
\left\| \overline{S}_{n} - H \right\|_{F} = O \left( \max \left\lbrace \frac{c_{\beta}}{n^{\beta}} , \sqrt{\frac{(\ln n)^{1+\delta}}{n^{\alpha}}} \right\rbrace \right) \quad a.s
\]
\end{rmq}
\end{proof}
\subsection{Proof of Theorem \ref{theothetatilde}\label{prooftilde}}
Only the main lines of the proof are given since it is a mix between the proof of Theorem~\ref{ratethetabar} and the ones in \cite{BGBP2019}.
\begin{proof}[Proof of THeorem \ref{theothetatilde}]
Let us denote $\overline{H}_{n}^{-1} = (n+1) \widetilde{H}_{n}^{-1}$. First, remark that as in the proof of Corollary \ref{ratesn}, one can check that that on $\widetilde{\Gamma}_{\theta}$,
\[
\overline{H}_{n} \xrightarrow[n\to + \infty]{a.s} H \quad \quad \text{and} \quad \quad \overline{H}_{n}^{-1} \xrightarrow[n\to + \infty]{a.s} H^{-1} .
\]
Furthermore, decomposition \eqref{decxi} can be rewritten as
\begin{equation}
\label{decxitilde} \widetilde{\theta}_{n+1} = \widetilde{\theta}_{n} - \theta - \frac{1}{n+1} \overline{S}_{n}^{-1} \nabla G \left( \widetilde{\theta}_{n} \right) + \frac{1}{n+1}\overline{H}_{n}^{-1} \widetilde{\xi}_{n+1},
\end{equation}
where $\widetilde{\xi}_{n+1} := \nabla G \left( \widetilde{\theta}_{n} \right) - \nabla_{h} g \left( X_{n+1} , Y_{n+1} , \widetilde{\theta}_{n} \right)$. Then, $\left( \widetilde{\xi}_{n} \right)$ is a sequence of martingale differences adapted to the filtration $\left( \mathcal{F}_{n} \right)$. Linearizing the gradient, decomposition \eqref{decdelta} can be rewritten as
\begin{align}
\notag \widetilde{\theta}_{n+1} - \theta & = \frac{n}{n+1} \left( \widetilde{\theta}_{n} - \theta \right) + \frac{1}{n+1}\left( H^{-1} - \overline{H}_{n}^{-1} \right)H \left( \widetilde{\theta}_{n} - \theta \right) \\
\label{decdeltatilde} & + \frac{1}{n+1}\overline{H}_{n}^{-1}\widetilde{\xi}_{n+1} - \frac{1}{n+1}\overline{H}_{n}^{-1} \widetilde{\delta}_{n}
\end{align}
where $\widetilde{\delta}_{n} = \nabla G \left( \widetilde{\theta}_{n} \right) - H \left( \widetilde{\theta}_{n} - \theta \right)$ is the reminder term in the Taylor's decomposition of the gradient. Then, by induction, it comes
\begin{align}
\label{dectot} \widetilde{\theta}_{n} - \theta = \frac{1}{n}\left( \widetilde{\theta}_{0} - \theta \right)+ \frac{1}{n}\sum_{k=0}^{n-1} \left( H^{-1} - \overline{H}_{k}^{-1} \right) H \left( \widetilde{\theta}_{k} - \theta \right) - \frac{1}{n}\sum_{k=0}^{n-1} \overline{H}_{k}^{-1} \widetilde{\delta}_{k} + \frac{1}{n}\sum_{k=0}^{n-1}\overline{H}_{k}^{-1}\widetilde{\xi}_{k+1} .
\end{align}
Since $\overline{H}_{k}^{-1}$ converges almost surely to $H^{-1}$, on $\widetilde{\Gamma}_{\theta}$, one can check that
\[
\frac{1}{n}\sum_{k=0}^{n-1} \overline{H}_{k}^{-1} \widetilde{\xi}_{k+1}\widetilde{\xi}_{k+1}^{T}\overline{H}_{k}^{-1} \xrightarrow[n\to + \infty]{a.s} \sigma^{2}H^{-1}.
\]
Thanks to assumption \textbf{(H5)}, applying a law of large numbers for martingales, one can check that
\begin{equation}\label{vitxitilde}
\left\|\frac{1}{n}\sum_{k=0}^{n-1} \overline{H}_{k}^{-1} \widetilde{\xi}_{k+1} \right\|^{2} = \mathcal{O} \left( \frac{\ln n}{n} \right) \quad a.s
\end{equation}
In the same way, applying a central limit theorem, it comes
\begin{equation}\label{tlctilde}
\frac{1}{\sqrt{n}} \sum_{k=0}^{n-1} \overline{H}_{k}^{-1} \widetilde{\xi}_{k+1} \xrightarrow[n\to + \infty]{\mathcal{L}} \mathcal{N}\left( 0 , \sigma^{2}H^{-1} \right) .
\end{equation}
Let us now prove that the other terms in decomposition \eqref{dectot} are negligible. First, clearly
\begin{equation}
\label{vitdebile}\frac{1}{n}\left\| \widetilde{\theta}_{0} - \theta \right\| = \mathcal{O} \left( \frac{1}{n} \right) \quad a.s.
\end{equation}
Furthermore, let us denote
\[
\widetilde{\Delta}_{n} = \frac{1}{n}\sum_{k=0}^{n-1} \left( H^{-1} - \overline{H}_{k}^{-1} \right) H \left( \widetilde{\theta}_{k} - \theta \right) - \frac{1}{n}\sum_{k=0}^{n-1} \overline{H}_{k}^{-1} \widetilde{\delta}_{k} .
\]
Furthermore, as in the proof of Theorem \ref{ratetheta}, one can verify
\begin{align*}
& \left\| \left( H^{-1} - \overline{H}_{n}^{-1} \right) H \left( \widetilde{\theta}_{n} - \theta \right) \right\| = o \left( \left\| \widetilde{\theta}_{n} - \theta \right\| \right) \quad a.s
& \left\| \widetilde{\delta}_{n} \right\| = o \left( \left\| \widetilde{\theta}_{n} - \theta \right\| \right) \quad a.s
\end{align*}
Then,
\begin{equation}\label{deltatilde}
\left\| \widetilde{\Delta}_{n+1} \right\| = \frac{n}{n+1} \left\| \widetilde{\Delta}_{n} \right\| + o \left( \widetilde{\theta}_{n} - \theta \right) \quad a.s.
\end{equation}
As in the proof of Theorem 6.2 in \cite{BGBP2019} (see equations (6.24) to (6.32)), it comes
\begin{equation}
\label{vitdeltatilde}\left\| \widetilde{\Delta}_{n} \right\|^{2} = \mathcal{O} \left( \frac{\ln n}{n} \right) \quad a.s.
\end{equation}
Then, thanks to equalities \eqref{vitxitilde},\eqref{vitdebile} and \eqref{vitdeltatilde}, it comes
\begin{equation}\label{vitthetatilde}
\left\|\widetilde{\theta}_{n} - \theta \right\|^{2} = \mathcal{O} \left( \frac{\ln n}{n} \right) \quad a.s.
\end{equation}
In order to get the asymptotic normality of $\widetilde{\theta}_{n}$, let us now give the rate of convergence of each term on the right-hand side of decomposition \eqref{dectot}. First, since
\[
\widetilde{\delta}_{n} = \mathcal{O} \left( \left\| \widetilde{\theta}_{n} - \theta \right\|^{2} \right) \quad a.s,
\]
and since $\overline{H}_{n}^{-1}$ converges almost surely to $H^{-1}$, thanks to equality \eqref{vitthetatilde}, for all $\delta > 0$
\[
\frac{1}{n}\left\| \sum_{k=0}^{n-1} \overline{H}_{k}^{-1}\widetilde{\delta}_{k} \right\| = o \left( \frac{(\ln n)^{2+\delta}}{n} \right) \quad a.s
\]
which is so negligible. Furthermore, as in the proof of Corollary \ref{ratesn}, one can check that for all $\delta > 0$,
\[
\left\| \overline{H}_{n}^{-1} - H^{-1} \right\|^{2} = \mathcal{O} \left( \max \left\lbrace \frac{c_{\beta}^{2}}{n^{2\beta}} , \frac{(\ln n)^{1+\delta}}{n} \right\rbrace \right) \quad a.s .
\]
Then, for all $\delta > 0$,
\[
\frac{1}{n}\left\|\sum_{k=1}^{n} \left( \overline{H}_{k}^{-1} - H^{-1} \right) H \left( \widetilde{\theta}_{k} - \theta \right) \right\| = o \left( \max \left\lbrace \frac{c_{\beta}(\ln n)^{1/2+\delta}}{n^{\beta + 1/2}} , \frac{(\ln n)^{2+\delta}}{n} \right\rbrace \right) \quad a.s
\]
and this term is no negligible.
\end{proof}
\subsection{Proof of Corollary \ref{estsigma}}
First, note that
\[
\left( \hat{Y}_{k} - Y_{k} \right)^{2} - \sigma^{2} = \left( f \left( X_{k} , \overline{\theta}_{k-1} \right) - f \left( X_{k} , \theta \right) \right)^{2} -2 \epsilon_{k} \left( f \left( X_{k} , \overline{\theta}_{k-1} \right) - f \left( X_{k} , \theta \right) \right) + \left( \epsilon_{k}^{2} - \sigma^{2} \right) .
\]
Thanks to a Taylor's decomposition, there are $U_{0},\ldots,U_{n-1} \in \mathbb{R}^{q}$ such that
\[
R_{1} := \frac{1}{n}\sum_{k=1}^{n} \left( f \left( X_{k} , \overline{\theta}_{k-1} \right) - f \left( X_{k} , \theta \right) \right)^{2} \leq \frac{1}{n}\sum_{k=1}^{n} \left\| \nabla_{h} f \left( X_{k} , U_{k-1} \right) \right\|^{2} \left\| \overline{\theta}_{k-1} - \theta \right\|^{2}
\]
Let us consider the filtration $\left( \mathcal{F}^{(1)}_{n} \right)$ defined by $\mathcal{F}_{n}^{(1)} = \sigma \left( \left( X_{k} , \epsilon_{k-1}\right), k=1,\ldots ,n \right)$. Then, considering $\widetilde{\xi}_{k} = \mathbb{E}\left[ \left\| \nabla_{h} f \left( X_{k} , U_{k-1} \right) \right\|^{2} |\mathcal{F}^{(1)}_{k-1} \right] - \left\| \nabla_{h} f \left( X_{k} , U_{k-1} \right) \right\|^{2}$, it comes thanks to assumption \textbf{(H1b)},
\[
R_{1} \leq \frac{1}{n}\sum_{k=1}^{n}\sqrt{C''} \left\| \overline{\theta}_{k-1} - \theta \right\|^{2} - \frac{1}{n}\sum_{k=1}^{n} \widetilde{\xi}_{k} \left\| \overline{\theta}_{k-1} - \theta \right\|^{2}
\]
Then, applying Toeplitz Lemma and Theorem \ref{ratethetabar} to the term on the left hand-side of previous inequality, one can check that for all $\delta > 0$,
\[
\frac{1}{n}\sum_{k=1}^{n}\sqrt{C''} \left\| \overline{\theta}_{k-1} - \theta \right\|^{2} = o \left( \frac{(\ln n)^{2+ \delta}}{n}\right) \quad a.s.
\]
Furthermore, since $\left( \widetilde{\xi}_{n} \right)$ is a sequence of martingale differences with bounded squared moments, with the help of Theorems \ref{ratethetabar} and \ref{theomartmoy}, it comes
\[
\frac{1}{n}\sum_{k=1}^{n} \widetilde{\xi}_{k} \left\| \overline{\theta}_{k-1} - \theta \right\|^{2} = \mathcal{O} \left( \frac{1}{n} \right) \quad a.s
\]
so that
\[
R_{1} = o \left( \frac{(\ln n)^{2+\delta}}{n}\right) \quad a.s.
\]
Furthermore, let us consider
\[
R_{2} = \frac{1}{n}\sum_{k=1}^{n}\epsilon_{k} \left( f \left( X_{k} , \overline{\theta}_{k-1} \right) - f \left( X_{k} , \theta \right) \right) .
\]
We have a sum of martingale differences, and thanks to Theorems \ref{ratethetabar} and \ref{theomartmoy}, one can check that
\[
\left\| R_{2} \right\|^{2} = o \left( \frac{(\ln n)^{2+\delta}}{n^{2}} \right) \quad a.s.
\]
Then, considering that
\[
\epsilon_{n}^{2} - \sigma^{2} = \epsilon_{n}^{2} - \mathbb{E}\left[ \epsilon_{n}^{2} |\mathcal{F}^{(1)}_{n-1} \right]
\]
one can apply a Central Limit Theorem for martingale to get the asymptotic normality, and a strong law of large numbers for martingales to get the almost sure rate of convergence.
\section{Convergence results}\label{sectiontheo}
We focus here on the convergence of the Averaged Stochastic Gauss-Newton algorithms since the proofs are more unusual than the ones for the non averaged version. Indeed, these last ones are quite closed to the proofs in \cite{BGBP2019}.
\subsection{Convergence results on the averaged estimates}
The first theorem deals with the almost sure convergence of a subsequence of $\nabla G \left( \theta_{n} \right) $.
\begin{theo}\label{consistency}
Under assumptions \textbf{(H1)} and \textbf{(H2)} with $c_{\beta}>0$, $G \left( \theta_{n} \right)$ converges almost surely to a finite random variable and there is a subsequence $(\theta_{\varphi_{n}})$ such that
\[
\left\| \nabla G \left( \theta_{\varphi_{n}} \right) \right\| \xrightarrow[n\to + \infty]{a.s} 0
\]
\end{theo}
Remark that if the functional $G$ is convex or if we project the algorithm on a convex subspace where $G$ is convex, previous theorem leads to the almost sure convergence of the estimates. In order to stay as general as possible, let us now introduce the event
\[
\Gamma_{\theta} = \left\lbrace \omega \in \Omega, \quad \theta_{n}(\omega) \xrightarrow[n\to + \infty]{} \theta \right\rbrace .
\]
It is not unusual to introduce this kind of events for studying convergence of stochastic algorithms without loss of generality: see for instance \citep{pelletier1998almost, Pel00}.
Many criteria can ensure that $\mathbb{P}\left[ \Gamma_{\theta} \right] =1$, i.e that $\theta_{n}$ converges almost surely to $\theta$ (see \cite{Duf97}, \cite{KY03} for stochastic gradient descents and \cite{BGBP2019} for an example of stochastic Newton algorithm). The following corollary gives the almost sure convergence of the estimates of $L(\theta)$.
\begin{cor}\label{corconvsn}
Under assumptions \textbf{(H1)} to \textbf{(H3)}, on $\Gamma_{\theta}$, the following almost sure convergences hold:
\[
\overline{S}_{n} \xrightarrow[n\to + \infty]{a.s} H \quad \quad \text{and} \quad \quad \overline{S}_{n}^{-1} \xrightarrow[n\to + \infty]{a.s} H^{-1} .
\]
\end{cor}
In order to get the rates of convergence of the estimates $(\theta_{n})$, let us first introduce a new assumption:
\begin{itemize}
\item[\textbf{(H5)}] There are positive constants $\eta , C_{\eta}$ such that $\eta > \frac{1}{\alpha} -1$ and for all $h \in \mathbb{R}^{q}$,
\begin{equation}
\label{momentdemerde} \mathbb{E}\left[ \left\| \nabla_{h} g \left( X, Y ,h \right) \right\|^{2 \eta +2} \right] \leq C_{\eta} .
\end{equation}
\end{itemize}
\begin{theo}\label{ratetheta}
Assume assumptions \textbf{(H1)} to \textbf{(H4a)} and \textbf{(H5)} hold. Then, on $\Gamma_{\theta}$,
\begin{equation}
\label{ratethetaas}\left\| \theta_{n} - \theta \right\|^{2} = \mathcal{O}\left( \frac{\ln n}{n^{\alpha}}\right) \quad a.s.
\end{equation}
Besides, adding assumption \textbf{(H4b)}, assuming that the function $L$ is $C_{f}$-Lipschitz on a neighborhood of $\theta$, and that the function $h \longmapsto \mathbb{E}\left[ \nabla_{h}g\left( X,Y,h \right) \nabla_{h} g \left( X,Y ,h \right)^{T} \right]$ is $C_{g}$-Lipschitz on a neighborhood of $\theta$, then on $\Gamma_{\theta}$,
\begin{equation}
\label{tlc}\sqrt{\frac{n^{\alpha}}{c_{\alpha}}} \left( \theta_{n} - \theta \right) \xrightarrow[n\to + \infty]{\mathcal{L}} \mathcal{N}\left( 0,\frac{\sigma^{2}}{2} L(\theta)^{-1} \right)
\end{equation}
\end{theo}
These are quite usual results for a step sequence of order $n^{-\alpha}$. Indeed, as expected, we have a "loss" on the rate of convergence of $(\theta_{n})$, but the averaged step enables to get an asymptotically optimal behaviour, which is given by the following theorem.
\begin{theo}\label{ratethetabar}
Assuming \textbf{(H1)} to \textbf{(H4a)} together with \textbf{(H5)}, on $\Gamma_{\theta}$,
\[
\left\| \overline{\theta}_{n} - \theta \right\|^{2} = \mathcal{O}\left( \frac{\ln n}{n}\right) \quad a.s .
\]
Moreover, suppose that the function $h \longmapsto \mathbb{E}\left[ \nabla_{h}g\left( X,Y,h \right) \nabla_{h} g \left( X,Y ,h \right)^{T} \right]$ is continuous at $\theta$, then on $\Gamma_{\theta}$,
\[
\sqrt{n} \left( \overline{\theta}_{n} - \theta \right) \xrightarrow[n\to + \infty]{\mathcal{L}} \mathcal{N}\left( 0 , \sigma^{2}L(\theta)^{-1} \right) .
\]
\end{theo}
\begin{cor}\label{ratesn}
Assuming \textbf{(H1)} to \textbf{(H5)} and assuming that the functional $L$ is $C_{f}$-Lipschitz on a neighborhood of $\theta$, then on $\Gamma_{\theta}$, for all $\delta > 0$,
\begin{align*}
\left\| \overline{S}_{n} - H \right\|_{F}^{2}& =\mathcal{O}\left( \max \left\lbrace \frac{c_{\beta}^{2}}{n^{2\beta}} , \frac{(\ln n)^{1+\delta}}{n} \right\rbrace \right) a.s, \\ \left\| \overline{S}_{n}^{-1} - H^{-1}\right\|_{F}^{2} & = \mathcal{O}\left( \max \left\lbrace \frac{c_{\beta}^{2}}{n^{2\beta}} , \frac{(\ln n)^{1+\delta}}{n} \right\rbrace \right) a.s.
\end{align*}
\end{cor}
Recall here that if \textbf{(H*)} holds, then one can take $c_{\beta} = 0$ leading to a rate of convergence of order $\frac{1}{n}$ (up to a log term).
\subsection{Convergence results on the Stochastic Gauss-Newton algorithm}
\begin{theo}\label{theothetatilde}
Assume assumptions \textbf{(H1)} to \textbf{(H5)} hold. Then, on $\widetilde{\Gamma}_{\theta}:= \left\lbrace \omega \in \Omega, \quad \widetilde{\theta}_{n}(\omega) \xrightarrow[n\to + \infty]{a.s} \theta \right\rbrace$,
\[
\left\| \tilde{\theta}_{n} - \theta \right\|^{2} = \mathcal{O} \left( \frac{\ln n}{n}\right) \quad a.s .
\]
Moreover, suppose that the functional $h \longmapsto \mathbb{E}\left[ \nabla_{h}g\left( X,Y,h \right) \nabla_{h} g \left( X,Y ,h \right)^{T} \right]$ is continuous at $\theta$, then on $\widetilde{\Gamma}_{\theta}$,
\[
\sqrt{n} \left( \widetilde{\theta}_{n} - \theta \right) \xrightarrow[n\to + \infty]{\mathcal{L}} \mathcal{N}\left( 0 , \sigma^{2}L(\theta)^{-1} \right) .
\]
\end{theo}
\subsection{Estimating the variance $\sigma^{2}$}
We now focus on the estimation of the variance $\sigma^{2}$ of the errors. First, consider the sequence of predictors $\left( \hat{Y}_{n} \right)_{n\geq 1}$ of $Y$ defined for all $n \geq 1$ by
\[
\hat{Y}_{n} = f \left( X_{n} , \overline{\theta}_{n-1}\right).
\]
Then, one can estimate $\sigma^{2}$ by the recursive estimate $\hat{\sigma}_{n}$ defined for all $n \geq 1$ by
\[
\hat{\sigma}_{n} = \frac{1}{n} \sum_{k=1}^{n} \left( \hat{Y}_{k} - Y_{k} \right)^{2}.
\]
\begin{cor}\label{estsigma}
Assume assumptions \textbf{(H1)} to \textbf{(H5)} hold and that $\epsilon$ admits a $4$-th order moment. Then, on $\Gamma_{\theta}$,
\[
\left| \hat{\sigma}_{n}^{2} - \sigma^{2} \right| = \mathcal{O} \left( \sqrt{\frac{\ln n}{n}} \right) \quad a.s.,
\]
and
\[
\sqrt{n} \left( \hat{\sigma}_{n}^{2} - \sigma^{2} \right) \xrightarrow[n\to + \infty]{\mathcal{L}} \mathcal{N}\left( 0 , \mathbb{V}\left[ \epsilon^{2} \right] \right).
\]
\end{cor}
\section{Simulation study}\label{sectionsimu}
In this section, we present a short simulation study to illustrate convergence results
given in Section \ref{sectiontheo}.
Simulations were carried out using the statistical software \protect\includegraphics[height=1.8ex,keepaspectratio]{Rlogo.pdf}.
\subsection{The model}
Consider the following model
\[
Y = \theta_1 \left( 1- \exp (- \theta_2 X)\right) +\epsilon,
\]
with $\theta = (\theta_1, \theta_2)^T = (21,12)^T$, $X \sim \mathcal{U}([0,1])$, and $\epsilon \sim \mathcal{N}( 0, 1)$.
For sure, this model is very simple.
However, it allows us to explore
the behaviour of the different algorithms presented in this paper by comparing our methods with the stochastic gradient algorithm and its averaged version and by looking at the influence of the step sequence on the estimates.
In that special case, matrix $L(\theta)=\nabla^2 G(\theta)$ is equal to:
\[
L ( \theta) = \mathbb{E}\left[ \begin{pmatrix}
\left( 1- \exp \left( - \theta_{2}X \right) \right)^{2} & \theta_{1}X \left( 1- \exp \left( - \theta_{2}X \right) \right) \exp \left( - \theta_{2}X \right) \\
\theta_{1}X \left( 1- \exp \left( - \theta_{2}X \right) \right) \exp \left( - \theta_{2}X \right) & \theta_{1}^{2}X^{2} \exp \left( - 2 \theta_{2}X\right)
\end{pmatrix} \right] .
\]
Then, taking $\theta = ( 21 , 12 )^T$, we obtain
\[
L ( 21 , 12) \simeq \begin{pmatrix}
0.875 & 0.109 \\
0.109 & 0.063
\end{pmatrix}
\]
and in particular, the eigenvalues are about equal (in decreasing order) to $0.889$ and $0.049$.
\subsection{Comparison with stochastic gradient algorithm and influence of the step-sequence}
To avoid some computational problems,
we consider projected versions of the different algorithms: more precisely, each algorithm is projected on the ball of center $(21, 12)^T$ and of radius 12.
For each algorithm, we calculate the mean squared error
based on 100 independent samples of size $n=10\ 000$, with initialization $\theta_{0} = \theta + 10 U$, where $U$ follows an uniform law on the unit sphere of $\mathbb{R}^{2}$.
We can see in Tables \ref{table1} and \ref{tablegrad2}
that Gauss-Newton methods perform globally better than gradient descents.
This is certainly due to the fact that the eigenvalues of $L(\theta)$ are at quite different scales,
so that the step sequence in gradient descent is less adapted to each direction. Remark that we could have been less fair play, considering an example where the eigenvalues of $L(\theta)$ would have been at most sensitively different scales.
Nevertheless, without surprise, the estimates seem to be quite sensitive to the choices of the parameters $c_{\alpha}$ and $\alpha$.
\begin{table}[H]
\centering
\small{\begin{tabular}{r|rrrr}
\backslashbox{$c_{\alpha}$}{$\alpha$} & 0.55 & 0.66 & 0.75 & 0.9 \\
\hline
0.1 & 0.0241 & 0.3873 & 2.1115 & 9.1682 \\
0.5 & 0.1229 & 0.0130 & 0.0057 & 0.0171 \\
1 & 0.0732 & 0.0257 & 0.0113 & 0.0030 \\
2 & 0.1203 & 0.0503 & 0.0213 & 0.0073 \\
5 & 0.4029 & 0.1647 & 0.0762 & 0.0168 \\
\end{tabular} \quad \begin{tabular}{r|rrrr}
\backslashbox{$c_{\alpha}$}{$\alpha$} & 0.55 & 0.66 & 0.75 & 0.9 \\
\hline
0.1 & 0.3280 & 1.3746 & 4.1304 & 13.5156 \\
0.5 & 0.1393 & 0.0078 & 0.0135 & 0.0928 \\
1 & 0.0068 & 0.0049 & 0.0085 & 0.0440 \\
2 & 0.0104 & 0.0058 & 0.0052 & 0.0082 \\
5 & 0.2076 & 0.0260 & 0.0067 & 0.0027 \\
\end{tabular}}
\caption{\label{table1}
Mean squared errors of Stochastic Newton estimates defined by \eqref{defsgnalpha} (on the left) and its averaged version defined by \eqref{asgn} (on the right) for different parameters $\alpha$ and $c_{\alpha}$, for $n=10\ 000$. }
\end{table}
\begin{table}[H]
\centering
\small{\begin{tabular}{r|rrrr}
\backslashbox{$c_{\alpha}$}{$\alpha$} & 0.55 & 0.66 & 0.75 & 0.9 \\
\hline
0.1 & 15.40 & 24.69 & 35.32 & 40.42 \\
0.5 & 1.30 & 8.36 & 15.90 & 22.80 \\
1 & 0.24 & 2.66 & 9.76 & 28.52 \\
2 & 0.29 & 0.06 & 3.02 & 22.64 \\
5 & 0.26 & 0.02 & 0.01 & 3.89 \\
\end{tabular} \quad \begin{tabular}{r|rrrr}
\backslashbox{$c_{\alpha}$}{$\alpha$} & 0.55 & 0.66 & 0.75 & 0.9 \\
\hline
0.1 & 19.78 & 28.03 & 38.49 & 43.01 \\
0.5 & 4.49 & 12.48 & 18.79 & 24.20 \\
1 & 1.16 & 7.28 & 13.68 & 30.84 \\
2 & 0.41 & 1.75 & 7.46 & 26.90 \\
5 & 0.27 & 0.02 & 0.18 & 7.45 \\
\end{tabular}}
\caption{\label{tablegrad2} Mean squared errors of Stochastic Gradient estimates with step $c_{\alpha}n^{-\alpha}$ (on the left) and its averaged version (on the right) for different parameters $\alpha$ and $c_{\alpha}$, for $n=10\ 000$. }
\end{table}
To complete this study, let us now examine
the behaviour of the mean squared error in function of the sample size
for the standard Stochastic Gauss-Newton algorithm ("SN"), and its averaged version ("ASN"), for the Stochastic Gauss-Newton algorithm defined by \eqref{defsgnalpha} ("ND")
and for the stochastic gradient algorithm ("SGD") as well as its averaged version ("ASGD"). The stochastic Gauss-Newton algorithms, has been computed with $c_{\beta}=0$ and $S_0 = I_2$.
For the averaged stochastic Newton algorithm a step sequence of the form $c_{\alpha}n^{-\alpha}$ with $c_{\alpha}=1$ and $\alpha = 0.66$ has been chosen, while we have taken $c_{\alpha} = 5$ and $\alpha = 0.66$ for the stochastic gradient algorithm and its averaged version.
Finally, we have considered three different initializations: $\theta_{0} = \theta + r_{0}Z$, where $Z $ follows an uniform law on the unit sphere of $\mathbb{R}^{2}$ and $r_{0} = 1,5,12$.
\begin{figure}[H]\centering
\includegraphics[scale=1]{newtonplot}
\caption{Evolution of the mean squared error in relation with the sample size with, from the left to the right, $r_{0} = 1,5,12$. \label{newtonplot}}
\end{figure}
One can see in Figure \ref{newtonplot}
that stochastic Gauss-Newton algorithms perform better than gradient descents and their averaged version for quite good initialization.
As explained before, this is due to the fact that stochastic Gauss-Newton methods enable to adapt the step sequence to each direction. Furthermore, one can see that when we have a quite good initialization, Stochastic Gauss-Newton and the averaged version give similar results. Nevertheless, when we deal with a bad initialization, to take a step sequence of the form $c_{\alpha}n^{-\alpha}$ enables the estimates to move faster, so that the averaged Gauss Newton estimates have better results compare to the non averaged version. Finally, on Figure~\ref{figboxplot}, one can see that Gauss-Newton methods globally perform better than gradient methods, but there are some bad trajectories due to bad initialization.
\begin{figure}[H]\centering
\includegraphics[scale=0.8]{newtonboxplot}
\caption{Mean squared errors for the different methods for $n=10\ 000$ and $r_{0} = 12$. \label{figboxplot}}
\end{figure}
\subsection{Influence of $\beta_{n}$}
We now focus on the influence of $\beta_n$ on the behaviour of the estimates. All the results are calculated from $100$ independent samples of size $n$.
In table~\ref{tablebeta}, we have chosen $c_{\alpha}=0.66$ and $c=1$, and initialize the algorithms taking $\theta_{0} = \theta + 5 U$. Choosing small $c_{\beta}$ leads to goods results, which, without surprise, suggests that the use of the term $\sum_{k=1}^{n}\beta_{k}Z_{k}Z_{k}^{T}$ is only theoretical, but has no use in practice.
\begin{table}[H]
\centering
\scalebox{0.92}{
\scriptsize{\begin{tabular}{r|rrrr}
\backslashbox{$c_{\beta}$}{$\beta$} & 0.01 & 0.08 & 0.2 & 0.5 \\
\hline
$10^{-10}$ & 2.59 & 3.12 & 2.84 & 2.66 \\
$10^{-5}$ & 2.59 & 2.90 & 2.42 & 1.88 \\
$10^{-2}$ & 2.11 & 2.32 & 2.23 & 1.83 \\
$10^{-1}$ & 0.69 & 1.09 & 1.98 & 2.64 \\
$1$ & 4.04 & 0.61 & 0.66 & 2.06 \\
\end{tabular}
\quad \begin{tabular}{r|rrrr}
\backslashbox{$c_{\beta}$}{$\beta$} & 0.01 & 0.08 & 0.2 & 0.5 \\
\hline
$10^{-10}$ & 0.24 & 0.22 & 0.30 & 0.17 \\
$10^{-5}$ & 0.29 & 0.26 & 0.20 & 0.23 \\
$10^{-2}$ & 0.22 & 0.26 & 0.23 & 0.32 \\
$10^{-1}$ & 0.25 & 0.24 & 0.21 & 0.27 \\
$1$ & 26.37 & 11.19 & 1.46 & 0.30 \\
\end{tabular} \quad \begin{tabular}{r|rrrr}
\backslashbox{$c_{\beta}$}{$\beta$} & 0.01 & 0.08 & 0.2 & 0.5 \\
\hline
$10^{-10}$ & 0.22 & 0.21 & 0.27 & 0.19 \\
$10^{-5}$ & 0.27 & 0.24 & 0.19 & 0.21 \\
$10^{-2}$ & 0.25 & 0.23 & 0.22 & 0.28 \\
$10^{-1}$ & 11.77 & 3.89 & 0.85 & 0.26 \\
$1$ & 444.61 & 409.27 & 184.09 & 9.77 \\
\end{tabular}
}}
\caption{Mean squared errors ($.10^{-2}$) of, from left to right, Stochastic Newton estimates with $c_{\alpha}n^{-\alpha}$ defined by \eqref{defsgnalpha}, its averaged version defined by \eqref{asgn} and Stochastic Newton estimates definded by \eqref{defsgn} for different values of $\beta$ and $c_{\beta}$. }
\label{tablebeta}
\end{table}
\subsection{Asymptotic efficiency}
We now illustrate the asymptotic normality of the estimates.
In order to consider all the components of parameter $\theta$,
we shall in fact examine
the two following central limit theorem.
\[
C_n := \left( \widetilde{\theta}_{n} - \theta \right)^T\widetilde{H}_n \left( \widetilde{\theta}_n - \theta \right) \xrightarrow[n\to + \infty]{\mathcal{L}} \chi_2^2 \quad \quad \text{and} \quad \quad \overline{C}_n := \left( \overline{\theta}_{n} - \theta \right)^{T}S_{n} \left( \overline{\theta}_{n} - \theta \right) \xrightarrow[n\to + \infty]{\mathcal{L}} \chi_{2}^{2}.
\]
These two results are straightforward applications of Theorems \ref{ratethetabar} and \ref{theothetatilde}, taking $\sigma^2 = 1$.
From $1000$ independent samples of size $n$,
and using the kernel method, we estimate the probability density function (pdf for short) of $C_n$ and $\overline{C}_n$
that we compare to the pdf of a chi-squared with 2 degrees of freedom (df).
Estimates $\widetilde{\theta}_{n}$ and $\overline{\theta}_n$ are computed taking
$\theta_{0} = \theta + U$, $c_{\alpha} = 1$ and $\alpha = 0.66$.
One can observe in Figure~\ref{chisq} that the estimated densities are quite similar to the chi-squared pdf. Remark that a Kolmogorov-Smirnov test leads to $p$-values equal to $0.1259$ for $C_{n}$ and $0.33$ for $\overline{C}_{n}$. Therefore, the gaussian approximation provided by the TLC given by \ref{ratethetabar} and \ref{theothetatilde} is pretty good, and so, even for quite moderate sample sizes.
\begin{figure}[H]\centering
\includegraphics[scale=0.6]{chisq}
\caption{Density function of a Chi squared with 2 df (in black)
and kernel-based density estimates of $C_{n}$ (in green) and $\overline{C}_{n}$ (in red) for $n= 5000$.}
\label{chisq}
\end{figure}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,528
|
require 'spec_helper'
require 'horizon'
describe "horizon" do
class Dog
include Horizon::Publisher
attr_accessor :hungry
alias_method :hungry?, :hungry
def initialize
self.hungry = true
end
def feed
return unless hungry?
self.hungry = false
publish :dog_fed, self
end
end
class DogOwnerNotifier
include Horizon::Handler
def dog_fed(dog)
mail_owner(dog)
end
handler :dog_fed
def mail_owner
end
end
it "lets you publish and handle domain events" do
context = Horizon::Context.current
handler = DogOwnerNotifier.new
context.add_handler handler
handler.stub(:mail_owner)
dog = Dog.new
dog.feed
handler.should have_received(:mail_owner).with(dog)
end
end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,053
|
Seznam televizních filmů Disney+ uvádí přehled televizních filmů, které jsou premiérově uváděny na americké placené streamovací televizi Disney+.
Celovečerní
Premiérově na D+
Filmy původně určené pro uvedení do kin, ale nakonec uvedené na Disney+.
Dokumenty
Speciály
Krátké filmy
Živé přenosy
Regionální filmy
Připravované
Filmy
Dokumenty
Speciály
Živé přenosy
Krátké filmy
Cizojazyčné filmy
Odkazy
Reference
Externí odkazy
Disney+
Televizní filmy
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,623
|
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